A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration responses of arbitrarily laminated anisotropic composite rectangular thin plates. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite rectangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The finite element results are compared with available approximate continuum solutions. The amplitude-frequency relations for convergence with gridwork refinement, different boundary conditions, aspect ratios, lamination angles, number of plies, and uniform versus concentrated loads are presented.
Finite Element Large-Amplitude Free and Forced Vibrations of Rectangular Thin Composite Plates
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Chiang, C. K., Mei, C., and Gray, C. E., Jr. (July 1, 1991). "Finite Element Large-Amplitude Free and Forced Vibrations of Rectangular Thin Composite Plates." ASME. J. Vib. Acoust. July 1991; 113(3): 309–315. https://doi.org/10.1115/1.2930186
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