This example is about fluid-structure-interaction (FSI) and vibroacoustics. The figure shows the pressure field produced by a vibrating elastic membrane at the right bottom corner of a closed cavity filled with compressible fluid. The membrane is first loaded from the bottom and then suddenly released resulting in periodic motion. The interaction between the fluid and structure produces pressure waves which propagate with the speed of sound. The walls of the cavity are assumed reflecting. The red and blue colors in the figure indicate positive and negative pressures, respectively. Note that the shape of the cavity changes as the membrane vibrates.

The membrane was modeled by the full non-linear elasticity equations. The equations were first linearized by Newton's method and then discretized by biquadratic finite elements. The fluid was modeled by the compressible Navier-Stokes equations. The numerical solution of the equations was obtained by Newton's method and biquadratic finite elements with two-level RFB (Residual Free Bubbles) stabilization. The coupled system was solved by the method of sequential iteration.

Remark: In vibroacoustics, the pressure waves are usually modelled by the wave equation which in periodic cases reduces to the Helmholtz equation. The structural models are usually based on the linearized elasticity theory. Here, the modeling is based directly on the more general Navier-Stokes and non-linear elasticity equations. In this way ElmerSolver is able to account for large displacements (which change the computational domain), convection of momentum and viscous damping, which can be essential physical phenomenon in vibroacoustic problems. The classical approach based on the wave equation and linear elasticity with small displacements is also possible in ElmerSolver.

Here, you can download an animation of the results mpeg: [~1MB]