Keywords: dynamic stiffness method, higher-order theory, modal analysis, laminates, composites, Wittrick-Williams algorithm, cylindrical shells..

An exact free vibration analysis of laminated composite cylindrical shallow shells has been carried out by combining the dynamic stiffness method (DSM) and a higher order shear deformation theory (HSDT). In essence, the HSDT has been exploited to develop first the element dynamic stiffness (DS) matrix and then the global DS matrix of composite cylindrical shallow shell structures by assembling the individual DS elements. As an essential prerequisite, Hamilton's principle is used to derive the governing differential equations and the related natural boundary conditions. The equations are solved symbolically in an exact sense and the DS matrix is formulated by imposing the natural boundary conditions in algebraic form. The Wittrick-Williams algorithm is used as a solution technique to extract the natural frequencies from the overall DS matrix. The effect of several parameters such as boundary conditions, orthotropic ratio, length-to-thickness ratio, radius-to-length ratio and stacking sequence on the natural frequencies and mode shapes is investigated in detail. Some assessment and reliable benchmark solution for theory validation are carried out and results are compared with those available in the literature. Finally some concluding remarks are given.

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