materials.dynamic_stiffness

Dynamic stiffness of resilient materials under floating floors (EN 29052-1:1992).

A floating floor is a heavy floating slab resting on a resilient layer; the combination is a mass-spring system whose natural frequency governs the impact and airborne improvement of the floor. EN 29052-1 (identical to ISO 9052-1:1989) measures the dynamic stiffness per unit area s' of the resilient layer from the resonance of a standard load plate on a 200 mm x 200 mm specimen.

The dynamic stiffness per unit area is the ratio of a dynamic force per area to the resulting change in thickness (Formula 1):

s' = (F / S) / dd     [N/m3]

The resiliently supported floor is a mass-spring resonator; its natural frequency (Formula 2) and, in the laboratory arrangement, the measured resonant frequency (Formula 3) are:

f0 = (1 / 2pi) * sqrt(s'  / m' )        (installed floor)
fr = (1 / 2pi) * sqrt(s't / m't)        (test arrangement)

so the apparent dynamic stiffness follows from the resonance (Formula 4):

s't = 4 * pi**2 * m't * fr**2

With an air-permeable resilient material the enclosed gas adds a parallel stiffness (Formula 7), from the isothermal compression of the pore air:

s'a = p0 / (d * epsilon)

(s'a = 111 / d MN/m3 for p0 = 0,1 MPa, epsilon = 0,9 and d in mm, the standard’s worked NOTE). The dynamic stiffness of the installed material is then obtained by airflow resistivity r (clause 8.2):

r >= 100 kPa.s/m2         s' = s't                     (Formula 5)
10 <= r < 100 kPa.s/m2    s' = s't + s'a               (Formula 6)
r < 10 kPa.s/m2           s'a from Formula 7; the method only applies when
                          s't >> s'a, otherwise s' cannot be resolved.

This module is the resilient-layer characterisation feeding the floating-floor term of the EN 12354-2 impact model (phonometry.building.building_prediction). It does not feed ISO 16251-1 (phonometry.building.floor_covering_improvement), whose scope is limited to soft, locally-reacting floor coverings; floating floors are explicitly excluded there.

Auto-generated from the source docstrings by scripts/generate_api_docs.py (make api-docs). Do not edit by hand.

apparent_dynamic_stiffness

apparent_dynamic_stiffness(
    resonant_frequency: ArrayLike,
    total_mass_per_area: float,
) -> np.ndarray | float

Apparent dynamic stiffness per unit area s't (Formula 4).

Inverts the test resonance fr = (1/2pi) sqrt(s't/m't) to s't = 4 pi**2 m't fr**2.

Parameters

Name	Description
resonant_frequency	Extrapolated resonant frequency fr, in hertz (scalar or array).
total_mass_per_area	Total mass per unit area used during the test m't, in kg/m2 (the load plate plus fittings over the 0,04 m2 specimen; the standard’s plate gives m't = 8 kg / 0,04 m2 = 200 kg/m2).

Returns: The apparent dynamic stiffness per unit area s't, in N/m3 (numerically MN/m3 when divided by 1e6).

DynamicStiffnessResult

DynamicStiffnessResult(
    apparent_stiffness: float,
    gas_stiffness: float,
    dynamic_stiffness: float,
    resonant_frequency: float,
    floor_mass_per_area: float,
    natural_frequency: float,
)

Dynamic stiffness of a resilient layer and the floating-floor resonance.

Attributes

Name	Description
apparent_stiffness	Apparent dynamic stiffness s't, in N/m3.
gas_stiffness	Enclosed-gas dynamic stiffness s'a, in N/m3.
dynamic_stiffness	Installed dynamic stiffness s', in N/m3.
resonant_frequency	Measured test resonant frequency fr, in hertz.
floor_mass_per_area	Supported-floor mass per unit area m', kg/m2.
natural_frequency	Installed-floor natural frequency f0, in hertz.

DynamicStiffnessResult.plot()

DynamicStiffnessResult.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot f0(s') with this design point marked.

Requires matplotlib (pip install phonometry[plot]); returns the Axes.

DynamicStiffnessResult.report()

DynamicStiffnessResult.report(
    path: str,
    *,
    metadata: ReportMetadata | None = None,
    engine: str = 'reportlab',
    verbose: bool = False,
    language: str = 'en',
) -> str

Render an EN 29052-1 dynamic-stiffness test-report fiche to a PDF.

Writes a one-page accredited dynamic-stiffness report (EN 29052-1:1992, identical to ISO 9052-1:1989): the standard-basis line, an optional metadata header block (client, specimen, the total mass per unit area m't used during the test, the loaded specimen thickness d, test facility, date, climate …), a two-panel body with a compact metrics table (the resonant frequency fr, the apparent dynamic stiffness s't of Formula 4, the enclosed-gas term s'a of Formula 7 when it applies, the installed dynamic stiffness s' of Clause 8.2 and the supported-floor natural frequency f0 of Formula 2) beside the f0(s') design curve, a boxed apparent dynamic stiffness s't with the installed s' and the resonance fr alongside, and a footer with the fixed disclaimer. EN 29052-1 is a characterisation, so there is no pass/fail verdict.

Clause 9 requires every dynamic stiffness per unit area to be stated in meganewtons per cubic metre to the nearest meganewton per cubic metre, so the stiffness values are rounded to the nearest MN/m3; the frequencies are shown to 0,1 Hz.

Parameters

Name	Description
path	Destination path of the PDF file.
metadata	Optional ReportMetadata; None produces a body-and-disclaimer fiche. The applicable descriptive fields are client, manufacturer, specimen, mass_per_area (the total mass per unit area m't), thickness (the loaded specimen thickness d, in metres, shown in millimetres), test_room, test_date, temperature, relative_humidity, measurement_standard, laboratory, operator, report_id and notes. The requirement field is ignored (EN 29052-1 has no verdict).
engine	Rendering back end; only "reportlab" is supported.
verbose	Accepted for a uniform .report() signature; the dynamic-stiffness fiche has a single body layout, so it has no effect.
language	Fiche language: "en" (default, English, decimal point) or "es" (Spanish, decimal comma).

Returns: The written path as a str.

Raises

Exception	When
ValueError	If engine is not "reportlab".
ImportError	If reportlab or matplotlib is not installed. The fiche always embeds the f0(s') design curve, so both are required (pip install "phonometry[report,plot]").

DynamicStiffnessWarning

Advisory when the enclosed-gas term makes s' unresolvable (clause 8.2).

enclosed_gas_stiffness

enclosed_gas_stiffness(
    thickness: ArrayLike,
    porosity: float,
    *,
    atmospheric_pressure: float = 100000.0,
) -> np.ndarray | float

Enclosed-gas dynamic stiffness per unit area s'a (Formula 7).

The isothermal compression of the pore air adds a stiffness in parallel with the material’s structure: s'a = p0 / (d * epsilon).

Parameters

Name	Description
thickness	Thickness d of the specimen under the static load, in metres (scalar or array).
porosity	Porosity epsilon of the specimen (0-1).
atmospheric_pressure	Atmospheric pressure p0, in pascals (default STANDARD_ATMOSPHERIC_PRESSURE, the standard’s 0,1 MPa).

Returns: The enclosed-gas dynamic stiffness per unit area s'a, in N/m3.

Note

With the standard’s p0 = 0,1 MPa and epsilon = 0,9 this reduces to s'a = 111 / d MN/m3 for d in millimetres (clause 8.2 NOTE).

floating_floor_resonance

floating_floor_resonance(
    resonant_frequency: float,
    total_mass_per_area: float,
    floor_mass_per_area: float,
    *,
    airflow_resistivity: float = inf,
    thickness: float | None = None,
    porosity: float | None = None,
    atmospheric_pressure: float = 100000.0,
) -> DynamicStiffnessResult

Full EN 29052-1 chain: measured resonance -> installed s' and f0.

Chains the apparent dynamic stiffness (Formula 4), the enclosed-gas term (Formula 7, when thickness and porosity are given), the airflow resistivity combination (clause 8.2) and the installed-floor natural frequency (Formula 2).

Parameters

Name	Description
resonant_frequency	Measured resonant frequency fr, in hertz.
total_mass_per_area	Test total mass per unit area m't, kg/m2.
floor_mass_per_area	Supported-floor mass per unit area m', kg/m2.
airflow_resistivity	Lateral airflow resistivity r, in kPa.s/m2 (default inf -> the high-resistivity case s' = s't).
thickness	Specimen thickness d under load, in metres (required for the enclosed-gas term when r < 100 kPa.s/m2).
porosity	Specimen porosity epsilon (required with thickness).
atmospheric_pressure	Atmospheric pressure p0, in pascals.

Returns: The DynamicStiffnessResult.

installed_dynamic_stiffness

installed_dynamic_stiffness(
    apparent_stiffness: float,
    airflow_resistivity: float,
    *,
    gas_stiffness: float = 0.0,
) -> float

Dynamic stiffness per unit area s' of the installed material (clause 8.2).

Combines the apparent stiffness with the enclosed-gas term according to the lateral airflow resistivity r:

• r >= 100 kPa.s/m2 -> s' = s't (Formula 5);
• 10 <= r < 100 kPa.s/m2 -> s' = s't + s'a (Formula 6);
• r < 10 kPa.s/m2 -> the standard only requires the qualitative criterion s't >> s'a (clause 8.2). This implementation applies its own engineering threshold: s'a below 10 % of s't is treated as negligible and s' = s't (a DynamicStiffnessWarning is emitted; clause 8.2 requires the error caused by disregarding s'a to be stated in the test report); above it the result is nan, as the method cannot resolve s'.

Parameters

Name	Description
apparent_stiffness	Apparent dynamic stiffness s't, in N/m3.
airflow_resistivity	Lateral airflow resistivity r, in kPa.s/m2 (ISO 9053).
gas_stiffness	Enclosed-gas dynamic stiffness s'a, in N/m3 (see enclosed_gas_stiffness); needed for r < 100 kPa.s/m2.

Returns: The installed dynamic stiffness per unit area s', in N/m3 (nan when the method cannot resolve it).

natural_frequency

natural_frequency(
    dynamic_stiffness: ArrayLike,
    mass_per_area: float,
) -> np.ndarray | float

Natural frequency f0 of the resiliently supported floor (Formula 2).

f0 = (1 / 2pi) sqrt(s' / m').

Parameters

Name	Description
dynamic_stiffness	Dynamic stiffness per unit area s', in N/m3 (scalar or array).
mass_per_area	Mass per unit area of the supported floor m', in kg/m2.

Returns: The natural frequency f0, in hertz.