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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 106
Edited by:
Paper 162

Natural Frequencies of Composite Cross-Ply Spherical Panels using the Dynamic Stiffness Method and the Wittrick-Williams Algorithm

F.A. Fazzolari and J.R. Banerjee

School of Engineering and Mathematical Sciences, City University London, United Kingdom

Full Bibliographic Reference for this paper
F.A. Fazzolari, J.R. Banerjee, "Natural Frequencies of Composite Cross-Ply Spherical Panels using the Dynamic Stiffness Method and the Wittrick-Williams Algorithm", in , (Editors), "Proceedings of the Twelfth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 162, 2014. doi:10.4203/ccp.106.162
Keywords: direct stiffness method, free vibration, composites, Wittrick-Williams, spherical shells, symbolic computation..

An exact free vibration analysis of doubly-curved laminated composite shells has been carried out by combining the dynamic stiffness method (DSM) and a higher order shear deformation theory (HSDT) for the first time. In essence, the HSDT has then been fruitfully exploited to develop first the shell element dynamic stiffness (DS) matrix and then the global DS matrix of spherical shell structures by assembling the individual DS elements. As an essential prerequisite, Hamilton's principle is used to derive the governing differential equations and natural boundary conditions. The equations are solved symbolically in an exact sense and the DSmatrix is formulated by imposing the natural boundary conditions in an algebraic form. TheWittrick-Williams algorithm is used as a solution technique to compute the eigenvalues of the overall DS matrix. The effect of several parameters such as boundary conditions, orthotropic ratio, length-to-thickness ratio and length-to-radius ratio on the natural frequencies and mode shapes is investigated in details. The results are compared with those available in the literature and also by using commercial software. Finally some concluding remarks given.

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