Vibrations of Cylinders and Cylindrical Shells of Transversely Isotropic Materials

Abstract

This chapter analyses the free vibration of transversely isotropic cylinders or cylindrical shells based on the three-dimensional theory of elasticity. The aim of the chapter is two fold. One is to promote the physical understanding of the fundamentals of vibration, which will be realized by introducing first the three simple vibration modes, i.e., the axisymmetric torsional vibration, breathing mode vibration and thickness-shear vibration and then the general asymmetric vibration. The second is to solve some problems closely related to engineering applications. Thus the coupled vibrations of cylindrical shells interacting with fluid and elastic media will be discussed. Most published studies are based on the two-dimensional shell theories or numerical methods such as the finite element method and the boundary element method. The three-dimensional analysis presented in this chapter provides a benchmark for determining the validity and suitability of these approximate shell theories and numerical methods.