Wave‐Based Method for Free Vibration Analysis of Orthotropic Cylindrical Shells with Arbitrary Boundary Conditions

Abstract

The wave-based method (WBM) is a feasible method which investigates the free vibration characteristics of orthotropic cylindrical shells under general boundary conditions. Based on Reissner–Naghid’s shell theory, the governing motion equation is established, and the displacement variables are transformed into wave functions formed to satisfy the governing equations. On the basis of the kinematic relationship between the force resultant and displacement vector, the overall matrix of the shell is established. Comparison studies of this paper with the solutions in the literatures were carried out to validate the accuracy of the present method. Furthermore, by analyzing some numerical examples, the free vibration characteristics of orthogonal anisotropic cylindrical shells under classical boundary conditions, elastic boundary conditions, and their combinations are studied. Also, the effects of the material parameter and geometric constant on the natural frequencies for the orthotropic circular cylindrical shell under general boundary conditions are discussed. The conclusions obtained can be used as data reference for future calculation methods.

Wave propagation in magneto-electro-thermo-elastic nanobeams based on nonlocal theory

“…Submitting Eq. (27) into Eq. (25), the governing equation of the nanobeam related to the wave functions form in the matrix form can be obtained as: (27) w = We jkx e −j t = Θe jkx e −j t Φ = Γe jkx e −j t = Υe jkx e −j t…”

“…He et al [20] proposed WBM in the free vibration characteristics of cross-ply composite laminated cylindrical shell with arbitrary boundary conditions. At the same time, wavebased method is used to study the vibration characteristics of many engineering application structures, such as cylindrical shell structures [21][22][23], submerged ring-stiffened conical shells [24], elastic coupling structure of cylindrical shell and annular plate [25], rotating shell with ring stiffener in T cross section [26] and some composite laminated structures [27][28][29]. From the above literature analysis, it can be shown that there is no related reference to analyze the wave propagation characteristics of magneto-electro-thermo-elastic nanobeam by WBM.…”

Programming for solving plane rigid frame based on MATLAB

“…Subsequently, with the development of Aerospace Engineering, the finite element method gradually formed a complete system. Besides, because the matrix displacement method is the elementary form of the finite element method [5][6][7][8]. The matrix displacement method is also called the member finite element method.…”