Acoustic model change: steady state

This problem contains basic test cases for one or more Abaqus elements and features.

The following topics are discussed:

Elements tested
Features tested
Problem description
Reference solution
Results and discussion
Input files

ProductsAbaqus/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 x–y plane, with an out-of-plane dimension of 1.0.

Material:

Bulk modulus, $K_{f}$	1.42176 × 10⁵
Density, $ρ_{f}$	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

d^{2} p / d x^{2} + k^{2} p = 0,

where $k = \sqrt{K_{f} / ρ_{f}}$ is the acoustic wave number. Using the boundary conditions that $p = 1.0$ at $x = 0$ and that $d p / d x = - i k p$ at $x = L$ , the solution for the continuum model is

| p (x) | = 1,

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.