tailieunhanh - Numerical analysis of free vibration of cross-ply thick laminated composite cylindrical shells by continuous element method

This paper presents the vibration analysis of thick laminated composite cylindrical shells by a new approach using the Continuous Element Method (CEM). Based on the analytical solutions for the differential equations of thick composite cylindrical shell taking into account shear deflection effects, the dynamic transfer matrix is built from which natural frequencies are easily calculated. | Vietnam Journal of Mechanics, VAST, Vol. 35, No. 1 (2013), pp. 17 – 30 NUMERICAL ANALYSIS OF FREE VIBRATION OF CROSS-PLY THICK LAMINATED COMPOSITE CYLINDRICAL SHELLS BY CONTINUOUS ELEMENT METHOD Ta Thi Hien, Tran Ich Thinh, Nguyen Manh Cuong Hanoi University of Science and Technology, Vietnam Abstract. This paper presents the vibration analysis of thick laminated composite cylindrical shells by a new approach using the Continuous Element Method (CEM). Based on the analytical solutions for the differential equations of thick composite cylindrical shell taking into account shear deflection effects, the dynamic transfer matrix is built from which natural frequencies are easily calculated. A computer program is developed for performing numerical calculations and results from specific cases are presented. Numerical results of this work are compared with published analytical and Finite Element Method (FEM) results. Through different examples, advantages of CEM are confirmed: reduced size of model, higher precision, reduced time of computation and larger range of studied frequencies. Keywords: Free vibration, continuous element method, dynamic stiffness matrix, thick laminated composite cylindrical shell, dynamic transfer matrix. 1. INTRODUCTION With the increasing use of composites as structural elements, studies on the vibration of laminated composite cylindrical shells receive a considerable attention. In the literature, various solution methods based on different beams, plates and shells theories have been applied to the vibration analysis of metallic and composite structures: analytical approaches [1, 2, 3, 4], mode superposition method [5], spline function method [6], wave-train closure principle [7], Rayleigh–Ritz method [8], finite element method (FEM) [9, 10] etc. The FEM is certainly one of the most popular methods used for analyzing composite structures. However, it is well known that a sufficiently large number of finite elements is inevitable in order to