Application of matched asymptotic expansions to the free vibration of a hermetic shell

Abstract

The low frequency branch of the torsion free axisymmetric modes of thin cylindrical shell with hemispherical caps vibrating in vacuo is investigated using membrane approximation. The joint conditions needed at the seams are derived by taking the effect of bending into account in narrow bending layers, using the method of matched asymptotic expansions. A closed form equation is obtained for the normal frequencies. The mode structure exhibits finite jumps in the normal displacement across the seams, which are smoothed over in the bending layers. The normal frequencies are obtained numerically for general shapes and approximately for elongated shapes. Comparisons with the finite element method shows good agreement. © 1998 Academic Press Limited.