Free vibration analysis of cylindrical shells using the Haar wavelet method

Abstract

This paper presents a novel and efficient solution for free vibrations of thin cylindrical shells subjected to various boundary conditions by using the Haar wavelet discretization method. The Goldenveizer–Novozhilov shell theory is adopted to formulate the theoretical model. The displacements and their derivatives in the governing equations are represented by Haar wavelet series and their integrals in the axial direction and the Fourier series in the circumferential direction . The constants appearing from the integrating process are determined by boundary conditions and thus the partial differential equations are transformed into a set of algebraic equations . The frequency parameters of the cylindrical shells are obtained by solving the algebraic equations. The present solution is verified by comparing the numerical results with those previously published in literature. Very good agreement is observed. It is shown that accurate frequency parameters can be obtained by using a small number of collocation points and boundary conditions can be easily achieved. The advantages of this current solution method consist in its simplicity, fast convergence, low computational cost and high precision. • An efficient solution based on the Haar wavelet discretization method is developed for free vibration of cylindrical shells. • Each of displacements and their derivatives in the governing equations are expanded using Haar wavelet series and their integrals. • Accurate solution can be obtained using a small number of collocation points and boundary conditions can be easily achieved. • The advantage of this present method consists in its simplicity, fast convergence, low computational cost and high precision.