Silencing performance analysis of a membrane cavity with different edge conditions

Abstract

The current study reports the application of Galerkin and tailored-Galerkin procedures to model the vibrational response of a membrane bounded cavity connected to the elastic plates with different types of edge conditions. The plates contain clamped or pin-jointed type of edge conditions on finite edges, while the membranes are assumed to contain fixed, free, or spring-like edge conditions. Both Galerkin and tailored-Galerkin techniques require the priori solutions to determine the displacements of bridging membranes. In the first approach, the priori solution is expressed in terms of Fourier series which changes by varying the conditions on the edges of membranes. However, in late approach, a unique description of displacements can address a variety of edge conditions. The accuracy of these approaches is confirmed through the satisfaction of conserved power identity and through the reconstruction of matching condition with the truncated form of the solutions. In the modeled configuration, the vibrational energy propagates along the walls as well as through the fluid, and is affected by the variation of edge conditions. Moreover, the role of edge conditions is significant for structure-borne radiation only and is negligible for fluid-borne radiations.