building.prediction.installed_structure_borne

La referencia de la API se publica en inglés en los dos idiomas: se genera a partir de los docstrings del código, que son su texto original.

Installed structure-borne sound from service equipment (EN 12354-5:2009).

EN 12354-5 predicts the sound pressure level in a receiving room caused by building service equipment that injects structure-borne sound into the building. The chain closes the structural-vibroacoustics series:

The source strength is its characteristic structure-borne sound power level L_Ws,c. It is not the raw reception-plate power of EN 15657 Formula (14): that plate-injected level must first be converted to the plate-independent L_Ws,n (EN 15657 Formulae (15)/(17); see phonometry.building.measurement.structure_borne_power) and then referred to the actual receiver with the Annex I mobility correction (installed_power_from_reception_plate), $L_{W s, inst, i} = L_{W s, n} + 10 lo g_{10} (Y_{\infty, i} / Y_{\infty, rec})$ with the reference plate mobility $Y_{\infty, rec} = 5 \cdot 1 0^{- 6}$ m/(N.s), or equivalently to the characteristic level $L_{W s, c} = L_{W s, n} + 10 lo g_{10} (Y_{s} / Y_{\infty, rec})$ with the source mobility (Annex I.3, Table I.8), from which D_C is subtracted.
Only part of that power is actually injected into the supporting element; the loss is the coupling term D_C (clause 4.4.3), positive in the usual mobility-mismatched cases (see coupling_term for the exception), set by the source mobility Y_s and the receiver mobility Y_i (Formula 19b): $D_{C, i} = 10 lo g_{10} (∣ Y_{s} + Y_{i} ∣^{2} / (∣ Y_{s} ∣ Re {Y_{i}}))$ , which reduces to $10 lo g_{10} (∣ Y_{s} ∣/ Re {Y_{i}})$ for a force source (high source mobility, Formula 19c) and to $- 10 lo g_{10} (∣ Y_{s} ∣ Re {Z_{i}})$ for a velocity source (low source mobility, Formula 19d). An elastic support adds its transfer mobility Y_k inside the modulus (Formula 19e).
The installed power level is then $L_{W s, inst, i} = L_{W s, c} - D_{C, i}$ (Formula 18b).
The normalised sound pressure level in the receiving room for one path (i->j) follows from the installed power, the structure-to-airborne adjustment term D_sa (clause 4.4.4), the flanking sound reduction index R_ij,ref and the element area (Formula 18a): $L_{n, s, ij} = L_{W s, inst, i} - D_{sa, i} - R_{ij, ref} - 10 lo g_{10} (S_{i} / S_{0}) - 10 lo g_{10} (A_{0} /4)$ with $S_{0} = A_{0} = 10$ m²; the paths combine energetically (Formula 17).

The source and receiver mobilities/impedances are those of phonometry.vibration.structural.mechanical_mobility and phonometry.vibration.structural.transfer_stiffness.

The informative tables. Every term of that chain is a number the user would otherwise copy out of the standard, so the two tables of the informative annexes are here as named lookups:

Table D.1 (Annex D) estimates the mobility of typical construction elements from their own dimensions, which is how clause D.1.3 builds up a source mobility Y_s for step 2 out of the machine’s mass, feet, chassis panels and pipework: typical_element_mobility, whose structure argument is the table’s first column and whose keywords are its second (TABLE_D1_QUANTITIES).
Table F.1 (Annex F) gives the octave-band force level L_F of the ISO tapping machine, the substitution source of clause D.1.2.3: tapping_machine_force_level, with tapping_machine_characteristic_power_level and tapping_machine_coupling_term turning it into the L_Ws,c and D_C of step 3.

Annex F also supplies the two terms step 4 takes: the adjustment term D_sa of Formula (F.3) (structure_to_airborne_adjustment) and the multi-junction adjustment dK of clause F.1 (multi_junction_adjustment), which the flanking reduction index R_ij,ref of a path more than one junction away is built with.

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

coupling_term

coupling_term(
    source_mobility: ArrayLike,
    receiver_mobility: ArrayLike,
    *,
    transfer_mobility: ArrayLike = 0.0,
) -> np.ndarray

Coupling term D_C for a point excitation (EN 12354-5, Formula 19b/19e).

$D_{C} = 10 lo g_{10} (∣ Y_{s} + Y_{i} + Y_{k} ∣^{2} / (∣ Y_{s} ∣ Re {Y_{i}}))$ — the loss between the characteristic and the injected structure-borne power. Y_k is the transfer mobility of an elastic support (Formula 19e; 0 for a rigid connection, Formula 19b).

Parameters

Name	Description
`source_mobility`	Source point mobility `Y_s` (complex, non-zero), in m/(N.s).
`receiver_mobility`	Receiver point mobility `Y_i` (complex, positive real part).
`transfer_mobility`	Elastic-support transfer mobility `Y_k` (Default: 0.0).

Returns: The coupling term D_C, in dB. Positive whenever the source and receiver mobilities are well mismatched (the usual installed case), but not guaranteed non-negative: near a mounting resonance where Y_s and Y_i are of comparable magnitude and opposite phase the numerator $∣ Y_{s} + Y_{i} ∣^{2}$ collapses and D_C goes negative (the installed power then exceeds the characteristic level; e.g. $Y_{s} = j \cdot 1 0^{- 4}$ , $Y_{i} = 1 0^{- 5} - j \cdot 1 0^{- 4}$ m/(N·s) gives $D_{C} \approx - 10$ dB).

Raises

Exception	When
ValueError	if `Y_s` is zero/non-finite or `Re{Y_i}` is not positive and finite.

coupling_term_force_source

coupling_term_force_source(
    source_mobility: ArrayLike,
    receiver_mobility: ArrayLike,
) -> np.ndarray

Coupling term for a force source, high source mobility (Formula 19c).

D_{C} = 10 lo g_{10} \frac{∣ Y _{s} ∣}{Re { Y _{i} }}

Parameters

Name	Description
`source_mobility`	Source point mobility `Y_s` (complex, non-zero).
`receiver_mobility`	Receiver point mobility `Y_i` (complex, positive real part).

Returns: The coupling term D_C, in dB.

Raises

Exception	When
ValueError	if `Y_s` is zero/non-finite or `Re{Y_i}` is not positive and finite.

coupling_term_velocity_source

coupling_term_velocity_source(
    source_mobility: ArrayLike,
    receiver_impedance: ArrayLike,
) -> np.ndarray

Coupling term for a velocity source, low source mobility (Formula 19d).

D_{C} = - 10 lo g_{10} (∣ Y_{s} ∣ Re {Z_{i}})

Parameters

Name	Description
`source_mobility`	Source point mobility `Y_s` (complex, non-zero).
`receiver_impedance`	Receiver point impedance `Z_i` (complex, positive real part).

Returns: The coupling term D_C, in dB.

Raises

Exception	When
ValueError	if `Y_s` is zero/non-finite or `Re{Z_i}` is not positive and finite.

installed_power_from_reception_plate

installed_power_from_reception_plate(
    reception_plate_level: ArrayLike,
    receiver_mobility: ArrayLike,
    *,
    plate_mobility: float = 5e-06,
) -> np.ndarray

Mobility correction of the reception-plate power (EN 12354-5, Annex I).

$L_{W s, inst, i} = L_{W s, n, i} + 10 lo g_{10} (Y_{\infty, i} / Y_{\infty, rec})$ , which refers the characteristic reception-plate power level L_Ws,n (EN 15657 Formula (17), re the 10 cm concrete plate $Y_{\infty, rec} = 5 \cdot 1 0^{- 6}$ m/(N.s)) to the characteristic mobility Y_inf,i of the actual receiving element (floor, wall), yielding the installed power of that element as in the Annex I.2 whirlpool example. The same correction with the source mobility instead of Y_inf,i yields the characteristic level L_Ws,c (Annex I.3, Table I.8), from which installed_structure_borne_power_level subtracts D_C.

Parameters

Name	Description
`reception_plate_level`	Power level to re-refer (per band), in dB re 1 pW: either the characteristic level `L_Ws,n` (EN 15657 Formula 17, referred to the default 5e-6 m/(N.s) plate) or a raw Formula (14) plate power together with the mobility of the plate it was measured on, passed as `plate_mobility`.
`receiver_mobility`	Characteristic mobility `Y_inf,i` of the receiving element (per band; complex values use their magnitude), in m/(N.s).
`plate_mobility`	Mobility the input level is referred to (Default: the EN 15657 reference plate, $Y_{\infty, rec} = 5 \cdot 1 0^{- 6}$ m/(N.s); pass the measured plate mobility when the input is a raw Formula (14) level).

Returns: The mobility-corrected power level, in dB re 1 pW.

Raises

Exception	When
ValueError	for a non-positive receiver or plate mobility.

installed_source_prediction

installed_source_prediction(
    characteristic_power_level: ArrayLike,
    coupling_term: ArrayLike,
    paths: list[dict[str, Any]],
    *,
    frequencies: ArrayLike | None = None,
) -> InstalledSourceResult

Predict the installed structure-borne SPL over several paths (EN 12354-5).

The band count is set by the widest per-band input (the characteristic power level, the coupling_term or any path’s adjustment_term / flanking_reduction_index); every per-band input must carry one value or that count, and single values broadcast across the bands (a single-number source level with per-band path data is valid, and the result’s installed_power_level is broadcast to the band count).

Parameters

Name	Description
`characteristic_power_level`	Characteristic level `L_Ws,c` (per band or a single value), in dB.
`coupling_term`	Coupling term `D_C` (per band or a single value), in dB.
`paths`	One dict per transmission path with keys `adjustment_term` (`D_sa`), `flanking_reduction_index` (`R_ij,ref`) and `element_area` (`S_i`), each per band where applicable.
`frequencies`	Band centre frequencies, in hertz, or `None`.

Returns: The InstalledSourceResult.

Raises

Exception	When
ValueError	if `paths` is empty, a path is missing a required key, or a per-band input matches neither one value nor the band count.

installed_structure_borne_power_level

installed_structure_borne_power_level(
    characteristic_power_level: ArrayLike,
    coupling_term: ArrayLike,
) -> np.ndarray

Installed structure-borne power level (EN 12354-5, Formula 18b).

L_{W s, inst, i} = L_{W s, c} - D_{C, i}

Parameters

Name	Description
`characteristic_power_level`	Characteristic level `L_Ws,c` (per band), in dB: the EN 15657 reception-plate level converted with Formulae (15)/(17) and the source-mobility correction (see the module docstring), not the raw plate-injected Formula (14) level.
`coupling_term`	Coupling term `D_C,i` (per band), in dB.

Returns: The installed structure-borne power level L_Ws,inst, in dB.

InstalledSourceResult

InstalledSourceResult(
    path_levels: np.ndarray,
    total_level: np.ndarray,
    installed_power_level: np.ndarray,
    frequencies: np.ndarray | None = None,
)

Installed structure-borne sound prediction (EN 12354-5).

Attributes

Name	Description
`frequencies`	Band centre frequencies, in hertz, or `None`.
`path_levels`	Per-path normalised SPL `L_n,s,ij` (paths x bands), dB.
`total_level`	Combined normalised SPL `L_n,s` per band, in dB.
`installed_power_level`	Installed power level `L_Ws,inst` per band, dB.

InstalledSourceResult.overall_level

property

Band-summed total level $10 lo g_{10} (\sum 1 0^{0.1 L_{n, s}})$ , in dB.

InstalledSourceResult.plot()

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

Plot the per-path and total normalised sound pressure levels.

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

InstalledSourceResult.report()

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

Render an EN 12354-5 installed structure-borne prediction fiche.

Writes a one-page prediction sheet (an estimate, not a measurement): a prediction-basis line naming EN 12354-5:2009, an optional metadata header (client, source equipment, receiving room, instrumentation, climate, date), a per-band table (nominal octave/one-third-octave frequency, the installed structure-borne power level L_Ws,inst, each transmission path’s normalised SPL L_n,s,ij and the combined total L_n,s), the per-path and total L_n,s(f) spectra, the boxed band-summed total L_n,s (dB) with the installed power total and the path count, an optional verdict row against a declared limit, and a basis strip stating Formulae 18a/17 and the prediction disclaimer.

Parameters

Name	Description
`path`	Destination path of the PDF file.
`metadata`	Optional `ReportMetadata` supplying the header (`client`, `specimen` the source equipment, `test_room` the receiving room, `instrumentation`, `temperature`, `relative_humidity`, `pressure`, `test_date`), the footer identity (`laboratory`, `operator`, `report_id`, `notes`) and, via `requirement`, a declared upper limit on the overall `L_n,s` (lower is better).
`engine`	Rendering back end; only `"reportlab"` is supported.
`verbose`	When `True` the per-band table adds one column per transmission path (up to five); otherwise only the installed power and the combined total are shown.
`language`	Fiche language: `"en"` (default) or `"es"`.

Returns: The written path as a str.

Raises

Exception	When
ValueError	If `engine` is not `"reportlab"` or `language` is unknown.
ImportError	If reportlab (or, for the figure, matplotlib) is not installed (`pip install phonometry[report]`).

MINIMUM_MULTI_JUNCTION_KIJ

Constant (float).

MINIMUM_MULTI_JUNCTION_KIJ = -5.0

multi_junction_adjustment

multi_junction_adjustment(junctions: int) -> float

Vibration reduction index adjustment dK (EN 12354-5, clause F.1).

When the receiving room is more than one junction away from the equipment, Formula (F.1) sums the junction Kij along the path and subtracts an adjustment dK that covers the transmission by wave types other than bending waves. Clause F.1 estimates it from published data as 4 dB for two junctions and 6 dB for three or more, with the resulting Kij floored at MINIMUM_MULTI_JUNCTION_KIJ.

Parameters

Name	Description
`junctions`	Number of junctions the transmission path crosses (>= 1).

Returns: The adjustment dK, in dB (0,0 for a single junction).

Raises

Exception	When
ValueError	for fewer than one junction.

REFERENCE_AREA

Constant (float).

REFERENCE_AREA = 10.0

structure_borne_pressure_level_path

structure_borne_pressure_level_path(
    installed_power_level: ArrayLike,
    adjustment_term: ArrayLike,
    flanking_reduction_index: ArrayLike,
    element_area: float,
    *,
    reference_area: float = 10.0,
) -> np.ndarray

Normalised structure-borne SPL for one path i->j (Formula 18a).

L_{n, s, ij} = L_{W s, inst, i} - D_{sa, i} - R_{ij, ref} - 10 lo g_{10} \frac{S _{i}}{S _{0}} - 10 lo g_{10} \frac{A _{0}}{4}

Parameters

Name	Description
`installed_power_level`	Installed power level `L_Ws,inst,i`, in dB.
`adjustment_term`	Structure-to-airborne adjustment `D_sa,i` (clause 4.4.4 / Annex F), in dB.
`flanking_reduction_index`	Flanking sound reduction index `R_ij,ref` re `S0` (EN 12354-1), in dB.
`element_area`	Supporting-element area `S_i`, in m^2 (> 0).
`reference_area`	Reference area $S_{0} = A_{0}$ (Default: 10 m^2).

Returns: The normalised path sound pressure level L_n,s,ij, in dB.

Raises

Exception	When
ValueError	for a non-positive area.

structure_to_airborne_adjustment

structure_to_airborne_adjustment(
    frequency: ArrayLike,
    critical_frequency: float,
    mass_per_area: float,
    *,
    radiation_factor: ArrayLike = 1.0,
) -> np.ndarray

Adjustment term D_sa of a supporting element (Formula F.3).

D_{sa, i} = 10 lo g_{10} \frac{400 f _{c, i} σ _{i}}{m _{i} f ^{2}}

the ratio of injected structure-borne power to incident airborne power that leaves the same free-vibration energy in the element. Clause F.2 gives it for a force excitation perpendicular to a homogeneous supporting element, exact above the critical frequency (where the radiation factor saturates at

and a good approximation over the whole range.

D_sa is normally negative, and Formula (18a) subtracts it, so it raises the predicted level: this is the value structure_borne_pressure_level_path takes as adjustment_term, sign included.

Parameters

Name	Description
`frequency`	Band centre frequency `f`, in hertz (> 0).
`critical_frequency`	Critical frequency `fc,i` of the element, in hertz (> 0).
`mass_per_area`	Mass per unit area `mi` of the element, in kg/m^2 (> 0).
`radiation_factor`	Radiation factor `sigma_i` of the element (Default: 1.0, its value above `fc`; EN 12354-1:2000 Annex B estimates it below).

Returns: The adjustment term D_sa,i, in dB.

Raises

Exception	When
ValueError	for a non-positive frequency, critical frequency, mass or radiation factor.

TABLE_D1_QUANTITIES

Constant (dict).

TABLE_D1_QUANTITIES = {'mass': ('mass',), 'bar_end': ('density', 'longitudinal_velocity', 'area'), 'beam': ('density', 'longitudinal_velocity', 'thickness', 'width'), 'plate': ('density', 'longitudinal_velocity', 'thickness'), 'pipe': ('density', 'longitudinal_velocity', 'thickness', 'radius'), 'mass_spring': ('mass', 'stiffness', 'loss_factor')}

TABLE_F1_FORCE_LEVEL

Constant (tuple).

TABLE_F1_FORCE_LEVEL = (139.0, 142.0, 145.0, 148.0, 151.0, 154.0, 156.0, 156.0)

TABLE_F1_OCTAVE_BANDS

Constant (tuple).

TABLE_F1_OCTAVE_BANDS = (31.5, 63.0, 125.0, 250.0, 500.0, 1000.0, 2000.0, 4000.0)

tapping_machine_characteristic_power_level

tapping_machine_characteristic_power_level(
    frequency: ArrayLike,
    force_level: ArrayLike,
) -> np.ndarray

Characteristic power level of the tapping machine (Formula D.9a).

L_{W s, c} = L_{F} - 5 - 10 lo g_{10} f

The standard notes the result is about 115 dB re 1 pW per one-third octave for the ISO tapping machine, treated in clause D.1.3 as a force source with the mass-like source mobility of its 0,5 kg hammers. Pair it with tapping_machine_coupling_term and hand both to installed_source_prediction.

The formula only balances with the reference force F_0 = 1e-6 N, since it carries no term for $F_{0}^{2} / W_{0}$ ; that is what pins the reading of Table F.1 against its own printed “re 1 pN” caption.

Parameters

Name	Description
`frequency`	Band centre frequency `f`, in hertz (> 0).
`force_level`	Force level `L_F`, in dB re 1e-6 N (Table F.1 or `tapping_machine_force_level_estimate`).

Returns: The characteristic power level L_Ws,c, in dB re 1 pW.

Raises

Exception	When
ValueError	for a non-positive frequency.

tapping_machine_coupling_term

tapping_machine_coupling_term(
    frequency: ArrayLike,
    receiver_mobility: ArrayLike,
    *,
    hammer_mass: float = 0.5,
) -> np.ndarray

Coupling term of the tapping machine (EN 12354-5, Formula D.9b).

D_{C, i} = - 10 lo g_{10} (ω M Y_{i}) + 10 lo g_{10} [1 + (ω M Y_{i})^{2}]

with $ω = 2 π f$ and M the hammer mass of clause D.1.3, which the standard takes as 0,5 kg. It is the mass-like-source form of Formula (19b), for a machine standing on a plate-like element of real mobility Y_i; Annex F Formulae (F.4) to (F.6b) estimate that Y_i.

Parameters

Name	Description
`frequency`	Band centre frequency `f`, in hertz (> 0).
`receiver_mobility`	Real mobility `Y_i` of the supporting element, in m/(N.s) (> 0).
`hammer_mass`	Source mass `M`, in kilograms (Default: `TAPPING_HAMMER_MASS`, the 0,5 kg of clause D.1.3 and ISO 10140-5).

Returns: The coupling term D_C,i, in dB.

Raises

Exception	When
ValueError	for a non-positive frequency, mobility or mass.

tapping_machine_force_level

tapping_machine_force_level() -> np.ndarray

Tabulated ISO tapping machine force level (EN 12354-5, Table F.1).

The eight octave-band values of Table F.1, in the order of TABLE_F1_OCTAVE_BANDS (31,5 Hz to 4 kHz). Clause F.4.2 offers them for the tapping machine used in place of an electrodynamic shaker when measuring D_Fp,n (Formula F.9), and clause D.1.2.3 restricts the source to low-mobility receiving structures.

Feed them to tapping_machine_characteristic_power_level for the L_Ws,c that installed_source_prediction takes.

Returns: The force level L_F per octave band, in dB re 1e-6 N (the table caption prints “re 1 pN”; see docs/ERRATA.md).

tapping_machine_force_level_estimate

tapping_machine_force_level_estimate(
    frequency: ArrayLike,
    *,
    bandwidth: str = 'octave',
) -> np.ndarray

Closed form printed under Table F.1 for the tapping machine force level.

L_{F} = 10 lo g_{10} \frac{2 , 5 f}{1 0 ^{- 12}} (octave), L_{F} = 10 lo g_{10} \frac{0 , 8 f}{1 0 ^{- 12}} (1/3 octave)

The standard qualifies this with “up till about 1000 Hz”: it reproduces the first six tabulated values to the printed decibel, and above that it departs from the table, which flattens at 156 dB (the closed form gives 157 dB at 2 kHz and 160 dB at 4 kHz). Use tapping_machine_force_level for the octave bands the table covers and this only where it does not, chiefly the one-third-octave bands the standard does not tabulate.

Parameters

Name	Description
`frequency`	Band centre frequency `f`, in hertz (> 0).
`bandwidth`	`"octave"` (coefficient 2,5) or `"third"` (coefficient 0,8).

Returns: The force level L_F, in dB re 1e-6 N (the standard prints “re 1 pN”; see docs/ERRATA.md).

Raises

Exception	When
ValueError	for a non-positive frequency or an unknown bandwidth.

total_structure_borne_pressure_level

total_structure_borne_pressure_level(path_levels: ArrayLike) -> np.ndarray

Combine path sound pressure levels energetically (Formula 17).

L_{n, s} = 10 lo g_{10} (j \sum 1 0^{L_{n, s, ij} /10})

Parameters

Name	Description
`path_levels`	Path levels `L_n,s,ij`; sum is over the first axis (paths), broadcasting any trailing band axis.

Returns: The total normalised sound pressure level L_n,s, in dB.

typical_element_mobility

typical_element_mobility(
    structure: str,
    *,
    frequency: ArrayLike | None = None,
    mass: float | None = None,
    density: float | None = None,
    longitudinal_velocity: float | None = None,
    thickness: float | None = None,
    width: float | None = None,
    area: float | None = None,
    radius: float | None = None,
    stiffness: float | None = None,
    loss_factor: float | None = None,
) -> np.ndarray

Named lookup of EN 12354-5, Table D.1 (mobility of typical elements).

Returns the mobility magnitude |Y| the third column of Table D.1 prints, in m/(N.s), for the row named by structure:

"mass", described by mass $M$ [kg]: $∣ Y ∣ = [2 π f M]^{- 1}$ .
"bar_end", described by density $ρ$ [kg/m3], longitudinal_velocity $c_{L}$ [m/s] and area $S$ [m2]: $∣ Y ∣ = [ρ c_{L} S]^{- 1}$ .
"beam", described by $ρ$ , $c_{L}$ , thickness $t$ [m] and width $w$ [m]: $∣ Y ∣ = [7, 6 ρtw c_{L} t f]^{- 1}$ .
"plate", described by $ρ$ , $c_{L}$ and $t$ : $∣ Y ∣ = [2, 3 c_{L} ρ t^{2}]^{- 1}$ .
"pipe", described by $ρ$ , $c_{L}$ , $t$ and radius $r$ [m]: $∣ Y ∣ = [63 ρt r c_{L} r f]^{- 1}$ .
"mass_spring", described by $M$ , stiffness $s$ [N/m] and loss_factor $η$ [-]: $∣ Y ∣ = [(\frac{2 π f η}{s ( 1 + η ^{2} )})^{2} + (\frac{2 π f}{s ( 1 + η ^{2} )} - \frac{1}{2 π f M})^{2}]^{1/2}$ .

TABLE_D1_QUANTITIES carries the “Describing quantities” column as the keyword names of this function, and only the quantities a row describes may be supplied. Frequency is not among them, because it is the band frequency of the prediction and not a property of the element, but it appears in four of the six expressions: "mass", "beam", "pipe" and "mass_spring" require frequency and the other two reject it.

Clause D.1.3 offers the table for building up a source mobility Y_s from the machine’s own parts, which is what coupling_term needs and what a measurement of the equipment does not give. Annex F Formulae (F.4) to (F.6b) cover the receiver mobility Y_i of the supporting element; the "plate" row is the same quantity as Formula (F.4) $Y_{i, \infty} = 1/ (8 m B^{'})$ and as phonometry.vibration.structural.point_mobility.infinite_plate_mobility, written in $ρ$ , $c_{L}$ and $t$ instead of mass and bending stiffness.

The "mass_spring" row is the machine on non-rigid feet: its second bracket holds the two reactances, which cancel at the mass-spring resonance $f_{0} = (2 π)^{- 1} s (1 + η^{2}) / M$ and leave the mobility at its damping-limited minimum, the frequency at which the mount injects the most power. loss_factor=0 returns exactly zero there, which coupling_term then rejects.

Parameters

Name	Description
`structure`	Table D.1 row name.
`frequency`	Frequency `f`, in hertz, for the frequency-dependent rows only.
`mass`	Mass `M`, in kilograms (rows `"mass"`, `"mass_spring"`).
`density`	Density `rho`, in kg/m^3.
`longitudinal_velocity`	Quasi-longitudinal wave speed `cL`, in m/s.
`thickness`	Thickness `t`, in metres.
`width`	Beam width `w`, in metres (row `"beam"`).
`area`	Cross-sectional area `S`, in m^2 (row `"bar_end"`).
`radius`	Pipe radius `r`, in metres (row `"pipe"`).
`stiffness`	Support stiffness `s`, in N/m (row `"mass_spring"`).
`loss_factor`	Support loss factor `eta` (row `"mass_spring"`).

Returns: The mobility magnitude |Y|, in m/(N.s).

Raises

Exception	When
ValueError	for an unknown row, a missing or surplus describing quantity, a `frequency` that the row does not take (or lacks), or a non-positive value.

Creado y mantenido por José Manuel Requena Plens ORCID Todos los proyectos