The natural vibration of a symmetric cross-ply laminated composite conical-plate shell

Abstract The feasibility of using the transfer matrix method to analyze a composite laminated conical-plate shell is explored theoretically. With the vibration theory and the transfer matrix method combined, the dynamic characteristics of a symmetric cross-ply laminated conical shell with an annular plate at the top end are investigated in detail. The governing equations of vibration for this system are expressed by the matrix differential equations, and the coefficient matrixes and joining matrix are derived. After the relationship between the transfer matrix and the coefficient matrix is established, the fourth order Runge–Kutta method is used numerically to solve the matrix equation. Once the transfer matrix of single component has been obtained, the product of each component matrix and the joining matrix can compose the matrix of entire structure. The frequency equations, mode shape and force vector are formulated in terms of the elements of the structural matrices. The 3D finite element numerical simulation has validated the present formulas of natural frequencies and mode shapes. The conclusions illustrate that this investigation will provide an important foundation for the advanced development of the laminated composite combination shells.

[1]  G. A. Cohen.  Computer analysis of asymmetric free vibrations of ring-stiffened orthotropic shells of revolution. , 1965 .

[2]  Chih‐Ping Wu,et al.  A refined asymptotic theory of laminated circular conical shells , 2002 .

[3]  A. Kalnins,et al.  Free Vibration of Rotationally Symmetric Shells , 1964 .

[4]  G. N. Jazar,et al.  Natural frequencies of laminated composite plates using third order shear deformation theory , 2006 .

[5]  In Lee,et al.  Vibration Analysis of Twisted Cantilevered Conical Composite Shells , 2002 .

[6]  H. Tottenham,et al.  Analysis of the free vibration of cantilever cylindrical thin elastic shells by the matrix progression method , 1972 .

[7]  A. Nayfeh,et al.  Natural frequencies of heated annular and circular plates , 2004 .

[8]  Liyong Tong,et al.  Free vibration of composite laminated conical shells , 1993 .

[9]  Hiroshi Matsuda,et al.  Vibration of twisted laminated composite conical shells , 2002 .

[10]  Manfred Heckl,et al.  Investigations on the Vibrations of Grillages and Other Simple Beam Structures , 1964 .

[11]  V. R. Murthy,et al.  Dynamic characteristics of rotor blades , 1976 .

[12]  D. Yadav,et al.  Forced nonlinear vibration of laminated composite plates with random material properties , 2005 .

[13]  T. Y. Ng,et al.  GENERALIZED DIFFERENTIAL QUADRATURE METHOD FOR THE FREE VIBRATION OF TRUNCATED CONICAL PANELS , 2002 .

[14]  Gen Yamada,et al.  Natural frequencies of in-plane vibration of annular plates , 1984 .

[15]  K. S. Kim,et al.  Geometrically nonlinear analysis of laminated composite plates by two new displacement-based quadrilateral plate elements , 2006 .

[16]  L. Hua.  Frequency characteristics of a rotating truncated circular layered conical shell , 2000 .

[17]  José Herskovits,et al.  Analysis of laminated conical shell structures using higher order models , 2003 .

[18]  Liyong Tong,et al.  Free vibration of orthotropic conical shells , 1993 .

[19]  Chun-Sheng Chen,et al.  Nonlinear vibration of laminated plates on a nonlinear elastic foundation , 2005 .

[20]  Gen Yamada,et al.  Free vibration of a conical shell with variable thickness , 1982 .

[21]  A. A. El Damatty,et al.  Experimental and analytical evaluation of the dynamic characteristics of conical shells , 2002 .

[22]  K. M. Liew,et al.  Free vibration analysis of conical shells via the element-free kp-Ritz method , 2005 .