AcousticImpedanceValue
AcousticImpedanceValue[pred,vars,pars]
represents a time or frequency domain impedance boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.
AcousticImpedanceValue[pred,vars,pars,lkey]
represents a time or frequency domain boundary condition with local parameters specified in pars[lkey].
Details
- AcousticImpedanceValue specifies a boundary condition for AcousticPDEComponent and is used as part of the modeling equation:
- AcousticImpedanceValue is typically used to model a boundary material that is partially transparent to sound.
- AcousticImpedanceValue models a time or frequency domain impedance with dependent variable pressure in , independent variables in and time variable in or frequency variable in .
- Time-dependent variables vars are vars={p[t,x1,…,xn],t,{x1,…,xn}}.
- Frequency-dependent variables vars are vars={p[x1,…,xn],ω,{x1,…,xn}}.
- The time domain acoustics model AcousticPDEComponent is based on a wave equation with time variable , density , sound speed and sound sources and :
- The frequency domain acoustics model AcousticPDEComponent is based on a Helmholtz equation with angular frequency :
- The time domain impedance value AcousticImpedanceValue with impedance in and boundary unit normal models:
- The frequency domain impedance value AcousticImpedanceValue models:
- Model parameters pars are specified as for AcousticPDEComponent.
- The following model parameters pars can be given:
-
parameter default symbol "SpecificAcousticImpedance" Infinity , acoustic impedance in - AcousticImpedanceValue evaluates to a generalized NeumannValue.
- The boundary predicate pred can be specified as in NeumannValue.
- An impedance boundary can be used with:
-
analysis type applicable Time Domain Yes Frequency Domain Yes Eigenfrequency No - If the AcousticImpedanceValue depends on parameters that are specified in the association pars as …,keypi…,pivi,…], the parameters are replaced with .
Examples
open allclose allBasic Examples (5)
Set up a time domain acoustic impedance boundary:
Set up a frequency domain acoustic impedance boundary:
Set up a time-independent acoustic impedance boundary:
Define model variables vars for a transient acoustic pressure field with model parameters pars:
Define initial conditions ics of a right-going plane wave :
Set up the equation with an acoustic impedance boundary at the right and an impedance of :
Define model variables vars for a frequency domain acoustic pressure field with model parameters pars:
Set up the equation with a radiation boundary at the left, an acoustic impedance boundary at the right and an impedance of :
Visualize the solution in the frequency domain at various frequencies :
Scope (2)
Applications (1)
The following acoustic model describes an open pipe, wherein a vibrating piston is placed inside one end of the pipe while the other end of the pipe opens into an infinite domain. In this case, an impedance boundary condition is placed on one end to model the infinite domain. The pipe that will be modeled is a flanged circular pipe, as shown in the following figure below:
Since the geometry of the pipe and the boundary conditions are rotationally symmetric about the axis, an axisymmetric model can be used. The governing equation for describing the sound wave propagation is the axisymmetric Helmholtz equation.
Set up the variables and parameters:
The axisymmetric geometry can be approximated by a 2D rectangle, which represents a cross-section of the pipe in the plane:
Set up the rectangle region with as the radius of the tube and as the length of the tube:
In the model, there are two boundary conditions. One is a NeumannValue that expresses the acceleration of the piston with :
The second boundary condition is an AcousticImpedanceValue with impedance . The impedance is given by the following approximation, where is the wavenumber:
Solve the PDE with with a MaxCellMeasure defined by and with a resolution of 12 to get an accurate result:
Possible Issues (1)
The default value for "SpecificAcousticImpedance" is Infinity:
Text
Wolfram Research (2020), AcousticImpedanceValue, Wolfram Language function, https://reference.wolfram.com/language/ref/AcousticImpedanceValue.html.
CMS
Wolfram Language. 2020. "AcousticImpedanceValue." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AcousticImpedanceValue.html.
APA
Wolfram Language. (2020). AcousticImpedanceValue. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AcousticImpedanceValue.html