Abstract
We consider problem of the spatial vibrations of plates with complex shape within Timoshenko's theory of plates. We write the constitutive equations in a local oblique coordinate system where all the bounding contours coincide with coordinate lines. We have demonstrated the effectiveness of the proposed method using as an example the vibration of a rectangular plate weakened by a regular hexagonal hole under the action of an impulsive surface load. We analyze the effect of nonlinear terms on the frequency and amplitude of normal displacements of the shell as a function of the load amplitude.
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