Modal Method for Free Vibration of Oval Cylindrical Shells With Simply Supported or Clamped Ends

Abstract

The free vibration of an oval cylindrical shell of finite length was investigated with the aid of the kinematic relations of the first-order shell theory of Sanders. Transverse and in-plane inertia terms were retained throughout. A method incorporating a type of eigen-function expansion into Hamilton’s principle, was developed and found to be far more convenient than a parallel Fourier analysis. In addition to the determination of the natural frequencies and deformation characteristics, attention was focused on the influence of various types of simple support and clamped end conditions. Two modes of deformation corresponding to a “higher” and a “lower” frequency were observed for every pair of axial and circumferential wave numbers, depending upon the degree of circumferential symmetry in the deformation pattern.