Interactions of an Oscillating Rectangular Membrane with a Compressible Fluid

Abstract

Interaction of an oscillating membrane with a fluid is important because the wide variety of technological applications. A boundary element method has been employed for the analysis of a vibrating rectangular membrane in contact with a compressible fluid at rest. The deformation modes of the membrane correspond to the vacuum case. For the calculation of the pressure jump over the membrane, the Helmholtz’s integral equation for the fluid pressure is employed taking into account the fluid-membrane interface boundary condition. Considering the membrane equation and applying a collocation method, the natural frequencies of the interacting system are obtained. The influence of various parameters such as aspect ratio, fluid density and membrane dimension on these frequencies is evaluated. Furthermore, the influence of the wave number on the fluid mass coefficient and the acoustic damping ratio are evaluated. The validity of the method is deduced when comparing the results obtained by other authors and theories.