Nonlinear Dynamics Of A Cantilever Rectangular Plate Subjected To Large Overall Motion

This thesis presents a systematic study on the nonlinear vibration of a cantilever rectangular plate subject to a large overall motion. The plate model of concern in-cludes the quadratic coupling deformation, as well as the inertial and geometrical nonlinearities up to the third order, and yields a set of governing equations derived from Kane's dynamic equation and assumed mode method.To gain an insight into the linear modal properties of the plate subject to the ro-tation around a fixed axis, one can check the linear out-of-plane vibration of the plate when the in-plane vibration of the plate is neglected. It is quite straightforward to see that the natural frequencies of the plate increases with an increase in the rotational speed and the radius of rigid basement. However the growth rates of natural frequen-cies vary from mode to mode. Consequently, the eigenvalue loci exhibit veering and crossing phenomena.The periodic vibration of a cantilever rectangular plate subject to a harmonic axial excitation of its basement is investigated via the method of multiple scales with Cartesian transformation. It is revealed that the characteristics of the periodic vibra-tions vary from order to order since the inertial and geometrical nonlinearities influ-ence the system motions quite differently. Moreover, the vibration characteristics greatly depends on the nonlinearies on the geometry size of the plate.Furthermore, the method of the multiple scales is used to investigate the dynam-ics of cantilever rectangular plate under the rotational and the harmonic excitation. The primary resonance of the system is analyzed for the case when the excitation frequency is close to a natural frequency. Finally, the modulation equations are for-mulated for studying the 1:3 internal resonance of the plate subject to the basement rotation and linear harmonic motion.The case studies of numerical simulation well demonstrate the dynamic res-ponses of the cantilever plate undergoing the basement rotation and linear harmonic excitation via Matlab programming.