Elastic Constants of Thick Orthotropic Composite Plates

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Abstract
This paper gives a method of obtaining the three-dimensional elastic constants of a completely free orthotropic plate from experimental plate vibration data, using an optimized three-mode Rayleigh formulation that incorporates through-the-thickness shear and rotatory inertia. The author believes this is the first reported attempt employing this formulation for obtaining the frequencies of thick plates with the incorporation of these two phenomena. The primary purpose of this paper is to develop the basic theory and method for this class of plates. The author had earlier utilized the classical lamination theory (which does not include these two effects) with both three and six optimized modes. The forward problem of computing plate vibration frequencies from given elastic constants by the Rayleigh method is solved for three thickness ratios (.075, .1, .125) for an isotropic (aluminum) and an orthotropic (graphite/epoxy) material. The inverse method for extracting the elastic constants from experimental vibration data is then applied to two thick plates fabricated from these materials. The results suggest that the proposed method is potentially useful for rapid, inexpensive extraction of in situ elastic constants of composite plates. The major original contribution of this paper is the novel approach for formulating and solving both the forward and inverse problems for thick plates.