3.7.3 Transient acoustic wave propagation

Products: ABAQUS/Standard ABAQUS/Explicit

Elements tested

AC1D2 AC1D3

AC2D3 AC2D4 AC2D4R AC2D6 AC2D8

AC3D4 AC3D6 AC3D8 AC3D8R AC3D10 AC3D15 AC3D20

ACAX3 ACAX4 ACAX4R ACAX6 ACAX8

ASI1 ASI2 ASI3

ASI4 ASI8

ASI2A ASI3A

Feature tested

Transient wave propagation in an acoustic medium with nonreflective end condition.

Problem description

The model consists of a column of fluid 1 m long with a constant cross-sectional area. The tube lies horizontally (along the -axis), and the acoustic medium has a prescribed constant inward particle acceleration of 1 m/s² at 0 m. A nonreflective boundary is specified at 1 m using the nonreflective feature of the *IMPEDANCE and *SIMPEDANCE options.

The acoustic material in the column is air with a bulk modulus 1.424 × 10⁵ N/m² and a density 1.21 kg/m³. The speed of sound is calculated as = 343.05 m/s. The analytical result for the pressure is

The column is modeled using either 100 first-order or 50 second-order acoustic elements. For each acoustic element tested, the acceleration is specified in each of two ways:

There is no ASI element or *TIE option, and an inward volume acceleration is specified on degree of freedom 8 as a *CLOAD (“afav” files).
In ABAQUS/Standard an ASI element is placed at 0 with its normal pointing into the fluid (this activates the displacement degree of freedom on the node at 0), and in ABAQUS/Explicit a structural element with the *TIE option is used to define the interaction between the fluid and structure. An acceleration is prescribed directly with *BOUNDARY, TYPE=ACCELERATION (“afas” files). In these cases the first time interval in the analysis is performed using the *IMPEDANCE option; the analysis continues in time using the *SIMPEDANCE option.

A transient dynamic analysis is performed for a period long enough to allow the wave to propagate past the nonreflective boundary.

Results and discussion

For both ABAQUS/Standard and ABAQUS/Explicit the results for pressure are within 0.4% of the analytical result for all tests, except for linear tetrahedra, which are within 3% of analytical results.