# Circular piston (38890)

### Axi-symmetric infinite element model for circular piston

**Karl Meerbergen**

*Free Field Technologies, 16, place de l'UniversitĂ©, 1348 Louvain-la-Neuve, Belgium*

This example is a model of the form

with M, C, and K non-symmetric matrices and M singular. This is thus a differential algebraic equation. It is shown that it has index [1]. The input of the system is f, the output is the state vector x. The motivation for using model reduction for this type of problems is the reduction of the computation time of a simulation.

This is an example from an acoustic radiation problem discussed in [3]. Consider a circular piston subtending a polar angle on a submerged massless and rigid sphere of radius . The piston vibrates harmonically with a uniform radial acceleration. The surrounding acoustic domain is unbounded and is characterized by its density and sound speed .

We denote by and the prescribed pressure and normal acceleration respectively. In order to have a steady state solution verifying

the transient boundary condition is chosen as:

The matrices K, C, M and the right-hand side f are computed by MSC.Actran [2]. The dimension of the second-order system is N=2025.

Download matrices in the Matrix Market format (File 1) (1983617 bytes).

1. J.-P. Coyette, K. Meerbergen, and M. RobbĂ©.

Time integration for spherical acoustic finite-infinite element
models, 2003.

2. Free Field Technologies.

MSC.Actran 2004, User's Manual, 2004.

3. P. M. Pinsky and N. N. Abboud.

Finite element solution of the transient exterior structural
acoustics problem based on the use of radially asymptotic boundary
conditions.
*Computer Methods in Applied Mechanics and Engineering*,
85:311-348, 1991.