3.6.14 Acoustic submodeling

Products: ABAQUS/Standard ABAQUS/Explicit

Elements tested

AC2D3 AC2D4 AC2D4R AC2D6 AC2D8

AC3D4 AC3D6 AC3D8 AC3D8R AC3D10 AC3D15 AC3D20

ACAX3 ACAX4 ACAX4R ACAX6 ACAX8

Features tested

The submodeling capability is applied to an acoustic model of a duct. The global model is represented by either 20 linear elements or 10 quadratic elements along the lengthwise direction of the duct. An absorbing boundary condition is applied at one end of the duct; loads are applied to the other end. The submodel models the part of the duct close to the absorbing end and has a finer mesh than the global model. The driven nodes of the submodel lie along the global model element boundaries. Two-dimensional, three-dimensional, and axisymmetric models are tested for the driven nodes' acoustic pressure; the *STEADY STATE DYNAMICS, DIRECT and *DYNAMIC procedures are used in ABAQUS/Standard, and the *DYNAMIC, EXPLICIT procedure is used in ABAQUS/Explicit. The transient simulations are performed for period of time long enough to allow the wave to propagate past the end of the duct. Each element type used in the global model can be tested against each other element type of similar dimensionality in the submodel.

Problem description

Model:

The two-dimensional and axisymmetric global models have dimensions of 1.0 × 10.0, and the three-dimensional global models have dimensions of 1.0 × 10.0 × 1.0. In the two- and three-dimensional cases the submodel covers the end of the duct from 8.5 to 10; the axisymmetric submodel is from 8.0 to 10.0.

Material:

Bulk modulus of acoustic medium	1.42176 × 10⁵
Density	1.293

Boundary conditions:

In the global linear models the bottom surface is subjected to acoustic pressures of 1.0 at the corner nodes; in the ABAQUS/Standard global quadratic models consistent loads corresponding to a uniform acoustic pressure load are applied. In the submodel analyses the boundary conditions are driven by the results from the global models.

Loading:

The top of the acoustic medium has an impedance boundary condition with the proportionality factors between pressure and displacement equal to 2.3323 × 10^–3.

Results and discussion

The amplitudes of acoustic pressures and their phases are correctly identified in the global analysis file output and applied at the driven nodes in the submodel analysis.