Impedance

The condition adds a boundary condition with the option to select between several built-in impedance models that allow modeling frequency dependent impedance conditions in the time domain. The impedance condition defines a relation between the local total acoustic pressure pt and the normal acoustic velocity n⋅ut, that is, the (normal) specific acoustic impedance Zn (SI unit Pa·s/m). The condition specifies the normal velocity

The boundary condition is a good approximation of a locally reacting surface — a surface for which the normal velocity at any point depends only on the pressure at that exact point. This condition can be used to model the properties of artificial boundaries like a wall treatment in room acoustics. When the impedance is set equal to the characteristic specific impedance of a propagating plane wave ρc, the condition represents the simplest nonreflecting boundary condition. This is also the default value of the impedance when the condition is added.

In many practical applications the surface impedance is known (measured or simulated) in term of its real and imaginary part as function of frequency. To capture this behavior in the time domain the condition has built-in functionality for setting up a General local reacting (rational approximation) impedance through a rational approximation. Fitting of the frequency domain data can be performed using the Partial Fraction Fit function.

	The acoustic impedance condition (with the default value ρc) should be used at the outer boundary when Absorbing Layers are used in a model.

	Wave-Based Time-Domain Room Acoustics with Frequency-Dependent Impedance. Application Library path Acoustics_Module/Building_and_Room_Acoustics/wave_based_room

Select the as (the default), , or . The different options are as follows:

For the option represents a purely resistive constant impedance. The values entered here can only be real valued and constant in time.

Enter a value or expression for the Zn (SI unit: Pa·s/m). The default expression is pate.c*pate.rho which is the characteristic specific impedance ρc of a propagating plane wave.

The option defines a simple spring-mass-damper system in the form of a serially coupled RCL circuit. This option can be used to approximate many systems that exhibit a simple damped resonant characteristic. The RCL condition will exhibit a simple frequency dependent behavior.

Enter values for the Rac (SI unit: kg/(m4·s)), the Cac (SI unit: m4·s2/kg), and the Lac (SI unit: kg/m4).

The option offers the most general and flexible form for defining a frequency dependent impedance condition in the time domain. The condition relies on a rational approximation (or rational expansion) of the frequency dependent admittance Y(f). This approximation has an analytical inverse Fourier transform and can thus be used to define the same frequency dependency in the time domain, by setting up a system of memory ODEs. These ODEs are automatically defined by the feature and solved on the impedance boundary. Approximating the frequency dependent admittance data can be performed by using the built-in Partial Fraction Fit function.

Select the fit as (the default) or .

•

For the option enter all the necessary parameters that are present in the rational approximation (rational expansion), that is, the

(SI unit: m2·s/kg), enter the (R and ξ) into the table, and enter the (Q and ζ) into the table (note that the conjugate terms are automatically added). The quantities can also be loaded from a file (remember to include the number column). Select if the rational approximation function is scaled for frequency data or angular frequency data by selecting the option (selected per default).

•

For the option select the which is a Partial Fraction Fit function defined in the model, then click the icon (

) to copy the fitted data to the admittance field, and the residues and poles tables. To go to the function source click the icon (