Haar wavelet method for frequency analysis of the combined functionally graded shells with elastic boundary condition

Abstract

Abstract In this paper, the Haar wavelet discretization method (HWDM), one of the effective, convenient and accurate numerical solution methods is presented for analyzing the free vibration of combined functionally graded shells (CFGSs). The combined shells consist of elliptic, hyperbolic, parabolic, and cylindrical shells, and each shells are composed of the same functionally graded material (FGM) determined by four parameters. The theoretical model of the CFGSs is formulated by the application of the first-order shear deformation theory (FSDT). The displacement components at any point of the CFGS are expressed as Haar wavelet series in the meridian direction and as a trigonometric function series in the circumferential direction. The boundary and the continuous condition are modeled by the spring stiffness technique, by adding boundary condition equations to the equation of the main system, the constant expressed in the integral form of the Haar wavelet series is satisfied. Then, by solving the characteristic equation of the whole system, the vibration characteristics of the CFGS such as the natural frequency and the corresponding mode shape can be obtained. Through comparison with previous literature and finite element method (FEM) results, it is shown that current method has high accuracy, reliability, and good convergence for free vibration analysis of CFGS. Finally, new free vibration results of the various CFGS, which can be used as benchmark data for researchers in this field, are reported along with parameter studies.