Background Pressure Field (for Transient Models)
Add a Background Pressure Field node to model a background/incident pressure wave to study the scattered pressure field ps, which is defined as the difference between the total acoustic pressure pt and the background pressure field pb:
This feature sets up the equations in a so-called scattered field formulation where the dependent variable is the scattered field p = ps. In a model where the background pressure field is not defined on all acoustic domains (or it is different), continuity is automatically applied in the total field pt on interior boundaries between domains.
Background Pressure Field
Select the Pressure field type as Plane wave (monochromatic) (the default), Modulated Gaussian pulse, or User defined.
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For Plane wave (monochromatic) enter a value for the Pressure amplitude p0 of the wave, select the Speed of sound as User defined (enter a value for c) or From material, enter a Wave direction vector ek, enter the Signal frequency f0 of the wave, and a possible Phase ϕ.
These settings defined a background pressure field pb as a plane propagating wave of the type:
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For Modulated Gaussian pulse enter a value for the Pressure amplitude p0 of the wave, select the Speed of sound as User defined (enter a value for c) or From material, enter a Wave direction vector ek and enter the Signal emitting plane coordinate x0. The latter two options define the initial location of the pulse and the propagation direction. When modeling scattering problems, the initial location should be placed outside the computational domain. Next define the frequency content of the Gaussian pulse. Select the Gaussian pulse bandwidth as Full width at half maximum, power (the default), Full width at half maximum, amplitude, Full duration at half maximum, power, Full duration at half maximum, amplitude, or Standard deviation. For the first two options enter a frequency bandwidth Δf and for the latter a time window Δt. Finally, enter the carrier Signal frequency (for time-dependent studies) f0.
These settings defined a background pressure field pb as a propagating modulated Gaussian pulse of the type:
where the standard deviation σ of the Gaussian G(x,t) depends on the bandwidth option selected. The modulated Gaussian pulse option only gives contributions when a time dependent model is solved. It has the advantage of having a defined frequency content and can be used for limited bandwidth simulations. In combination with the Exterior Field Calculation (for Transient Models) and an FFT study, the broadband scattering characteristics of an object can be analyzed.
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For User defined enter an analytical expression that can be a function of both space and time or use a solution from a previous study.
Advanced Settings
To display this section, when the Plane wave (monochromatic) option is selected, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog box.
Click to select the Use ramp function option (selected per default). With this option turned on, a ramp is automatically added to smoothly increase the background pressure field amplitude over the first period T = 1/f0. This option ensures numerical stability.