Abstract
We use the principle of virtual work to derive a higher-order shear and normal deformable theory for a plate comprised of a linear elastic incompressible anisotropic material. The theory does not use a shear correction factor and employs three components of displacement and the hydrostatic pressure as independent variables. For a K th order plate theory, a set of 4 ( K + 1 ) coupled equations need to be solved for the ( K + 1 ) pressures and the 3 ( K + 1 ) displacements defined on the reference surface of the plate. Equations for free vibrations of a plate are derived, and equations for the determination of frequencies and the corresponding mode shapes of a simply supported rectangular plate are given.
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