The Computional Time Efficient Finite Element Method for Large Amplitude Vibrations of Composite Plates

Publisher Summary This chapter presents a multimode time-domain formulation, based on the finite element method for nonlinear vibration of composite plates. The use of Finite Element Method (FEM) enables the present formulation to deal with composite plates of complex geometries and boundary conditions, and the use of the modal coordinate transformation enables to reduce the number of ordinary nonlinear differential modal equations to a much smaller one. The present procedure is able to obtain the general Duffing-type modal equations easily. The participation value of the linear mode to the nonlinear deflection is quantified. The nonlinear frequencies for symmetrically and unsymmetrically laminated rectangular composite plates are also obtained. The phase plot and power spectral density show that nonlinear displacement responses are no longer harmonic, and multiple modes are required for isotropic clamped beams, and isotropic and composite plates. The chapter also illustrates the frequency response characteristics, phase plots, time histories, and the power spectrums for the subharmonic, simple harmonic, and superharmonic responses.