Free vibrations of cylindrical shells with arbitrary boundary conditions: A comparison study

Abstract

In this paper, the free vibration characteristics of cylindrical shells with arbitrary boundary conditions are investigated. The Sanders shell theory is used to calculate the elastic strain energy. Artificial springs are implemented at the ends of the shells to represent the arbitrary boundary conditions. The shell displacements are expanded by three different sets of formulations, namely, the modified Fourier series, the Orthogonal polynomials, and the Chebyshev polynomials. A unified solution for the three different types of expansion functions is developed using the Rayleigh-Ritz method. The unified solution is validated by comparing with the available results in the literature. The accuracy, convergence rate, and computational efficiency of the three expansion functions are compared. Based on the comparison studies, the Chebyshev polynomials of high computational efficiency are selected to investigate the influence of boundary conditions on the free vibration characteristics of cylindrical shells.