A closed form solution for free vibration of orthotropic circular cylindrical shells with general boundary conditions

Abstract

In the past decades, the exact closed form solutions for the free vibration of thin orthotropic circular cylindrical shells have been merely restricted to some classical boundary conditions. Therefore, the target of the current paper is to present a new exact closed form solution for free vibration of orthotropic circular cylindrical shells with general boundary conditions by means of the method of reverberation-ray matrix (MRRM). Based on the Donnell–Mushtari shell theory, the wave solutions are constructed by the exact closed form solutions of the governing differential equations. The artificial spring technology is introduced to achieve the general boundary conditions of two end edges of shell. Hereby, the reverberation ray matrix can be easily obtained by using the MRRM together with the wave solutions, boundary conditions and dual coordinates of the orthotropic circular cylindrical shells. Then, the vibration results are obtained from the extrapolation method and golden section search (GSS) algorithm. By the comparison with other published methods and the finite element method, the accuracy of the present method is verified. On the basis of that, some new exact nature frequencies of the orthotropic circular cylindrical shells with general elastic restraints are shown which can serve as the benchmark data for the future computing method.