NATURAL FREQUENCIES OF ORTHOTROPIC RECTANGULAR PLATES OBTAINED BY ITERATIVE REDUCTION OF THE PARTIAL DIFFERENTIAL EQUATION

Authors: Sakata T.¹; Takahashi K.¹; Bhat R.B.²

Source: Journal of Sound and Vibration, Volume 189, Number 1, January 1996 , pp. 89-101(13)

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Abstract:

Natural frequencies of orthotropic rectangular plates are obtained by successive reduction of the plate partial differential equation and by solving the resulting ordinary differential equation exactly. The reduction of the partial differential equation is carried out by assuming an approximate solution satisfying the boundary conditions along one direction and employing a Galerkin averaging technique known as the Kantorovich method. The resulting ordinary differential equation along the other direction is solved exactly, which provides the natural frequencies of the plate. Natural frequencies of the orthotropic rectangular plates with various boundary conditions are obtained by using this approach, and presented along with the discussion of the convergence and accuracy of the results.

Language: English

Document Type: Research article

Affiliations: 1: Department of Mechanical Engineering, Chubu University, Kasugai, Aichi, 487, Japan 2: Department of Mechanical Engineering, Concordia University, Montreal, Quebec H3G 1M8, Canada

Publication date: 1996-01-01