[READ-ONLY] Mirror of https://github.com/jmrplens/PyOctaveBand. [Python3] Octave-Band and Fractional Octave-Band filter. For signal in time domain.
jmrplens.github.io/PyOctaveBand/
acoustics
audio
filter
frequency
frequency-analysis
frequency-domain
octave
python3
signal
time-domain
feat: dynamic stiffness of resilient materials (EN 29052-1:1992) (#135)
First module of the structure-borne / vibro-acoustic characterisation chain
that culminates in EN 12354-5. EN 29052-1 (= ISO 9052-1:1989) determines the
dynamic stiffness per unit area s' of resilient layers under floating floors
from the load-plate resonance:
- apparent_dynamic_stiffness s't = 4 pi^2 m't fr^2 (Formula 4)
- enclosed_gas_stiffness s'a = p0 / (d eps) (Formula 7)
- installed_dynamic_stiffness airflow-resistivity regimes (clause 8.2)
- natural_frequency f0 = (1/2pi) sqrt(s'/m') (Formula 2)
- floating_floor_resonance full chain -> DynamicStiffnessResult + .plot()
Conformance is anchored on the standard's own worked NOTE (s'a = 111/d MN/m3
for p0 = 0,1 MPa, eps = 0,9), reproduced exactly by the closed form, plus
hand-computed values of the resonance relations. s' feeds the ISO 16251 /
EN 12354-2 floating-floor impact improvement.
Docs (repo + bilingual site guide + API reference), the dynamic_stiffness
figure (4 variants), 3 conformance checks (123/123) and 17 tests.
authored by
José M. Requena Plens
and committed by
GitHub
(Jul 11, 2026, 5:10 PM +0200)
593fd207
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+3686
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</g>
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</g>
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<g clip-path="url(#p2990b744a2)">
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<rect x="47.289844" y="28.318125" width="658.597656" height="370.115313"/>
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</svg>
+5
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docs/CONFORMANCE.md
+5
-2
docs/CONFORMANCE.md
···
15
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16
16
## Numerical conformance report
17
17
18
-
✅ **120/120 conformance checks pass** across 23 domains and 74 standards - filters class 1 - weightings within IEC 61672-1 class 1.
18
+
✅ **123/123 conformance checks pass** across 23 domains and 75 standards - filters class 1 - weightings within IEC 61672-1 class 1.
19
19
20
20
### Numerical validation - filters & weightings
21
21
···
122
122
</details>
123
123
124
124
<details>
125
-
<summary>✅ <b>Room & building acoustics</b> — 100% (18/18)</summary>
125
+
<summary>✅ <b>Room & building acoustics</b> — 100% (21/21)</summary>
126
126
127
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| Standard | Quantity | Expected (norm) | Computed | Δ | Status |
128
128
|:---|:---|:---|:---|:---|:---:|
···
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144
| ISO 10848-1:2006 Formula (14) | Flanking Kij (simplified) matches closed form | Kij = 1.9897 dB | Kij = 1.9897 dB | exact | ✅ |
145
145
| ISO 10848-1:2006 Formula (12) | Flanking equivalent absorption length aj at f_ref | aj = 1.2661 m | aj = 1.2661 m | exact | ✅ |
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146
| ISO 10848-1:2006 Clause 7.3.1 | Flanking total loss factor η = 2,2/(f·Ts) | η = 0.0044 | η = 0.0044 | exact | ✅ |
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+
| EN 29052-1:1992 Formula 4 | Apparent dynamic stiffness s't = 4π²·m't·fr² (m't=200 kg/m², fr=25 Hz) | 4.934802 MN/m³ (+/-0.000001 MN/m³) | 4.934802 MN/m³ | 0 MN/m³ | ✅ |
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+
| EN 29052-1:1992 clause 8.2 NOTE | Enclosed-gas stiffness s'a·d = 111 MN·mm/m³ (p₀=0,1 MPa, ε=0,9) | 5.55556 MN/m³ (+/-0.0001 MN/m³) | 5.55556 MN/m³ | 0 MN/m³ | ✅ |
149
+
| EN 29052-1:1992 Formula 2 | Floating-floor natural frequency f0 = (1/2π)√(s'/m') (s'=10 MN/m³, m'=100 kg/m²) | 50.32921 Hz (+/-0 Hz) | 50.32921 Hz | 0 Hz | ✅ |
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</details>
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+1
docs/README.md
+1
docs/README.md
···
25
25
- [Room Acoustics](room-acoustics.md) — impulse-response acquisition (ISO 18233), reverberation and room parameters (ISO 3382-1/2), open-plan speech metrics (ISO 3382-3), reverberation-room sound absorption (ISO 354)
26
26
- [Sound absorption in enclosed spaces](enclosed-space-absorption.md) — the EN 12354-6:2003 prediction of a room's total equivalent absorption area and reverberation time from its surfaces and objects (Clause 4)
27
27
- [Reverberation-time prediction](reverberation-prediction.md) — the reverberation time from a room's volume and surface absorption by five statistical models (Sabine, Eyring, Millington-Sette, Fitzroy, Arau-Puchades), with the air-absorption term
28
+
- [Dynamic stiffness of resilient materials](dynamic-stiffness.md) — the EN 29052-1:1992 dynamic stiffness per unit area of floating-floor resilient layers from the load-plate resonance, and the floating-floor natural frequency
28
29
- [Room-noise criteria](room-noise.md) — the ANSI/ASA S12.2-2019 room-noise ratings: the NC tangency method (Table 1) and the RC Mark II rating with its rumble/hiss/neutral spectral tag (Annex D)
29
30
- [Acoustic Materials](materials.md) — sound-absorption rating α_w and classes (ISO 11654), airflow resistance static and alternating methods (ISO 9053-1/-2), and impedance-tube measurement of absorption, surface impedance and transmission loss (ISO 10534-1/-2, ASTM E2611)
30
31
- [Surface Scattering, Diffusion and In-situ Absorption](surface-scattering.md) — random-incidence scattering (ISO 17497-1), free-field diffusion coefficient (ISO 17497-2), and in-situ road-surface absorption by the extended-surface subtraction technique (ISO 13472-1) and the spot method (ISO 13472-2)
+7
-1
docs/api-reference.md
+7
-1
docs/api-reference.md
···
269
269
| `mean_absorption` | `function` | **Area-weighted mean absorption ᾱ = ΣSᵢαᵢ / ΣSᵢ.**<br>• `surfaces`: (area, α) pairs | `mean_absorption([(90.0, 0.1), (10.0, 0.9)]) # 0.18` |
270
270
| `reverberation_time_models` | `function` | **All five RT models for a shoebox room, per band.**<br>• `dimensions` (Lx, Ly, Lz) [m]<br>• `absorptions`: (αx, αy, αz) wall-pair means (scalar or per band)<br>• `air_attenuation` [Np/m], `frequencies` [Hz], `speed_of_sound` | `res = reverberation_time_models((10,7,3.5), (ax, ay, az), frequencies=f)`<br><br>• `ReverberationModelResult` |
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271
| `ReverberationModelResult` | `dataclass` | **Five-model RT comparison.**<br>• `frequencies` [Hz]<br>• `sabine`/`eyring`/`millington_sette`/`fitzroy`/`arau_puchades`: T per band [s]<br>• `volume` [m³], `surface_area` [m²]<br>• `.models`: dict keyed by name<br>• `.plot()` | `res.arau_puchades, res.models['Fitzroy']` |
272
+
| `apparent_dynamic_stiffness` | `function` | **Apparent dynamic stiffness s't (EN 29052-1 Formula 4).**<br>• `resonant_frequency` fr [Hz] (scalar/array)<br>• `total_mass_per_area` m't [kg/m²]<br>s't = 4π²·m't·fr² [N/m³] | `apparent_dynamic_stiffness(25.0, 200.0) # 4.935e6 N/m³` |
273
+
| `enclosed_gas_stiffness` | `function` | **Enclosed-gas dynamic stiffness s'a (EN 29052-1 Formula 7).**<br>• `thickness` d [m]<br>• `porosity` ε (0-1)<br>• `atmospheric_pressure` p₀ [Pa] (Default: 1e5 = 0,1 MPa)<br>s'a = p₀/(d·ε); NOTE ≈ 111/d MN/m³ (d in mm) | `enclosed_gas_stiffness(0.020, 0.9) # 5.56e6 N/m³` |
274
+
| `installed_dynamic_stiffness` | `function` | **Installed s' by airflow resistivity (EN 29052-1 clause 8.2).**<br>• `apparent_stiffness` s't [N/m³]<br>• `airflow_resistivity` r [kPa·s/m²]<br>• `gas_stiffness` s'a [N/m³]<br>r≥100 → s't · 10≤r<100 → s't+s'a · r<10 → s't if s'a negligible else nan (warns) | `installed_dynamic_stiffness(20e6, 50.0, gas_stiffness=3e6) # 23e6` |
275
+
| `natural_frequency` | `function` | **Floating-floor natural frequency f0 (EN 29052-1 Formula 2).**<br>• `dynamic_stiffness` s' [N/m³] (scalar/array)<br>• `mass_per_area` m' [kg/m²]<br>f0 = (1/2π)√(s'/m') | `natural_frequency(10e6, 120.0) # 45.9 Hz` |
276
+
| `floating_floor_resonance` | `function` | **Full EN 29052-1 chain → result.**<br>• `resonant_frequency`, `total_mass_per_area`, `floor_mass_per_area`<br>• `airflow_resistivity` (Default: inf), `thickness`, `porosity`, `atmospheric_pressure` | `res = floating_floor_resonance(25.0, 200.0, 120.0)`<br><br>• `DynamicStiffnessResult` |
277
+
| `DynamicStiffnessResult` | `dataclass` | **Dynamic-stiffness measurement result.**<br>• `apparent_stiffness`/`gas_stiffness`/`dynamic_stiffness` [N/m³]<br>• `resonant_frequency` [Hz], `floor_mass_per_area` [kg/m²]<br>• `natural_frequency` [Hz]<br>• `.plot()` | `res.dynamic_stiffness, res.natural_frequency` |
272
278
| `combine_uncertainty` | `function` | **GUM law of propagation of uncertainty (ISO/IEC Guide 98-3 clause 5).**<br>• `model`: measurement function f(x1…xN)<br>• `quantities`: input `Quantity` objects, in argument order<br>• `correlation`: optional N×N matrix r_ij (Default: None → uncorrelated) | `u = combine_uncertainty(lambda a, b: a*b, [Quantity(10.0, 0.1), Quantity(5.0, 0.2)])`<br><br>• `UncertaintyResult`; uc = 2.062 |
273
279
| `monte_carlo` | `function` | **Monte Carlo propagation (Guide 98-3-1, Supplement 1).**<br>• `model`: vectorised f(x1…xN)<br>• `quantities`: input `Quantity` objects<br>• `trials`: M (Default: 1000000)<br>• `coverage`: interval probability (Default: 0.95)<br>• `seed`: reproducibility (Default: None) | `mc = monte_carlo(model, quantities, seed=1)`<br><br>• `MonteCarloResult` (mean, u, coverage interval) |
274
280
| `rectangular` | `function` | **Type B quantity, rectangular PDF (GUM 4.3.7).**<br>• `value`, `half_width` a, `name` | `rectangular(20.0, 0.5)`<br><br>• `Quantity` with u = a/√3 = 0.289 |
···
422
428
| `TonalityWarning` | `warning class` | **Tonality advisory.**<br>Emitted for biased tonality estimates (e.g. coarse FFT resolution) | `warnings.simplefilter('error', TonalityWarning)` |
423
429
| `STIWarning` | `warning class` | **STI/STIPA advisory.**<br>Emitted for suspect speech-intelligibility measurements or inputs | `warnings.simplefilter('error', STIWarning)` |
424
430
| `__version__` | `str` | **Package version string.**<br>(no parameters) | `phonometry.__version__ # '3.0.0'` |
425
-
| `.plot()` | `method` | **One-line canonical figure on every result object (soft matplotlib dependency).**<br>Available on `ZwickerLoudness`, `MooreGlasbergLoudness`, `MooreGlasbergTimeVaryingLoudness`, `EcmaLoudness`, `EcmaTonality`, `EcmaRoughness`, `STIResult`, `SIIResult`, `NCResult`, `RCResult`, `AgeThresholdResult`, `NiptsResult`, `HtlanResult`, `ImpulseProminenceResult`, `MultipleShockResult`, `ImpulseResponseResult`, `DecayCurve`, `RoomAcousticsResult`, `ReverberationResult`, `ReverberationModelResult`, `WeightedRatingResult`, `ImpactRatingResult`, `FacadeInsulationResult`, `LabAirborneInsulationResult`, `LabImpactInsulationResult`, `SoundPowerResult`, `ReverberationSoundPowerResult`, `SoundPowerIntensityResult`, `PrecisionSoundPowerResult`, `PrecisionIntensityResult`, `IntensityResult`, `UncertaintyResult`, `AbsorptionRatingResult`, `ScatteringResult`, `DiffusionResult`, `InsituAbsorptionResult`, `WeightingResponse`, `WeightedSpectrum` and `DailyVibrationExposure`.<br>• `ax`: existing Axes, or None to build a fresh figure (Default: None)<br>• returns the Matplotlib `Axes` (an array of Axes for multi-panel figures); never calls `plt.show()`<br>• needs matplotlib (`pip install phonometry[plot]`) | `res.plot()`<br>`decay_curve(ir, fs).plot()` |
431
+
| `.plot()` | `method` | **One-line canonical figure on every result object (soft matplotlib dependency).**<br>Available on `ZwickerLoudness`, `MooreGlasbergLoudness`, `MooreGlasbergTimeVaryingLoudness`, `EcmaLoudness`, `EcmaTonality`, `EcmaRoughness`, `STIResult`, `SIIResult`, `NCResult`, `RCResult`, `AgeThresholdResult`, `NiptsResult`, `HtlanResult`, `ImpulseProminenceResult`, `MultipleShockResult`, `ImpulseResponseResult`, `DecayCurve`, `RoomAcousticsResult`, `ReverberationResult`, `ReverberationModelResult`, `DynamicStiffnessResult`, `WeightedRatingResult`, `ImpactRatingResult`, `FacadeInsulationResult`, `LabAirborneInsulationResult`, `LabImpactInsulationResult`, `SoundPowerResult`, `ReverberationSoundPowerResult`, `SoundPowerIntensityResult`, `PrecisionSoundPowerResult`, `PrecisionIntensityResult`, `IntensityResult`, `UncertaintyResult`, `AbsorptionRatingResult`, `ScatteringResult`, `DiffusionResult`, `InsituAbsorptionResult`, `WeightingResponse`, `WeightedSpectrum` and `DailyVibrationExposure`.<br>• `ax`: existing Axes, or None to build a fresh figure (Default: None)<br>• returns the Matplotlib `Axes` (an array of Axes for multi-panel figures); never calls `plt.show()`<br>• needs matplotlib (`pip install phonometry[plot]`) | `res.plot()`<br>`decay_curve(ir, fs).plot()` |
426
432
427
433
## Notes
428
434
+108
docs/dynamic-stiffness.md
+108
docs/dynamic-stiffness.md
···
1
+
← [Documentation index](README.md)
2
+
3
+
# Dynamic stiffness of resilient materials (EN 29052-1)
4
+
5
+
A **floating floor** is a heavy floating slab resting on a resilient layer; the
6
+
two form a mass-spring system whose **natural frequency** governs how much the
7
+
floor improves impact and airborne insulation. **EN 29052-1:1992** (identical to
8
+
ISO 9052-1:1989) measures the **dynamic stiffness per unit area** `s'` of the
9
+
resilient layer from the resonance of a standard load plate on a
10
+
200 mm × 200 mm specimen. `s'` is the input to the floating-floor impact
11
+
improvement (ISO 16251) covered in [Building acoustics](building-acoustics.md)
12
+
and to the EN 12354-2 impact model.
13
+
14
+
<picture><source media="(prefers-color-scheme: dark)" srcset="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/dynamic_stiffness_dark.svg"><img src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/dynamic_stiffness.svg" alt="Floating-floor natural frequency as a function of the resilient layer's dynamic stiffness per unit area, for a light 40 kg/m² and a heavy 120 kg/m² floating floor, on a logarithmic stiffness axis, with a worked design point at 10 MN/m³ marked" width="82%"></picture>
15
+
16
+
## 1. Dynamic stiffness and resonance
17
+
18
+
The dynamic stiffness per unit area is a dynamic force per area divided by the
19
+
resulting change in thickness (Formula 1): `s' = (F/S)/Δd`. The resiliently
20
+
supported floor is a resonator whose natural frequency (Formula 2) and,
21
+
in the laboratory arrangement, measured resonant frequency (Formula 3) are
22
+
23
+
$$
24
+
f_0 = \frac{1}{2\pi}\sqrt{\frac{s'}{m'}}, \qquad
25
+
f_r = \frac{1}{2\pi}\sqrt{\frac{s'_t}{m'_t}},
26
+
$$
27
+
28
+
so the **apparent** dynamic stiffness follows from the resonance (Formula 4):
29
+
30
+
$$
31
+
s'_t = 4\pi^2\,m'_t\,f_r^2 .
32
+
$$
33
+
34
+
```python
35
+
import phonometry as ph
36
+
37
+
# Standard 8 kg load plate on the 0.04 m2 specimen -> m't = 200 kg/m2;
38
+
# the fundamental resonance is measured at 25 Hz.
39
+
s_t = ph.apparent_dynamic_stiffness(resonant_frequency=25.0, total_mass_per_area=200.0)
40
+
print(round(s_t / 1e6, 3)) # 4.935 MN/m3
41
+
42
+
# Installed on a 120 kg/m2 floating screed with s' = 10 MN/m3:
43
+
print(round(ph.natural_frequency(10e6, 120.0), 1)) # 45.9 Hz
44
+
```
45
+
46
+
## 2. The enclosed-gas term and airflow resistivity
47
+
48
+
For an air-permeable material the enclosed pore air adds a parallel stiffness
49
+
from its isothermal compression (Formula 7): `s'a = p₀/(d·ε)`, with `p₀` the
50
+
atmospheric pressure, `d` the loaded thickness and `ε` the porosity. The
51
+
standard's worked NOTE (`p₀ = 0.1 MPa`, `ε = 0.9`) is `s'a = 111/d` MN/m³ for
52
+
`d` in millimetres:
53
+
54
+
```python
55
+
import phonometry as ph
56
+
57
+
print(round(ph.enclosed_gas_stiffness(thickness=0.020, porosity=0.9) / 1e6, 2))
58
+
# 5.56 MN/m3 (the NOTE's 111/20 = 5.55 MN/m3)
59
+
```
60
+
61
+
The dynamic stiffness of the *installed* material is then set by the lateral
62
+
airflow resistivity `r` (clause 8.2): `s' = s't` for `r ≥ 100 kPa·s/m²`,
63
+
`s' = s't + s'a` for `10 ≤ r < 100 kPa·s/m²`, and for `r < 10 kPa·s/m²` the
64
+
method only resolves `s' = s't` when the gas term is negligible. `floating_floor_resonance`
65
+
chains the whole determination:
66
+
67
+
```python
68
+
import phonometry as ph
69
+
70
+
res = ph.floating_floor_resonance(
71
+
resonant_frequency=25.0, total_mass_per_area=200.0,
72
+
floor_mass_per_area=120.0,
73
+
airflow_resistivity=50.0, thickness=0.020, porosity=0.9,
74
+
)
75
+
print(round(res.dynamic_stiffness / 1e6, 2), round(res.natural_frequency, 1))
76
+
# 10.49 47.1
77
+
```
78
+
79
+
<details>
80
+
<summary>Show the code for this figure</summary>
81
+
82
+
```python
83
+
import matplotlib.pyplot as plt
84
+
import numpy as np
85
+
import phonometry as ph
86
+
87
+
s = np.logspace(np.log10(2.0), np.log10(100.0), 300) # MN/m3
88
+
for m in (40.0, 120.0):
89
+
plt.semilogx(s, ph.natural_frequency(s * 1e6, m), label=f"m' = {m:g} kg/m²")
90
+
plt.xlabel("Dynamic stiffness s' [MN/m³]"); plt.ylabel("Natural frequency f₀ [Hz]")
91
+
plt.legend(); plt.show()
92
+
```
93
+
94
+
</details>
95
+
96
+
The `DynamicStiffnessResult` carries the apparent, enclosed-gas and installed
97
+
stiffnesses, the test resonance and the installed-floor natural frequency, and
98
+
its `.plot()` draws the `f₀(s')` design curve.
99
+
100
+
---
101
+
102
+
**Standards.** EN 29052-1:1992 (= ISO 9052-1:1989), *Acoustics — Determination
103
+
of dynamic stiffness — Part 1: Materials used under floating floors in
104
+
dwellings* — the dynamic stiffness per unit area (Formula 1), the resonance
105
+
relations (Formulae 2-4), the enclosed-gas term (Formula 7, clause 8.2 NOTE
106
+
`s'a = 111/d` MN/m³) and the airflow-resistivity regimes (clause 8.2, Formulae
107
+
5-6). Conformance is anchored on the standard's own numeric NOTE plus
108
+
hand-computed closed-form values of the resonance relations.
+34
scripts/conformance_report.py
+34
scripts/conformance_report.py
···
1236
1236
)
1237
1237
1238
1238
1239
+
# --- Dynamic stiffness of resilient materials (EN 29052-1:1992) ---
1240
+
@register(
1241
+
"Room & building acoustics",
1242
+
"EN 29052-1:1992 Formula 4",
1243
+
"Apparent dynamic stiffness s't = 4π²·m't·fr² (m't=200 kg/m², fr=25 Hz)",
1244
+
)
1245
+
def _chk_en29052_apparent() -> Outcome:
1246
+
computed = float(ph.apparent_dynamic_stiffness(25.0, 200.0)) / 1e6
1247
+
expected = 4.0 * math.pi**2 * 200.0 * 25.0**2 / 1e6
1248
+
return numeric(expected, computed, 1e-6, unit="MN/m³", places=6)
1249
+
1250
+
1251
+
@register(
1252
+
"Room & building acoustics",
1253
+
"EN 29052-1:1992 clause 8.2 NOTE",
1254
+
"Enclosed-gas stiffness s'a·d = 111 MN·mm/m³ (p₀=0,1 MPa, ε=0,9)",
1255
+
)
1256
+
def _chk_en29052_enclosed_gas() -> Outcome:
1257
+
# NOTE: s'a = 111/d MN/m3 for d in mm; the closed form gives 100/0,9 = 111.11.
1258
+
sa_mn = float(ph.enclosed_gas_stiffness(0.020, 0.9)) / 1e6 # d = 20 mm
1259
+
return numeric(111.111111 / 20.0, sa_mn, 1e-4, unit="MN/m³", places=5)
1260
+
1261
+
1262
+
@register(
1263
+
"Room & building acoustics",
1264
+
"EN 29052-1:1992 Formula 2",
1265
+
"Floating-floor natural frequency f0 = (1/2π)√(s'/m') (s'=10 MN/m³, m'=100 kg/m²)",
1266
+
)
1267
+
def _chk_en29052_resonance() -> Outcome:
1268
+
computed = float(ph.natural_frequency(10.0e6, 100.0))
1269
+
expected = math.sqrt(10.0e6 / 100.0) / (2.0 * math.pi)
1270
+
return numeric(expected, computed, 1e-6, unit="Hz", places=5)
1271
+
1272
+
1239
1273
# ===========================================================================
1240
1274
# Domain 7 - Building prediction & uncertainty
1241
1275
# ===========================================================================
+54
scripts/generate_graphs.py
+54
scripts/generate_graphs.py
···
206
206
# reverberation_models figure (Sabine / Eyring / Millington / Fitzroy / Arau)
207
207
"Reverberation-time prediction models":
208
208
"Modelos de predicción del tiempo de reverberación",
209
+
# dynamic_stiffness figure (EN 29052-1)
210
+
"EN 29052-1 Floating-Floor Resonance":
211
+
"Resonancia de suelo flotante EN 29052-1",
212
+
r"Dynamic stiffness per unit area $s'$ [MN/m³]":
213
+
r"Rigidez dinámica por unidad de área $s'$ [MN/m³]",
214
+
r"Natural frequency $f_0$ [Hz]": r"Frecuencia natural $f_0$ [Hz]",
215
+
"design point": "punto de diseño",
209
216
# facade_prediction figure (EN 12354-3 Annex F)
210
217
"EN 12354-3 Façade Sound Insulation (Annex F example)":
211
218
"Aislamiento acústico de fachada EN 12354-3 (ejemplo del Anexo F)",
···
3301
3308
plt.close()
3302
3309
3303
3310
3311
+
def generate_dynamic_stiffness(output_dir: str) -> None:
3312
+
"""EN 29052-1 floating-floor natural frequency f0(s') for typical floors."""
3313
+
print("Generating dynamic_stiffness...")
3314
+
from phonometry import natural_frequency
3315
+
3316
+
s_mn = np.logspace(np.log10(2.0), np.log10(100.0), 300) # MN/m3
3317
+
fig, ax = plt.subplots(figsize=(10, 6.2))
3318
+
# Two typical floating-floor masses per unit area (light vs heavy screed).
3319
+
for m, color, label in ((40.0, COLOR_SECONDARY, "m' = 40 kg/m^2"),
3320
+
(120.0, COLOR_PRIMARY, "m' = 120 kg/m^2")):
3321
+
f0 = np.asarray(natural_frequency(s_mn * 1e6, m), dtype=float)
3322
+
ax.plot(s_mn, f0, color=color, linewidth=2.2, label=label)
3323
+
3324
+
# A worked design point: s' = 10 MN/m3 on the 120 kg/m2 floor.
3325
+
s0, m0 = 10.0, 120.0
3326
+
f00 = float(natural_frequency(s0 * 1e6, m0))
3327
+
ax.scatter([s0], [f00], color=COLOR_TERTIARY, s=90, zorder=6,
3328
+
label=f"design point ({s0:g} MN/m^3, {f00:.0f} Hz)")
3329
+
ax.plot([s0, s0], [0, f00], color=COLOR_GRID, ls=":", lw=1.0, zorder=1)
3330
+
ax.plot([s_mn[0], s0], [f00, f00], color=COLOR_GRID, ls=":", lw=1.0, zorder=1)
3331
+
3332
+
ax.set_xscale("log")
3333
+
ax.set_xlabel(r"Dynamic stiffness per unit area $s'$ [MN/m³]")
3334
+
ax.set_ylabel(r"Natural frequency $f_0$ [Hz]")
3335
+
ax.set_title("EN 29052-1 Floating-Floor Resonance", fontweight="bold", pad=12)
3336
+
ax.set_ylim(bottom=0.0)
3337
+
ax.grid(which="both", color=COLOR_GRID, linestyle="--", alpha=0.5)
3338
+
ax.set_axisbelow(True)
3339
+
ax.legend(loc="upper left", fontsize=10)
3340
+
3341
+
panel = "#f0f2f5" if COLOR_FG == "black" else "#1c2128"
3342
+
info = [
3343
+
"f0 = (1/2pi) sqrt(s'/m') (Formula 2)",
3344
+
"s' = s't + s'a (clause 8.2)",
3345
+
"s't = 4 pi^2 m't fr^2 (Formula 4)",
3346
+
"s'a = p0/(d eps) ~ 111/d MN/m^3 (NOTE)",
3347
+
]
3348
+
ax.text(0.985, 0.03, "\n".join(info), transform=ax.transAxes,
3349
+
va="bottom", ha="right", fontsize=10, color=COLOR_FG,
3350
+
bbox={"boxstyle": "round,pad=0.5", "facecolor": panel,
3351
+
"edgecolor": COLOR_GRID})
3352
+
plt.tight_layout()
3353
+
save_figure(output_dir, "dynamic_stiffness.svg")
3354
+
plt.close()
3355
+
3356
+
3304
3357
def generate_absorption_uncertainty(output_dir: str) -> None:
3305
3358
"""ISO 12999-2 absorption-coefficient uncertainty: alpha_s with a +/-U ribbon."""
3306
3359
print("Generating absorption_uncertainty...")
···
4799
4852
generate_floor_covering_improvement(img_dir)
4800
4853
generate_flanking_transmission(img_dir)
4801
4854
generate_reverberation_models(img_dir)
4855
+
generate_dynamic_stiffness(img_dir)
4802
4856
generate_absorption_uncertainty(img_dir)
4803
4857
generate_insulation_uncertainty_demo(img_dir)
4804
4858
+1
-1
site/astro.config.mjs
+1
-1
site/astro.config.mjs
···
337
337
{
338
338
label: 'Building acoustics & insulation',
339
339
translations: { es: 'Acústica de la edificación y aislamiento' },
340
-
items: ['guides/building-acoustics'],
340
+
items: ['guides/building-acoustics', 'guides/dynamic-stiffness'],
341
341
},
342
342
{
343
343
label: 'Environmental acoustics',
+112
site/src/content/docs/es/guides/dynamic-stiffness.md
+112
site/src/content/docs/es/guides/dynamic-stiffness.md
···
1
+
---
2
+
title: "Rigidez dinámica de materiales resilientes (EN 29052-1)"
3
+
description: "La determinación según EN 29052-1:1992 de la rigidez dinámica por unidad de área de materiales resilientes bajo suelos flotantes a partir de la resonancia de la placa de carga: la rigidez aparente de la Fórmula 4, el término del gas encerrado de la Fórmula 7, los regímenes por resistividad al flujo de la cláusula 8.2 y la frecuencia natural del suelo flotante de la Fórmula 2."
4
+
---
5
+
6
+
Un **suelo flotante** es una losa pesada que descansa sobre una capa resiliente;
7
+
ambos forman un sistema masa-resorte cuya **frecuencia natural** determina cuánto
8
+
mejora el suelo el aislamiento a impacto y aéreo. **EN 29052-1:1992** (idéntica a
9
+
ISO 9052-1:1989) mide la **rigidez dinámica por unidad de área** `s'` de la capa
10
+
resiliente a partir de la resonancia de una placa de carga normalizada sobre una
11
+
probeta de 200 mm × 200 mm. `s'` es la entrada a la mejora a impacto del suelo
12
+
flotante (ISO 16251) tratada en
13
+
[Acústica de la edificación](/phonometry/es/guides/building-acoustics/) y al
14
+
modelo de impacto de EN 12354-2.
15
+
16
+
<img class="light-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/dynamic_stiffness_es.svg" alt="Frecuencia natural del suelo flotante frente a la rigidez dinámica por unidad de área de la capa resiliente para un suelo flotante ligero y uno pesado, con un punto de diseño" style="width:82%"><img class="dark-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/dynamic_stiffness_es_dark.svg" alt="Frecuencia natural del suelo flotante frente a la rigidez dinámica por unidad de área de la capa resiliente para un suelo flotante ligero y uno pesado, con un punto de diseño" style="width:82%">
17
+
18
+
## 1. Rigidez dinámica y resonancia
19
+
20
+
La rigidez dinámica por unidad de área es una fuerza dinámica por área dividida
21
+
entre el cambio de espesor resultante (Fórmula 1): `s' = (F/S)/Δd`. El suelo
22
+
soportado resilientemente es un resonador cuya frecuencia natural (Fórmula 2) y,
23
+
en la disposición de laboratorio, la frecuencia de resonancia medida (Fórmula 3)
24
+
son
25
+
26
+
$$
27
+
f_0 = \frac{1}{2\pi}\sqrt{\frac{s'}{m'}}, \qquad
28
+
f_r = \frac{1}{2\pi}\sqrt{\frac{s'_t}{m'_t}},
29
+
$$
30
+
31
+
por lo que la rigidez dinámica **aparente** se obtiene de la resonancia
32
+
(Fórmula 4):
33
+
34
+
$$
35
+
s'_t = 4\pi^2\,m'_t\,f_r^2 .
36
+
$$
37
+
38
+
```python
39
+
import phonometry as ph
40
+
41
+
# Placa de carga normalizada de 8 kg sobre la probeta de 0,04 m2 -> m't = 200 kg/m2;
42
+
# la resonancia fundamental se mide en 25 Hz.
43
+
s_t = ph.apparent_dynamic_stiffness(resonant_frequency=25.0, total_mass_per_area=200.0)
44
+
print(round(s_t / 1e6, 3)) # 4.935 MN/m3
45
+
46
+
# Instalada sobre una losa flotante de 120 kg/m2 con s' = 10 MN/m3:
47
+
print(round(ph.natural_frequency(10e6, 120.0), 1)) # 45.9 Hz
48
+
```
49
+
50
+
## 2. El término del gas encerrado y la resistividad al flujo
51
+
52
+
En un material permeable al aire, el aire de los poros añade una rigidez en
53
+
paralelo por su compresión isoterma (Fórmula 7): `s'a = p₀/(d·ε)`, con `p₀` la
54
+
presión atmosférica, `d` el espesor bajo carga y `ε` la porosidad. La NOTA
55
+
resuelta de la norma (`p₀ = 0,1 MPa`, `ε = 0,9`) es `s'a = 111/d` MN/m³ con `d`
56
+
en milímetros:
57
+
58
+
```python
59
+
import phonometry as ph
60
+
61
+
print(round(ph.enclosed_gas_stiffness(thickness=0.020, porosity=0.9) / 1e6, 2))
62
+
# 5.56 MN/m3 (los 111/20 = 5.55 MN/m3 de la NOTA)
63
+
```
64
+
65
+
La rigidez dinámica del material *instalado* la fija entonces la resistividad
66
+
lateral al flujo `r` (cláusula 8.2): `s' = s't` para `r ≥ 100 kPa·s/m²`,
67
+
`s' = s't + s'a` para `10 ≤ r < 100 kPa·s/m²`, y para `r < 10 kPa·s/m²` el método
68
+
solo resuelve `s' = s't` cuando el término del gas es despreciable.
69
+
`floating_floor_resonance` encadena toda la determinación:
70
+
71
+
```python
72
+
import phonometry as ph
73
+
74
+
res = ph.floating_floor_resonance(
75
+
resonant_frequency=25.0, total_mass_per_area=200.0,
76
+
floor_mass_per_area=120.0,
77
+
airflow_resistivity=50.0, thickness=0.020, porosity=0.9,
78
+
)
79
+
print(round(res.dynamic_stiffness / 1e6, 2), round(res.natural_frequency, 1))
80
+
# 10.49 47.1
81
+
```
82
+
83
+
<details>
84
+
<summary>Mostrar el código de esta figura</summary>
85
+
86
+
```python
87
+
import matplotlib.pyplot as plt
88
+
import numpy as np
89
+
import phonometry as ph
90
+
91
+
s = np.logspace(np.log10(2.0), np.log10(100.0), 300) # MN/m3
92
+
for m in (40.0, 120.0):
93
+
plt.semilogx(s, ph.natural_frequency(s * 1e6, m), label=f"m' = {m:g} kg/m²")
94
+
plt.xlabel("Rigidez dinámica s' [MN/m³]"); plt.ylabel("Frecuencia natural f₀ [Hz]")
95
+
plt.legend(); plt.show()
96
+
```
97
+
98
+
</details>
99
+
100
+
El `DynamicStiffnessResult` contiene las rigideces aparente, del gas encerrado e
101
+
instalada, la resonancia del ensayo y la frecuencia natural del suelo instalado,
102
+
y su `.plot()` dibuja la curva de diseño `f₀(s')`.
103
+
104
+
---
105
+
106
+
**Normas.** EN 29052-1:1992 (= ISO 9052-1:1989), *Acoustics — Determination of
107
+
dynamic stiffness — Part 1: Materials used under floating floors in dwellings*:
108
+
la rigidez dinámica por unidad de área (Fórmula 1), las relaciones de resonancia
109
+
(Fórmulas 2-4), el término del gas encerrado (Fórmula 7, NOTA de la cláusula 8.2
110
+
`s'a = 111/d` MN/m³) y los regímenes por resistividad al flujo (Fórmulas 5-6). La
111
+
conformidad se ancla en la NOTA numérica de la propia norma más valores en forma
112
+
cerrada calculados a mano de las relaciones de resonancia.
+110
site/src/content/docs/guides/dynamic-stiffness.md
+110
site/src/content/docs/guides/dynamic-stiffness.md
···
1
+
---
2
+
title: "Dynamic stiffness of resilient materials (EN 29052-1)"
3
+
description: "The EN 29052-1:1992 determination of the dynamic stiffness per unit area of resilient materials under floating floors from the load-plate resonance: the apparent stiffness of Formula 4, the enclosed-gas term of Formula 7, the airflow-resistivity regimes of clause 8.2, and the floating-floor natural frequency of Formula 2."
4
+
---
5
+
6
+
A **floating floor** is a heavy floating slab resting on a resilient layer; the
7
+
two form a mass-spring system whose **natural frequency** governs how much the
8
+
floor improves impact and airborne insulation. **EN 29052-1:1992** (identical to
9
+
ISO 9052-1:1989) measures the **dynamic stiffness per unit area** `s'` of the
10
+
resilient layer from the resonance of a standard load plate on a
11
+
200 mm × 200 mm specimen. `s'` is the input to the floating-floor impact
12
+
improvement (ISO 16251) covered in
13
+
[Building acoustics](/phonometry/guides/building-acoustics/) and to the
14
+
EN 12354-2 impact model.
15
+
16
+
<img class="light-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/dynamic_stiffness.svg" alt="Floating-floor natural frequency versus the resilient layer's dynamic stiffness per unit area for a light and a heavy floating floor, with a worked design point" style="width:82%"><img class="dark-only" src="https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/dynamic_stiffness_dark.svg" alt="Floating-floor natural frequency versus the resilient layer's dynamic stiffness per unit area for a light and a heavy floating floor, with a worked design point" style="width:82%">
17
+
18
+
## 1. Dynamic stiffness and resonance
19
+
20
+
The dynamic stiffness per unit area is a dynamic force per area divided by the
21
+
resulting change in thickness (Formula 1): `s' = (F/S)/Δd`. The resiliently
22
+
supported floor is a resonator whose natural frequency (Formula 2) and, in the
23
+
laboratory arrangement, measured resonant frequency (Formula 3) are
24
+
25
+
$$
26
+
f_0 = \frac{1}{2\pi}\sqrt{\frac{s'}{m'}}, \qquad
27
+
f_r = \frac{1}{2\pi}\sqrt{\frac{s'_t}{m'_t}},
28
+
$$
29
+
30
+
so the **apparent** dynamic stiffness follows from the resonance (Formula 4):
31
+
32
+
$$
33
+
s'_t = 4\pi^2\,m'_t\,f_r^2 .
34
+
$$
35
+
36
+
```python
37
+
import phonometry as ph
38
+
39
+
# Standard 8 kg load plate on the 0.04 m2 specimen -> m't = 200 kg/m2;
40
+
# the fundamental resonance is measured at 25 Hz.
41
+
s_t = ph.apparent_dynamic_stiffness(resonant_frequency=25.0, total_mass_per_area=200.0)
42
+
print(round(s_t / 1e6, 3)) # 4.935 MN/m3
43
+
44
+
# Installed on a 120 kg/m2 floating screed with s' = 10 MN/m3:
45
+
print(round(ph.natural_frequency(10e6, 120.0), 1)) # 45.9 Hz
46
+
```
47
+
48
+
## 2. The enclosed-gas term and airflow resistivity
49
+
50
+
For an air-permeable material the enclosed pore air adds a parallel stiffness
51
+
from its isothermal compression (Formula 7): `s'a = p₀/(d·ε)`, with `p₀` the
52
+
atmospheric pressure, `d` the loaded thickness and `ε` the porosity. The
53
+
standard's worked NOTE (`p₀ = 0.1 MPa`, `ε = 0.9`) is `s'a = 111/d` MN/m³ for
54
+
`d` in millimetres:
55
+
56
+
```python
57
+
import phonometry as ph
58
+
59
+
print(round(ph.enclosed_gas_stiffness(thickness=0.020, porosity=0.9) / 1e6, 2))
60
+
# 5.56 MN/m3 (the NOTE's 111/20 = 5.55 MN/m3)
61
+
```
62
+
63
+
The dynamic stiffness of the *installed* material is then set by the lateral
64
+
airflow resistivity `r` (clause 8.2): `s' = s't` for `r ≥ 100 kPa·s/m²`,
65
+
`s' = s't + s'a` for `10 ≤ r < 100 kPa·s/m²`, and for `r < 10 kPa·s/m²` the
66
+
method only resolves `s' = s't` when the gas term is negligible.
67
+
`floating_floor_resonance` chains the whole determination:
68
+
69
+
```python
70
+
import phonometry as ph
71
+
72
+
res = ph.floating_floor_resonance(
73
+
resonant_frequency=25.0, total_mass_per_area=200.0,
74
+
floor_mass_per_area=120.0,
75
+
airflow_resistivity=50.0, thickness=0.020, porosity=0.9,
76
+
)
77
+
print(round(res.dynamic_stiffness / 1e6, 2), round(res.natural_frequency, 1))
78
+
# 10.49 47.1
79
+
```
80
+
81
+
<details>
82
+
<summary>Show the code for this figure</summary>
83
+
84
+
```python
85
+
import matplotlib.pyplot as plt
86
+
import numpy as np
87
+
import phonometry as ph
88
+
89
+
s = np.logspace(np.log10(2.0), np.log10(100.0), 300) # MN/m3
90
+
for m in (40.0, 120.0):
91
+
plt.semilogx(s, ph.natural_frequency(s * 1e6, m), label=f"m' = {m:g} kg/m²")
92
+
plt.xlabel("Dynamic stiffness s' [MN/m³]"); plt.ylabel("Natural frequency f₀ [Hz]")
93
+
plt.legend(); plt.show()
94
+
```
95
+
96
+
</details>
97
+
98
+
The `DynamicStiffnessResult` carries the apparent, enclosed-gas and installed
99
+
stiffnesses, the test resonance and the installed-floor natural frequency, and
100
+
its `.plot()` draws the `f₀(s')` design curve.
101
+
102
+
---
103
+
104
+
**Standards.** EN 29052-1:1992 (= ISO 9052-1:1989), *Acoustics — Determination
105
+
of dynamic stiffness — Part 1: Materials used under floating floors in
106
+
dwellings*: the dynamic stiffness per unit area (Formula 1), the resonance
107
+
relations (Formulae 2-4), the enclosed-gas term (Formula 7, clause 8.2 NOTE
108
+
`s'a = 111/d` MN/m³) and the airflow-resistivity regimes (Formulae 5-6).
109
+
Conformance is anchored on the standard's own numeric NOTE plus hand-computed
110
+
closed-form values of the resonance relations.
+16
src/phonometry/__init__.py
+16
src/phonometry/__init__.py
···
97
97
reverberation_time_models,
98
98
sabine_reverberation_time,
99
99
)
100
+
from .dynamic_stiffness import (
101
+
DynamicStiffnessResult,
102
+
DynamicStiffnessWarning,
103
+
apparent_dynamic_stiffness,
104
+
enclosed_gas_stiffness,
105
+
floating_floor_resonance,
106
+
installed_dynamic_stiffness,
107
+
natural_frequency,
108
+
)
100
109
from .multiple_shock_vibration import (
101
110
MultipleShockResult,
102
111
acceleration_dose,
···
624
633
"arau_puchades_reverberation_time",
625
634
"reverberation_time_models",
626
635
"ReverberationModelResult",
636
+
"apparent_dynamic_stiffness",
637
+
"enclosed_gas_stiffness",
638
+
"installed_dynamic_stiffness",
639
+
"natural_frequency",
640
+
"floating_floor_resonance",
641
+
"DynamicStiffnessResult",
642
+
"DynamicStiffnessWarning",
627
643
"combine_uncertainty",
628
644
"monte_carlo",
629
645
"rectangular",
+38
src/phonometry/_plotting.py
+38
src/phonometry/_plotting.py
···
40
40
from .flanking_transmission import VibrationReductionResult
41
41
from .floor_covering_improvement import FloorCoveringImprovementResult
42
42
from .reverberation_prediction import ReverberationModelResult
43
+
from .dynamic_stiffness import DynamicStiffnessResult
43
44
from .impedance_tube import ImpedanceTubeResult
44
45
from .insulation import (
45
46
AirborneInsulationResult,
···
2006
2007
)
2007
2008
ax.set_ylim(bottom=0.0)
2008
2009
ax.legend(loc="best", fontsize="small")
2010
+
ax.grid(True, which="both", alpha=0.3)
2011
+
return ax
2012
+
2013
+
2014
+
def plot_dynamic_stiffness(
2015
+
result: "DynamicStiffnessResult", ax: Axes | None = None, **kwargs: Any
2016
+
) -> Axes:
2017
+
"""Floating-floor natural frequency ``f0(s')`` with the design point marked.
2018
+
2019
+
:param result: A
2020
+
:class:`~phonometry.dynamic_stiffness.DynamicStiffnessResult`.
2021
+
:param ax: Existing axes, or ``None`` to create a figure.
2022
+
:param kwargs: Forwarded to the design-point ``scatter``.
2023
+
:return: The axes.
2024
+
"""
2025
+
ax = ax if ax is not None else _new_axes()
2026
+
m = result.floor_mass_per_area
2027
+
s_mn = result.dynamic_stiffness / 1e6
2028
+
grid = np.logspace(np.log10(max(s_mn * 0.2, 1e-2)), np.log10(s_mn * 5.0), 240)
2029
+
f0 = np.sqrt(grid * 1e6 / m) / (2.0 * np.pi)
2030
+
ax.plot(grid, f0, color=_C_PRIMARY,
2031
+
label=rf"$f_0 = \frac{{1}}{{2\pi}}\sqrt{{s'/m'}}$, $m'$ = {m:g} kg/m²")
2032
+
ax.axhline(result.natural_frequency, color=_C_MUTED, ls=":", lw=0.8)
2033
+
ax.plot([s_mn, s_mn], [0.0, result.natural_frequency], color=_C_MUTED, ls=":", lw=0.8)
2034
+
2035
+
kwargs.setdefault("color", _C_REFERENCE)
2036
+
kwargs.setdefault("zorder", 5)
2037
+
kwargs.setdefault("s", 80)
2038
+
ax.scatter([s_mn], [result.natural_frequency],
2039
+
label=f"$s'$ = {s_mn:.2f} MN/m³, $f_0$ = {result.natural_frequency:.1f} Hz",
2040
+
**kwargs)
2041
+
ax.set_xscale("log")
2042
+
ax.set_xlabel("Dynamic stiffness per unit area $s'$ [MN/m³]")
2043
+
ax.set_ylabel("Natural frequency $f_0$ [Hz]")
2044
+
ax.set_title("EN 29052-1 floating-floor resonance")
2045
+
ax.set_ylim(bottom=0.0)
2046
+
ax.legend(loc="upper left", fontsize="small")
2009
2047
ax.grid(True, which="both", alpha=0.3)
2010
2048
return ax
2011
2049
+313
src/phonometry/dynamic_stiffness.py
+313
src/phonometry/dynamic_stiffness.py
···
1
+
# Copyright (c) 2026. Jose M. Requena-Plens
2
+
"""
3
+
Dynamic stiffness of resilient materials under floating floors (EN 29052-1:1992).
4
+
5
+
A floating floor is a heavy floating slab resting on a resilient layer; the
6
+
combination is a mass-spring system whose natural frequency governs the impact
7
+
and airborne improvement of the floor. EN 29052-1 (identical to ISO 9052-1:1989)
8
+
measures the **dynamic stiffness per unit area** ``s'`` of the resilient layer
9
+
from the resonance of a standard load plate on a 200 mm x 200 mm specimen.
10
+
11
+
The dynamic stiffness per unit area is the ratio of a dynamic force per area to
12
+
the resulting change in thickness (Formula 1)::
13
+
14
+
s' = (F / S) / dd [N/m3]
15
+
16
+
The resiliently supported floor is a mass-spring resonator; its natural
17
+
frequency (Formula 2) and, in the laboratory arrangement, the measured resonant
18
+
frequency (Formula 3) are::
19
+
20
+
f0 = (1 / 2pi) * sqrt(s' / m' ) (installed floor)
21
+
fr = (1 / 2pi) * sqrt(s't / m't) (test arrangement)
22
+
23
+
so the *apparent* dynamic stiffness follows from the resonance (Formula 4)::
24
+
25
+
s't = 4 * pi**2 * m't * fr**2
26
+
27
+
With an air-permeable resilient material the enclosed gas adds a parallel
28
+
stiffness (Formula 7), from the isothermal compression of the pore air::
29
+
30
+
s'a = p0 / (d * epsilon)
31
+
32
+
(``s'a = 111 / d`` MN/m3 for ``p0 = 0,1 MPa``, ``epsilon = 0,9`` and ``d`` in mm,
33
+
the standard's worked NOTE). The dynamic stiffness of the installed material is
34
+
then obtained by airflow resistivity ``r`` (clause 8.2)::
35
+
36
+
r >= 100 kPa.s/m2 s' = s't (Formula 5)
37
+
10 <= r < 100 kPa.s/m2 s' = s't + s'a (Formula 6)
38
+
r < 10 kPa.s/m2 s'a from Formula 7; the method only applies when
39
+
s't >> s'a, otherwise s' cannot be resolved.
40
+
41
+
This module is the resilient-layer characterisation feeding the floating-floor
42
+
impact improvement of :mod:`phonometry.floor_covering_improvement` (ISO 16251)
43
+
and the EN 12354-2 impact model.
44
+
"""
45
+
46
+
from __future__ import annotations
47
+
48
+
import warnings
49
+
from dataclasses import dataclass
50
+
from typing import TYPE_CHECKING, Any
51
+
52
+
import numpy as np
53
+
54
+
if TYPE_CHECKING:
55
+
from matplotlib.axes import Axes
56
+
57
+
from numpy.typing import ArrayLike
58
+
59
+
from ._types import as_float_or_array
60
+
from ._validation import require_positive
61
+
from ._warnings import PhonometryWarning
62
+
63
+
# ---------------------------------------------------------------------------
64
+
# Constants.
65
+
# ---------------------------------------------------------------------------
66
+
67
+
#: Atmospheric pressure ``p0`` used by EN 29052-1 for the enclosed-gas term
68
+
#: (clause 8.2 NOTE: ``p0 = 0,1 MPa``), in pascals. The standard rounds one
69
+
#: atmosphere to 0,1 MPa; pass the true 101 325 Pa explicitly if preferred.
70
+
STANDARD_ATMOSPHERIC_PRESSURE = 1.0e5
71
+
72
+
#: Airflow-resistivity thresholds of clause 8.2, in kPa.s/m2.
73
+
_HIGH_RESISTIVITY = 100.0
74
+
_LOW_RESISTIVITY = 10.0
75
+
76
+
#: ``2*pi`` and ``4*pi**2`` for the resonance relations.
77
+
_TWO_PI = 2.0 * np.pi
78
+
_FOUR_PI_SQ = 4.0 * np.pi**2
79
+
80
+
81
+
class DynamicStiffnessWarning(PhonometryWarning):
82
+
"""Advisory when the enclosed-gas term makes ``s'`` unresolvable (clause 8.2)."""
83
+
84
+
85
+
# ---------------------------------------------------------------------------
86
+
# Resonance relations (clauses 3, 8.1).
87
+
# ---------------------------------------------------------------------------
88
+
89
+
90
+
def apparent_dynamic_stiffness(
91
+
resonant_frequency: ArrayLike, total_mass_per_area: float
92
+
) -> np.ndarray | float:
93
+
"""Apparent dynamic stiffness per unit area ``s't`` (Formula 4).
94
+
95
+
Inverts the test resonance ``fr = (1/2pi) sqrt(s't/m't)`` to
96
+
``s't = 4 pi**2 m't fr**2``.
97
+
98
+
:param resonant_frequency: Extrapolated resonant frequency ``fr``, in hertz
99
+
(scalar or array).
100
+
:param total_mass_per_area: Total mass per unit area used during the test
101
+
``m't``, in kg/m2 (the load plate plus fittings over the 0,04 m2
102
+
specimen; the standard's plate gives ``m't = 8 kg / 0,04 m2 = 200
103
+
kg/m2``).
104
+
:return: The apparent dynamic stiffness per unit area ``s't``, in N/m3
105
+
(numerically MN/m3 when divided by 1e6).
106
+
"""
107
+
total_mass_per_area = require_positive(total_mass_per_area, "total_mass_per_area")
108
+
fr = np.asarray(resonant_frequency, dtype=np.float64)
109
+
if np.any(fr <= 0.0):
110
+
raise ValueError("'resonant_frequency' must be positive.")
111
+
return as_float_or_array(_FOUR_PI_SQ * total_mass_per_area * fr**2)
112
+
113
+
114
+
def enclosed_gas_stiffness(
115
+
thickness: ArrayLike,
116
+
porosity: float,
117
+
*,
118
+
atmospheric_pressure: float = STANDARD_ATMOSPHERIC_PRESSURE,
119
+
) -> np.ndarray | float:
120
+
"""Enclosed-gas dynamic stiffness per unit area ``s'a`` (Formula 7).
121
+
122
+
The isothermal compression of the pore air adds a stiffness in parallel with
123
+
the material's structure: ``s'a = p0 / (d * epsilon)``.
124
+
125
+
:param thickness: Thickness ``d`` of the specimen under the static load, in
126
+
**metres** (scalar or array).
127
+
:param porosity: Porosity ``epsilon`` of the specimen (0-1).
128
+
:param atmospheric_pressure: Atmospheric pressure ``p0``, in pascals
129
+
(default :data:`STANDARD_ATMOSPHERIC_PRESSURE`, the standard's 0,1 MPa).
130
+
:return: The enclosed-gas dynamic stiffness per unit area ``s'a``, in N/m3.
131
+
132
+
.. note::
133
+
With the standard's ``p0 = 0,1 MPa`` and ``epsilon = 0,9`` this reduces
134
+
to ``s'a = 111 / d`` MN/m3 for ``d`` in millimetres (clause 8.2 NOTE).
135
+
"""
136
+
atmospheric_pressure = require_positive(atmospheric_pressure, "atmospheric_pressure")
137
+
if not 0.0 < porosity <= 1.0:
138
+
raise ValueError("'porosity' must be in the range (0, 1].")
139
+
d = np.asarray(thickness, dtype=np.float64)
140
+
if np.any(d <= 0.0):
141
+
raise ValueError("'thickness' must be positive.")
142
+
return as_float_or_array(atmospheric_pressure / (d * porosity))
143
+
144
+
145
+
def installed_dynamic_stiffness(
146
+
apparent_stiffness: float,
147
+
airflow_resistivity: float,
148
+
*,
149
+
gas_stiffness: float = 0.0,
150
+
) -> float:
151
+
"""Dynamic stiffness per unit area ``s'`` of the installed material (clause 8.2).
152
+
153
+
Combines the apparent stiffness with the enclosed-gas term according to the
154
+
lateral airflow resistivity ``r``:
155
+
156
+
* ``r >= 100 kPa.s/m2`` -> ``s' = s't`` (Formula 5);
157
+
* ``10 <= r < 100 kPa.s/m2`` -> ``s' = s't + s'a`` (Formula 6);
158
+
* ``r < 10 kPa.s/m2`` -> the standard only requires the qualitative
159
+
criterion ``s't >> s'a`` (clause 8.2). This implementation applies its own
160
+
engineering threshold: ``s'a`` below 10 % of ``s't`` is treated as
161
+
negligible and ``s' = s't`` (a :class:`DynamicStiffnessWarning` is
162
+
emitted); above it the result is ``nan`` — the method cannot resolve
163
+
``s'``.
164
+
165
+
:param apparent_stiffness: Apparent dynamic stiffness ``s't``, in N/m3.
166
+
:param airflow_resistivity: Lateral airflow resistivity ``r``, in kPa.s/m2
167
+
(ISO 9053).
168
+
:param gas_stiffness: Enclosed-gas dynamic stiffness ``s'a``, in N/m3 (see
169
+
:func:`enclosed_gas_stiffness`); needed for ``r < 100 kPa.s/m2``.
170
+
:return: The installed dynamic stiffness per unit area ``s'``, in N/m3
171
+
(``nan`` when the method cannot resolve it).
172
+
"""
173
+
apparent_stiffness = require_positive(apparent_stiffness, "apparent_stiffness")
174
+
if airflow_resistivity <= 0.0:
175
+
raise ValueError("'airflow_resistivity' must be positive.")
176
+
if gas_stiffness < 0.0:
177
+
raise ValueError("'gas_stiffness' must be non-negative.")
178
+
179
+
if airflow_resistivity >= _HIGH_RESISTIVITY:
180
+
return apparent_stiffness
181
+
if airflow_resistivity >= _LOW_RESISTIVITY:
182
+
return apparent_stiffness + gas_stiffness
183
+
# r < 10 kPa.s/m2: the enclosed gas is only negligible for a firm structure.
184
+
if gas_stiffness > 0.1 * apparent_stiffness:
185
+
warnings.warn(
186
+
"for airflow resistivity below 10 kPa.s/m2 with a non-negligible "
187
+
"enclosed-gas stiffness, EN 29052-1 cannot resolve s' (clause 8.2); "
188
+
"returning nan.",
189
+
DynamicStiffnessWarning,
190
+
stacklevel=2,
191
+
)
192
+
return float("nan")
193
+
warnings.warn(
194
+
"airflow resistivity below 10 kPa.s/m2: s' is taken as s't with the "
195
+
"enclosed-gas term disregarded; state the estimated error (clause 8.2).",
196
+
DynamicStiffnessWarning,
197
+
stacklevel=2,
198
+
)
199
+
return apparent_stiffness
200
+
201
+
202
+
def natural_frequency(
203
+
dynamic_stiffness: ArrayLike, mass_per_area: float
204
+
) -> np.ndarray | float:
205
+
"""Natural frequency ``f0`` of the resiliently supported floor (Formula 2).
206
+
207
+
``f0 = (1 / 2pi) sqrt(s' / m')``.
208
+
209
+
:param dynamic_stiffness: Dynamic stiffness per unit area ``s'``, in N/m3
210
+
(scalar or array).
211
+
:param mass_per_area: Mass per unit area of the supported floor ``m'``, in
212
+
kg/m2.
213
+
:return: The natural frequency ``f0``, in hertz.
214
+
"""
215
+
mass_per_area = require_positive(mass_per_area, "mass_per_area")
216
+
s = np.asarray(dynamic_stiffness, dtype=np.float64)
217
+
if np.any(s <= 0.0):
218
+
raise ValueError("'dynamic_stiffness' must be positive.")
219
+
return as_float_or_array(np.sqrt(s / mass_per_area) / _TWO_PI)
220
+
221
+
222
+
# ---------------------------------------------------------------------------
223
+
# Bundled measurement result.
224
+
# ---------------------------------------------------------------------------
225
+
226
+
227
+
@dataclass(frozen=True)
228
+
class DynamicStiffnessResult:
229
+
"""Dynamic stiffness of a resilient layer and the floating-floor resonance.
230
+
231
+
:ivar apparent_stiffness: Apparent dynamic stiffness ``s't``, in N/m3.
232
+
:ivar gas_stiffness: Enclosed-gas dynamic stiffness ``s'a``, in N/m3.
233
+
:ivar dynamic_stiffness: Installed dynamic stiffness ``s'``, in N/m3.
234
+
:ivar resonant_frequency: Measured test resonant frequency ``fr``, in hertz.
235
+
:ivar floor_mass_per_area: Supported-floor mass per unit area ``m'``, kg/m2.
236
+
:ivar natural_frequency: Installed-floor natural frequency ``f0``, in hertz.
237
+
"""
238
+
239
+
apparent_stiffness: float
240
+
gas_stiffness: float
241
+
dynamic_stiffness: float
242
+
resonant_frequency: float
243
+
floor_mass_per_area: float
244
+
natural_frequency: float
245
+
246
+
def plot(self, ax: "Axes | None" = None, **kwargs: Any) -> "Axes":
247
+
"""Plot ``f0(s')`` with this design point marked.
248
+
249
+
Requires matplotlib (``pip install phonometry[plot]``); returns the
250
+
:class:`~matplotlib.axes.Axes`.
251
+
"""
252
+
from ._plotting import plot_dynamic_stiffness
253
+
254
+
return plot_dynamic_stiffness(self, ax=ax, **kwargs)
255
+
256
+
257
+
def floating_floor_resonance(
258
+
resonant_frequency: float,
259
+
total_mass_per_area: float,
260
+
floor_mass_per_area: float,
261
+
*,
262
+
airflow_resistivity: float = float("inf"),
263
+
thickness: float | None = None,
264
+
porosity: float | None = None,
265
+
atmospheric_pressure: float = STANDARD_ATMOSPHERIC_PRESSURE,
266
+
) -> DynamicStiffnessResult:
267
+
"""Full EN 29052-1 chain: measured resonance -> installed ``s'`` and ``f0``.
268
+
269
+
Chains the apparent dynamic stiffness (Formula 4), the enclosed-gas term
270
+
(Formula 7, when ``thickness`` and ``porosity`` are given), the airflow
271
+
resistivity combination (clause 8.2) and the installed-floor natural
272
+
frequency (Formula 2).
273
+
274
+
:param resonant_frequency: Measured resonant frequency ``fr``, in hertz.
275
+
:param total_mass_per_area: Test total mass per unit area ``m't``, kg/m2.
276
+
:param floor_mass_per_area: Supported-floor mass per unit area ``m'``, kg/m2.
277
+
:param airflow_resistivity: Lateral airflow resistivity ``r``, in kPa.s/m2
278
+
(default ``inf`` -> the high-resistivity case ``s' = s't``).
279
+
:param thickness: Specimen thickness ``d`` under load, in metres (required
280
+
for the enclosed-gas term when ``r < 100 kPa.s/m2``).
281
+
:param porosity: Specimen porosity ``epsilon`` (required with ``thickness``).
282
+
:param atmospheric_pressure: Atmospheric pressure ``p0``, in pascals.
283
+
:return: The :class:`DynamicStiffnessResult`.
284
+
"""
285
+
s_apparent = float(apparent_dynamic_stiffness(resonant_frequency, total_mass_per_area))
286
+
s_gas = 0.0
287
+
if airflow_resistivity < _HIGH_RESISTIVITY:
288
+
if thickness is None or porosity is None:
289
+
raise ValueError(
290
+
"'thickness' and 'porosity' are required for the enclosed-gas "
291
+
"term when airflow_resistivity < 100 kPa.s/m2."
292
+
)
293
+
s_gas = float(
294
+
enclosed_gas_stiffness(
295
+
thickness, porosity, atmospheric_pressure=atmospheric_pressure
296
+
)
297
+
)
298
+
s_installed = installed_dynamic_stiffness(
299
+
s_apparent, airflow_resistivity, gas_stiffness=s_gas
300
+
)
301
+
f0 = (
302
+
float(natural_frequency(s_installed, floor_mass_per_area))
303
+
if np.isfinite(s_installed)
304
+
else float("nan")
305
+
)
306
+
return DynamicStiffnessResult(
307
+
apparent_stiffness=s_apparent,
308
+
gas_stiffness=s_gas,
309
+
dynamic_stiffness=s_installed,
310
+
resonant_frequency=float(resonant_frequency),
311
+
floor_mass_per_area=float(floor_mass_per_area),
312
+
natural_frequency=f0,
313
+
)
+173
tests/test_dynamic_stiffness.py
+173
tests/test_dynamic_stiffness.py
···
1
+
# Copyright (c) 2026. Jose M. Requena-Plens
2
+
"""Tests for EN 29052-1:1992 dynamic stiffness of resilient materials.
3
+
4
+
Anchored on hand-computed closed-form values of the resonance relations
5
+
(Formulae 2-4) and on the standard's own worked NOTE for the enclosed-gas term
6
+
(``s'a = 111 / d`` MN/m3 for ``p0 = 0,1 MPa``, ``epsilon = 0,9``, clause 8.2) --
7
+
a genuine published numeric oracle.
8
+
"""
9
+
10
+
from __future__ import annotations
11
+
12
+
import math
13
+
14
+
import numpy as np
15
+
import pytest
16
+
17
+
from phonometry import (
18
+
DynamicStiffnessResult,
19
+
apparent_dynamic_stiffness,
20
+
enclosed_gas_stiffness,
21
+
floating_floor_resonance,
22
+
installed_dynamic_stiffness,
23
+
natural_frequency,
24
+
)
25
+
from phonometry.dynamic_stiffness import DynamicStiffnessWarning
26
+
27
+
28
+
# ---------------------------------------------------------------------------
29
+
# Apparent dynamic stiffness (Formula 4) and its resonance inverse (Formula 3)
30
+
# ---------------------------------------------------------------------------
31
+
def test_apparent_stiffness_hand_value() -> None:
32
+
"""s't = 4 pi^2 m't fr^2: 4 pi^2 * 200 * 25^2 = 4.934802 MN/m3."""
33
+
st = apparent_dynamic_stiffness(25.0, 200.0)
34
+
assert st == pytest.approx(4_934_802.200545, rel=1e-9)
35
+
assert st == pytest.approx(4.0 * math.pi**2 * 200.0 * 25.0**2, rel=1e-12)
36
+
37
+
38
+
def test_apparent_stiffness_inverts_the_resonance() -> None:
39
+
"""Recovering fr from s't via Formula 3 returns the input frequency."""
40
+
st = apparent_dynamic_stiffness(25.0, 200.0)
41
+
assert natural_frequency(st, 200.0) == pytest.approx(25.0, rel=1e-12)
42
+
43
+
44
+
def test_apparent_stiffness_vectorised() -> None:
45
+
st = apparent_dynamic_stiffness([20.0, 25.0, 30.0], 200.0)
46
+
assert isinstance(st, np.ndarray)
47
+
assert st.shape == (3,)
48
+
assert np.all(np.diff(st) > 0.0) # rises with fr^2
49
+
50
+
51
+
# ---------------------------------------------------------------------------
52
+
# Enclosed-gas stiffness (Formula 7) -- standard's 111/d NOTE oracle
53
+
# ---------------------------------------------------------------------------
54
+
def test_enclosed_gas_matches_standard_note() -> None:
55
+
"""s'a = p0/(d eps); with p0=0,1 MPa, eps=0,9 the NOTE gives ~111/d MN/m3.
56
+
57
+
The closed form yields 100000/(0,9) = 111.11.../d MN/m3 (d in mm); the
58
+
standard rounds the printed coefficient to 111.
59
+
"""
60
+
for d_mm in (10.0, 20.0, 50.0):
61
+
sa = enclosed_gas_stiffness(d_mm / 1000.0, 0.9) # thickness in metres
62
+
assert sa == pytest.approx(1.0e5 / ((d_mm / 1000.0) * 0.9), rel=1e-12)
63
+
# cross-check against the standard's printed 111/d relationship
64
+
assert sa / 1e6 == pytest.approx(111.0 / d_mm, rel=2e-3)
65
+
66
+
67
+
def test_enclosed_gas_true_atmosphere() -> None:
68
+
"""A real 101 325 Pa can be passed instead of the standard's 0,1 MPa."""
69
+
sa = enclosed_gas_stiffness(0.02, 0.9, atmospheric_pressure=101_325.0)
70
+
assert sa == pytest.approx(101_325.0 / (0.02 * 0.9), rel=1e-12)
71
+
72
+
73
+
def test_enclosed_gas_bad_porosity_raises() -> None:
74
+
with pytest.raises(ValueError, match="porosity"):
75
+
enclosed_gas_stiffness(0.02, 0.0)
76
+
with pytest.raises(ValueError, match="porosity"):
77
+
enclosed_gas_stiffness(0.02, 1.5)
78
+
79
+
80
+
# ---------------------------------------------------------------------------
81
+
# Natural frequency (Formula 2)
82
+
# ---------------------------------------------------------------------------
83
+
def test_natural_frequency_hand_value() -> None:
84
+
"""f0 = (1/2pi) sqrt(s'/m'): sqrt(10e6/100)/(2pi) = 50.329 Hz."""
85
+
assert natural_frequency(10.0e6, 100.0) == pytest.approx(50.3292121, rel=1e-6)
86
+
87
+
88
+
def test_natural_frequency_scales() -> None:
89
+
"""f0 scales with sqrt(s') and 1/sqrt(m')."""
90
+
base = float(natural_frequency(10.0e6, 100.0))
91
+
assert natural_frequency(40.0e6, 100.0) == pytest.approx(2.0 * base, rel=1e-9)
92
+
assert natural_frequency(10.0e6, 400.0) == pytest.approx(base / 2.0, rel=1e-9)
93
+
94
+
95
+
# ---------------------------------------------------------------------------
96
+
# Airflow-resistivity combination (clause 8.2)
97
+
# ---------------------------------------------------------------------------
98
+
def test_high_resistivity_uses_apparent_only() -> None:
99
+
assert installed_dynamic_stiffness(20e6, 150.0, gas_stiffness=3e6) == 20e6
100
+
101
+
102
+
def test_intermediate_resistivity_adds_gas() -> None:
103
+
assert installed_dynamic_stiffness(20e6, 50.0, gas_stiffness=3e6) == 23e6
104
+
# boundary at 10 kPa.s/m2 is inclusive of the intermediate branch
105
+
assert installed_dynamic_stiffness(20e6, 10.0, gas_stiffness=3e6) == 23e6
106
+
107
+
108
+
def test_low_resistivity_negligible_gas_warns_and_uses_apparent() -> None:
109
+
with pytest.warns(DynamicStiffnessWarning, match="disregarded"):
110
+
s = installed_dynamic_stiffness(20e6, 5.0, gas_stiffness=1e6) # 5 % of s't
111
+
assert s == 20e6
112
+
113
+
114
+
def test_low_resistivity_significant_gas_is_unresolvable() -> None:
115
+
with pytest.warns(DynamicStiffnessWarning, match="cannot resolve"):
116
+
s = installed_dynamic_stiffness(20e6, 5.0, gas_stiffness=5e6) # 25 % of s't
117
+
assert math.isnan(s)
118
+
119
+
120
+
# ---------------------------------------------------------------------------
121
+
# Full chain
122
+
# ---------------------------------------------------------------------------
123
+
def test_floating_floor_resonance_chain() -> None:
124
+
res = floating_floor_resonance(
125
+
25.0, 200.0, 100.0, airflow_resistivity=50.0, thickness=0.02, porosity=0.9
126
+
)
127
+
assert isinstance(res, DynamicStiffnessResult)
128
+
assert res.apparent_stiffness == pytest.approx(4_934_802.2, rel=1e-6)
129
+
assert res.gas_stiffness == pytest.approx(1.0e5 / (0.02 * 0.9), rel=1e-9)
130
+
assert res.dynamic_stiffness == pytest.approx(
131
+
res.apparent_stiffness + res.gas_stiffness, rel=1e-12
132
+
)
133
+
assert res.natural_frequency == pytest.approx(
134
+
math.sqrt(res.dynamic_stiffness / 100.0) / (2.0 * math.pi), rel=1e-9
135
+
)
136
+
137
+
138
+
def test_chain_high_resistivity_ignores_gas() -> None:
139
+
"""With r >= 100 kPa.s/m2 the gas term is not needed."""
140
+
res = floating_floor_resonance(25.0, 200.0, 100.0) # default r = inf
141
+
assert res.gas_stiffness == 0.0
142
+
assert res.dynamic_stiffness == res.apparent_stiffness
143
+
144
+
145
+
def test_chain_requires_gas_inputs_below_100() -> None:
146
+
with pytest.raises(ValueError, match="thickness.*porosity"):
147
+
floating_floor_resonance(25.0, 200.0, 100.0, airflow_resistivity=50.0)
148
+
149
+
150
+
# ---------------------------------------------------------------------------
151
+
# Validation
152
+
# ---------------------------------------------------------------------------
153
+
def test_non_positive_inputs_raise() -> None:
154
+
with pytest.raises(ValueError, match="resonant_frequency"):
155
+
apparent_dynamic_stiffness(0.0, 200.0)
156
+
with pytest.raises(ValueError, match="total_mass_per_area"):
157
+
apparent_dynamic_stiffness(25.0, 0.0)
158
+
with pytest.raises(ValueError, match="mass_per_area"):
159
+
natural_frequency(10e6, 0.0)
160
+
with pytest.raises(ValueError, match="airflow_resistivity"):
161
+
installed_dynamic_stiffness(20e6, 0.0)
162
+
163
+
164
+
# ---------------------------------------------------------------------------
165
+
# Plotting
166
+
# ---------------------------------------------------------------------------
167
+
def test_plot_returns_axes() -> None:
168
+
pytest.importorskip("matplotlib")
169
+
import matplotlib
170
+
171
+
matplotlib.use("Agg")
172
+
res = floating_floor_resonance(25.0, 200.0, 100.0)
173
+
assert res.plot() is not None