Non-linear flexural vibrations of anisotropic skew plates

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Abstract

The large amplitude free flexural vibrations of thin, elastic anisotropic skew plates are studied by using the von Karman field equations in which the governing non-linear dynamic equations are derived in terms of the stress function and the lateral displacement. Clamped boundary conditions are chosen and the in-plane edge conditions considered are either immovable or movable. Solutions are obtained by the Galerkin method on the basis of a one-term assumed vibration mode. The degree of non-linearity is obtained as a function of skew angle, aspect ratio and types of orthotropy. The results, on specializing for an isotropic skew plate and an orthotropic rectangular plate, agree well with those found in the literature. The use of the Berger approximation to study a skew plate with in-plane immovable edges is shown to lead to errors of both a quantitative and qualitative nature.

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