A new solution method for free vibration analysis of rectangular laminated composite plates with general stacking sequences and edge restraints

The free vibrations of laminates with general lay-ups and edge restraints are studied.The governing equations for rectangular plates are deduced via Hamilton's principle.A numerical strategy is proposed to obtain the natural frequencies and mode shapes.The method is validated against known results and then used for parametric studies. A method is presented to study the free vibrations of rectangular laminated composite plates with general layups and arbitrary boundary conditions. Based on the first-order shear deformation theory, the governing differential equations and boundary conditions are deduced via Hamilton's principle. Generalised displacements are expanded as series with Legendre polynomials as the base functions. A generalised eigenvalue problem is obtained by following a variational approach, where energy functional is extremised and boundary conditions are introduced by means of Lagrange multipliers. In order to overcome some difficulties in obtaining the natural frequencies and corresponding mode shapes, a new numerical strategy is proposed.

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