Based on a multiple-mode analysis, solutions to the nonlinear equations of motion are presented for elliptical plates in terms of variations of nonlinear periods with amplitudes of vibration. The governing equations are written in terms of lateral displacement w and stress function F and the effects of transverse shear deformation and rotatory inertia are incorporated into these equations. For the multiple-mode approach considered in this paper, an exact solution to the stress function is determined. Effects of geometric nonlinearity, shear deformation, rotatory inertia, plate geometry, and modal interaction on the vibration behaviors of elliptical plates are investigated in detail.
A Multiple-Mode Approach to Large-Amplitude Vibration of Moderately Thick Elliptical Plates
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Sathyamoorthy, M., and Prasad, M. E. (March 1, 1984). "A Multiple-Mode Approach to Large-Amplitude Vibration of Moderately Thick Elliptical Plates." ASME. J. Appl. Mech. March 1984; 51(1): 153–158. https://doi.org/10.1115/1.3167560
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