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Circular piston (38890)

Axi-symmetric infinite element model for circular piston

Karl Meerbergen

Free Field Technologies, 16, place de l'Université, 1348 Louvain-la-Neuve, Belgium

This example is a model of the form

 Figure x

 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  theta on a submerged massless and rigid sphere of radius delta image. The piston vibrates harmonically with a uniform radial acceleration. The surrounding acoustic domain is unbounded and is characterized by its density rho image and sound speed c image.

We denote by p image and a_r image the prescribed pressure and normal acceleration respectively. In order to have a steady state solution  p(r_theta_t) image verifying

 second formula

 the transient boundary condition is chosen as:

third formula 
The axisymmetric discrete finite-infinite element model relies on a mesh of linear quadrangle finite elements for the inner domain (region between spherical surfaces r_equal_delta image and r_equal_1,5_delta image). The numbers of divisions along radial and circumferential directions are 5 and 80, respectively. The outer domain relies on conjugated infinite elements of order 5. For this example we used delta_equals1(m) image, rho_equals1,225 image, rho_equals1,225 image,  azero image and azero image.

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.

File 1   1.9 MB  
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