Abstract
A general analytical method for the dynamic response of an elastic plate with arbitrarily-disposed voids is proposed by means of the extended Dirac function. The discontinuous variation in rigidity of the plate due to the voids is expressed under the category of a continuous function by the use of the extended Dirac function. The governing equation of motion for a damped plate with voids is formulated without modifying the rigidity of the plates. The treatment is independent of the equivalent plate analogy. First, natural frequencies for a plate with voids are presented by means of the Galerkin method. The validity of the proposed natural frequencies is shown for simply-supported and clamped plates with voids through a comparison with both the results of an experiment using acrylic plates and the results obtained from the FEM code NASTRAN. Second, a dynamic analysis method based on the linear acceleration method is presented from the governing equation. The closed-form approximate solutions for a damped plate with voids are proposed for general and harmonic external loads. The validity of the closed-form approximate solutions proposed here is shown by a comparison with the numerical results obtained from the linear acceleration method and NASTRAN.
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