Abstract

A model for a 3-D structural acoustic system, currently being used for parameter estimation and control experiments in the Acoustics Division, NASA Langley Research Center, is presented. This system consists of a hard-walled cylinder with a flexible circular plate at one end. An exterior noise source causes vibrations in the plate which in turn lead to unwanted noise inside the cylinder. Control is implemented through the excitation of piezoceramic patches bonded to the plate which generate in-plane forces and/or bending moments in response to an input voltage.

The plate and interior acoustic wave dynamics are approximated with expansions involving Fourier components in the circular direction and spline and spectral elements in the radial and axial directions. To guarantee uniqueness and differentiability at the coordinate singularity as well as to ensure stability and the expected convergence rate, the radial basis functions for both the wave and plate components are constructed in a manner that incorporates the Bessel or analytic behavior near the singularity while retaining sufficient generality so as to provide an approximation technique for discretizing complex coupled systems involving circular geometries.

Introduction

A growing area of research in the structural acoustics community concerns the problem of reducing structure-borne noise levels within an acoustic cavity.