3.8.4 Transient acoustic wave propagation

Products: Abaqus/Standard Abaqus/Explicit

Elements tested

AC1D2 AC1D3

AC2D3 AC2D4 AC2D4R AC2D6 AC2D8

AC3D4 AC3D5 AC3D6 AC3D8 AC3D8R AC3D10 AC3D15 AC3D20

ACAX3 ACAX4 ACAX4R ACAX6 ACAX8

ASI1 ASI2D2 ASI2D3

ASI3D3 ASI3D4 ASI3D6 ASI3D8

ASIAX2 ASIAX3

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 x-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 nonreflective impedance conditions.

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 constraint, and an inward volume acceleration is specified on degree of freedom 8 as a concentrated load (“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 a tie constraint is used to define the interaction between the fluid and structure. An acceleration is prescribed directly with a boundary condition (“afas” files). In these cases the first time interval in the analysis is performed using boundary impedances; the analysis continues in time using surface impedances

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

Results and discussion

Numerical results for the pressure distribution along the length of the acoustic medium are compared with the analytical results at time 0.0044 s.

In Abaqus/Standard for cases where the volume acceleration is specified (“afav” input files), the maximum errors are below 0.7%, except for linear tetrahedra, which are within 3% of the analytical results. For cases where a boundary acceleration is specified on the nodes of the ASI elements (“afas” input files), the maximum errors are below 4.2%, except for linear tetrahedra, which are within 5.9% of the analytical results.

In Abaqus/Explicit the results for pressure are within 0.2% of the analytical results for all tests, except for linear tetrahedra, which are within 3.2% of the analytical results.