Eur. Phys. J. Plus (2020) 135: 434
https://doi.org/10.1140/epjp/s13360-020-00438-0

Regular Article

Natural frequency calculation of open laminated conical and cylindrical shells by a meshless method

¹ College of Mechanical Science and Technology, Kim Chaek University of Technology, Pyongyang, 999093, Democratic People’s Republic of Korea
² Department of Engineering Machine, Pyongyang University of Mechanical Engineering, Pyongyang, 999093, Democratic People’s Republic of Korea

^* e-mail: kimkwanghun@163.com

Received: 10 December 2019
Accepted: 11 May 2020
Published online: 25 May 2020

Abstract

In this paper, a new and an efficient solution method based on local gradient smoothing method has been applied to free vibration problem of open composite laminated cylindrical and conical shells with elastic boundary conditions. The theoretical model is formulated by the first-order shear deformation theory, and the motion equation is obtained by the Hamilton’s principle. The motion equation is discretized by meshless shape function; in this process, the derivatives of the shape function are approximated by local gradient smoothing method. The accuracy, applicability and efficiency of this method are demonstrated for free vibrations of open composite laminated cylindrical and conical shells with different geometric, material parameters and boundary condition. The numerical results show good convergence characteristics and good agreement between the present method and the existing literature. And through several numerical examples, some useful results for free vibration results of open composite laminated cylindrical and conical shells are obtained, which may serve as a benchmark solutions for researchers to check their analytical and numerical methods.