A solution method for free vibration analysis of coupled laminated composite elliptical-cylindrical-elliptical shell with elastic boundary conditions

Abstract

In this paper, an efficient, convenient and explicit method based on the Haar wavelet discretization approach for analyzing the free vibration of the coupled laminated composite elliptical-cylindrical-elliptical shells (ECESs) with elastic boundary conditions is presented. Two elliptical double curved shells are coupled on both end of cylindrical shell. Based on the first-order shear deformation theory the equations of motion for ECES are derived by means of Hamilton's principle. The separation of variables is first performed; i.e. displacement components and rotations of any point of the ECES are expanded to the Haar wavelet series in the meridian direction and Fourier series in circumferential direction. The constants appearing from the integrating process are determined by boundary conditions, and thus the partial differential equations are transformed into algebraic equations. By solving the characteristic equation, the natural frequencies and mode shapes of coupled laminated composite ECES are obtained. The present results have been compared with those of the published literature. The comparison results show that this method has high accuracy, high reliability and also a higher convergence rate in attaining the frequencies of the coupled laminated composite ECESs. Then, the effects of the main parameters such as material properties, geometrical parameters, and various boundary conditions, on the vibrational behavior of the coupled ECESs, are investigated. Finally, new free vibration analysis results of the coupled laminated composited ECES, which can be used as benchmark data for researchers in this field, are reported through the parameter study.