Abstract
This paper addresses a new computer-aided implementation of classical analytical procedure to treat free vibration of rectangular plates supported at arbitrary interior points. An integral method which has been successfully applied to the analysis of transient heat conduction is adopted. This procedure is based on the Galerkin method but takes advantage of symbolic algebra software such as REDUCE or MACSYMA. For free vibration of plates, the lateral displacement is expressed as a series of polynomials each of which satisfies both the free boundary conditions and the supporting constraint conditions. Coefficients of these polynomials are determined by the standard Galerkin method. Symbolic algebra software is essential to perform necessary algebraic operations to generate admissible trial functions and generalized mass and stiffness matrices for the eigenvalue problem. The obtained expression is in closed form and unlike purely numerical methods such as finite element or finite difference methods, this method does not require excessive computational time nor huge memory storage. Numerical examples are presented and compared with existing data.
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