pyva.systems.acoustic1Dsystems.AcousticTube

class pyva.systems.acoustic1Dsystems.AcousticTube(L, fluid=<class 'pyva.properties.materialClasses.Fluid'>, area=1.0)

Bases: object

The acoustic tube class deals with one dimensional tubes filled with fluid

Many system desciptions are implemented because of the examples in [Pei2022] and therefor usually not required for system modelling but only for presentation purpose.

L

Type:: length of the tube

fluid

Type:: fluid in the tube

area

Type:: cross section

__init__(L, fluid=<class 'pyva.properties.materialClasses.Fluid'>, area=1.0)

Class contructor for acoustic tube

Parameters:

L (float) – Length.
fluid (fluid, optional) – fluid in the tube. The default is mc.Fluid.
area (float, optional) – area of tube cross section. The default is 1..

Return type:

None.

Examples

import acoustic1Dsystems as ac1Dsys myTube = ac1Dsys.AcousticTube(2.)

Methods

`__init__`(L[, fluid, area])	Class contructor for acoustic tube
`acoustic_FE`(omega[, ID])	Acoustic Finite Element of acoustic tubes
`acoustic_impedance`(omega)	Acoustic impedance at port 1 with fixed end at port 2
`f_mode`(n)	Modal frequency
`k2_mode`(n)	Squared wavenumnber for mode n
`k_mode`(n)	Wavenumnber for mode n
`omega_mode`(n)	Modal angular frequency
`p_N`(omega, q, x0, n)	Modal coordinates for acoustic source q at x0
`p_amp`(n, v)	Pressure amplitude for n-th resonance and velocity v
`p_modal`(omega, x, N[, v1])	Modal pressure reponse for velocity at port 1
`p_mode`(x, n)	Pressure mode shape for fixed ends
`p_mode_free`(x, n)	Pressure mode shape for free ends
`p_simpleV1`(omega, v)	Pressure at excited port 1 of the tube with vibrating surface
`power`(omega, v)	Power input into tube at port 1
`pressure`(omega, x, v)	Pressure along the tube with vibrating surface at port 1
`transfer_impedance`(omega[, ID, velocity])	Transferimpedance of acoustic tubes
`velocity`(omega, v, x)	Velocity along the tube with vibrating surface at port 1

acoustic_FE(omega, ID=[1, 2])

Acoustic Finite Element of acoustic tubes

Takes simple 1D transmission line model based on AcousticTube properties to model the so mobility matrix, given by

$\begin{bmatrix} Y_{a,11} & Y_{a,12} \\ Y_{a,21} & Y_{a,22} \end{bmatrix} \begin{Bmatrix} Q_1 \\ Q_2 \end{Bmatrix} = \begin{Bmatrix} p_1 \\ p_2 \end{Bmatrix}$

Parameters:

omega (float) – angular frequency.
ID (list of int, optional) – IDs of element ports. The default is [1,2].

Returns:

Mobility matrix of tube

Return type:

DynamicMatrix

acoustic_impedance(omega)

Acoustic impedance at port 1 with fixed end at port 2

Parameters:: omega (float) – angular frequency
Returns:: impedance
Return type:: complex

f_mode(n)

Modal frequency

Parameters:: n (mode number) –
Returns:: modal frequency
Return type:: float

k2_mode(n)

Squared wavenumnber for mode n

take simple 1D transmission line model based on AcousticTube properties

Parameters:: n (mode number) –
Returns:: squared wavenumber
Return type:: float

k_mode(n)

Wavenumnber for mode n

take simple 1D transmission line model based on AcousticTube properties

Parameters:: n (mode number) –
Returns:: wavenumber
Return type:: float

omega_mode(n)

Modal angular frequency

Parameters:: n (mode number) –
Returns:: angular modal frequency
Return type:: float

p_N(omega, q, x0, n)

Modal coordinates for acoustic source q at x0

Takes simple 1D transmission line model based on AcousticTube properties

Parameters:

omega (float) – angular frequency
q (complex) – volume source strengh, volume flow rate
x (float) – position in tube
n (int) – number of mode

Return type:

modal coordinate for n

p_amp(n, v)

Pressure amplitude for n-th resonance and velocity v

Culculates the pressure at the resonance frequencies

Parameters:

n (int) – number of resonance.
v (float) – velocit.

Returns:

pressure at resonance.

Return type:

float

p_modal(omega, x, N, v1=1.0)

Modal pressure reponse for velocity at port 1

Takes simple 1D transmission line model based on AcousticTube properties

Parameters:

omega (float) – angular frequency
v1 (complex) – velocity at port 1
x (float) – position in tube
N (int) – maximum number of mode

Return type:

pressure along tube

p_mode(x, n)

Pressure mode shape for fixed ends

Takes simple 1D transmission line model based on AcousticTube properties

Parameters:

x (position in tube) –
n (number of mode) –

Return type:

pressure shape of mode

p_mode_free(x, n)

Pressure mode shape for free ends

Parameters:

x (position in tube) –
n (number of mode) –

Return type:

pressure shape of mode

p_simpleV1(omega, v)

Pressure at excited port 1 of the tube with vibrating surface

Parameters:

omega (float) – angular frequency.
v (complex) – velocity at port 1.

Returns:

pressure response.

Return type:

complex

power(omega, v)

Power input into tube at port 1

Takes simple 1D transmission line model based on AcousticTube properties

Parameters:

omega (float) – angular frequency
v (complex) – velocity at node 1

Return type:

power input

pressure(omega, x, v)

Pressure along the tube with vibrating surface at port 1

take simple 1D transmission line model based on AcousticTube properties

Parameters:

omega (float) – angular frequency
x (float) – position in tube
v (complex) – velocity

Return type:

pressure amplitude due to velocity

transfer_impedance(omega, ID=[1, 2], velocity='v')

Transferimpedance of acoustic tubes

Takes simple 1D transmission line model based on AcousticTube properties to model the so called transfer impedance, given by

$\begin{Bmatrix} p_1 \\ v_1 \end{Bmatrix} = \begin{bmatrix} T_{11} & T_{12} \\ T_{21} & T_{22} \end{bmatrix} \begin{Bmatrix} p_2 \\ v_2 \end{Bmatrix}$

or

$\begin{Bmatrix} p_1 \\ q_1 \end{Bmatrix} = \begin{bmatrix} T_{a,11} & T_{a,12} \\ T_{a,21} & T_{a,22} \end{bmatrix} \begin{Bmatrix} p_2 \\ q_2 \end{Bmatrix}$

depending on the velocity paramter

Parameters:

omega (float) – angular frequency
ID (list of int) – IDs of input and output port
Kwargs – velocity = ‘q’:

Returns:

transfermatrix

Return type:

DynamicMatrix

velocity(omega, v, x)

Velocity along the tube with vibrating surface at port 1

take simple 1D transmission line model based on AcousticTube properties

Parameters:

omega (float) – angular frequency
x (float) – position in tube
v (complex) – velocity

Return type:

velocity amplitude due to velocity at port 1