Modal Analysis of a Non-Circular Cylindrical Laminated Shell Using Conformal Mapping

Abstract

This paper presents a method to analyze the free and forced vibration responses of a finite uniform cylindrical shell. The cross section of the shell is a square with rounded corners. This geometry makes the analysis of the system difficult. The approach in this work is to apply a conformal mapping to map the physical domain onto a circular cylindrical domain. The Rayleigh-Ritz method is applied to solve for the solution. Numerical results of the mode shapes and the forced response at different frequencies are presented.

Acoustic Response of a Non-Circular Cylindrical Enclosure Using Conformal Mapping

“…The velocity potential in the transformed domain can then be written as (10). By way of construction, the velocity potential in equation (11) satis"es all the boundary conditions in the transformed domain, but not the governing equation.…”