Product: ABAQUS/Standard
In this problem the acoustic behavior of a baffled planar piston is analyzed using the direct-solution steady-state dynamic procedure. An analytical solution for this problem also exists and is provided for comparison with the numerical result obtained.
The model is shown in Figure 1.10.7–1. No particular set of units is used in this case: all units used are assumed to be consistent. The acoustic model is a cylinder with radius 
= 10 and height 
= 15. The density and the bulk modulus are assumed to be 1.0 and 39.4784, respectively, which corresponds to a sound speed of 2
. Default nonreflecting boundary conditions are applied on the top and the lateral surfaces of the cylinder. The baffled condition is imposed by specifying no load or boundary condition at all on the planar baffle. The interaction between the piston and the acoustic medium is simulated by applying a uniform volumetric acceleration on the interface. Since the response of the model is axisymmetric, ACAX8 elements are adopted to model the acoustic medium. The analytical solution of the sound pressure along the axis of axisymmetry is given by the following equation:
defined by 
is the mass density of the material, 
is the sound speed of the material, 
is the wave number, 
is the particle velocity, 
is the radius of the baffled planar piston, and 
is the -coordinate along the axis of symmetry.The response is obtained by conducting a direct-solution steady-state dynamic analysis step. The analysis frequency is chosen as 
20 Hertz, and the amplitude of the volumetric acceleration is determined by the following equation:
by setting 
. The variation of sound pressure along the axis of symmetry is shown in Figure 1.10.7–2. Both analytical and numerical data are plotted. As can be seen, the numerical result agrees well with the analytical solution. The numerical data in Figure 1.10.7–2 are obtained in the Visualization module of ABAQUS/CAE by creating the X–Y data along a predefined path, while the analytical data are read into ABAQUS/CAE from an ASCII file. The analytical data file is provided along with the input file for this model. Direct-solution steady-state dynamic analysis.
Analytical result.
