Vibration Mode Analysis Of Laminated Frames By The Method Reverberation Ray Matrix

The Method of Reverberation Ray Matrix (MRRM) is a novel matrix method for solveing the problem of dynamics in frequency domain which is proposed by Pao and his colleagues. This method will transform the dynamic equation into the frequency domain, and then build equilibrium and compatibility equations in which the wave amplitudes are taken as basic unknowns. After the analytic solution is obtained, the time domain histories of these variables are produced by Inverse Fast Fourier Transformation.In this study, the reverberation ray matrix method (MRRM) for analyzing dynamic response of elastic trusses or frames is extended and used to solve the natural frequency and vibration mode of laminated frames. In this study, the MRRM is employed to obtain the frequency response function (FRF) of displacement of a laminated frame under the action of a unit impulse load. The natural frequencies are determined from the FRF, since the curve of FRF has peak when a resonant frequency is approached. And the vibration mode is retrieved from the adjoint matrix of the coefficient matrix of the governing equations of MRRM. The accuracy of result of MRRM is verified by a simply supported symmetrically laminated beam compared with the analytical solution of classical theory. The calculations of nine-bar laminated plane frames demonstrate that MRRM could obtain natural frequencies and vibration modes of laminated frame structures effectively.