Natural Frequencies of Rectangular Membrane With Boundary Perturbation

Abstract

A perturbation approach, coupled with the adjoint concept, is used to derive an analytic expression for the natural frequencies of a nearly rectangular membrane. The method is applied for a rectangular membrane with a semicircle at one of the boundaries. The fundamental natural frequency results for this configuration are presented and compared with results from a finite-element method and results from an approximate Galerkin method. The agreement between the fundamental natural frequencies calculated with the perturbation approach and those calculated with the finite-element method improves as the radius of the semicircle decreases and as the semicircle location becomes more eccentric.