3.9.8 Acoustic model change: steady state

Product: Abaqus/Standard  

Elements tested

AC1D2    AC1D3   

AC2D3    AC2D4    AC2D6    AC2D8   

AC3D4    AC3D5    AC3D6    AC3D8    AC3D10    AC3D15    AC3D20   

ACAX3    ACAX4    ACAX6    ACAX8   

ACINAX2    ACINAX3    ACIN2D2    ACIN2D3    ACIN3D3    ACIN3D4    ACIN3D6    ACIN3D6   

Features tested

Continuum acoustic elements are removed during a steady-state acoustic analysis.

Problem description

Model:

The models have dimensions 10.0 × 1.0 in the xy plane, with an out-of-plane dimension of 1.0.

Material:

Bulk modulus, 1.42176 × 105
Density, 1.293

Loading and boundary conditions:

The pressure at the left side of the model is constrained to equal one; there is a plane-wave radiation condition on the right side of the model. A steady-state solution at unit frequency is obtained. Then, one-half of the model is removed. When the elements are removed, the radiation condition is applied along the new external boundary.

Reference solution

The one-dimensional Helmholtz equation for steady-state acoustics is

where is the acoustic wave number. Using the boundary conditions that at and that at , the solution for the continuum model is

while the phase is consistent with a sine wave at the specified frequency, 1 Hertz.

Results and discussion

The model gives the theoretical results in both the first and second steps.

Input files

pmcp_ac1d2.inp

General test of AC1D2 elements in steady-state analysis.

pmcp_ac1d3.inp

AC1D3 elements.

pmcp_ac2d3.inp

AC2D3 elements.

pmcp_ac2d4.inp

AC2D4 elements.

pmcp_ac2d6.inp

AC2D6 elements.

pmcp_ac2d8.inp

AC2D8 elements.

pmcp_ac3d4.inp

AC3D4 elements.

pmcp_ac3d5.inp

AC3D5 elements.

pmcp_ac3d6.inp

AC3D6 elements.

pmcp_ac3d8.inp

AC3D8 elements.

pmcp_ac3d10.inp

AC3D10 elements.

pmcp_ac3d15.inp

AC3D15 elements.

pmcp_ac3d20.inp

AC3D20 elements.

pmcp_acax3.inp

ACAX3 elements.

pmcp_acax4.inp

ACAX4 elements.

pmcp_acax6.inp

ACAX6 elements.

pmcp_acax8.inp

ACAX8 elements.

pmcp_acinax2.inp

ACINAX2 elements.

pmcp_acinax3.inp

ACINAX3 elements.

pmcp_acin2d2.inp

ACIN2D2 elements.

pmcp_acin2d3.inp

ACIN2D3 elements.

pmcp_acin3d3.inp

ACIN3D3 elements.

pmcp_acin3d4.inp

ACIN3D4 elements.

pmcp_acin3d6.inp

ACIN3D6 elements.

pmcp_acin3d8.inp

ACIN3D8 elements.