3-D Exact Free Vibration Analysis of Transversely Isotropic Cylindrical Panels

Abstract

This paper presents an exact analysis of the free vibration of simply supported, transversely isotropic cylindrical panels. Based on the three dimensional elasticity for transversely isotropic media, three displacement functions are introduced so that the equations of motion are uncoupled and simplified. After expanding these functions with orthogonal series, the equations of free vibration problems are further reduced to three second order ordinary differential equations. A modified Bessel function solution with complex arguments is then directly used for the case of complex eigenvalues, which, to the authors’ knowledge, has never been reported before. To clarify the correctness and effectiveness of the developed method, numerical examples are presented and compared to the results of existent papers.