Mathematics Analysis For Nonlinear Vibration Of An Elastic Thin Plate

Theoretical analysis and numerical simulations of vibration of elastic thin plates areimportant both in practical applications and theories, which is always one of central topicsin theories and applications of partial diferential equations. Up to now, the most of worksonly concern the transverse vibration or longitudinal vibration. However, for the practicalapplications, the two kinds of vibrations should be considered simultaneously, especiallytheir coupling efect. This is the motivation of this paper.In this paper, by using the Hamilton Principle, we consider nonlinear vibration of a thinplate in non-inertial frame of reference and derive the corresponding partial diferential equa-tions of this model. Then, the energy estimates of solutions to the linearized equations of thevibration model are derived. Using the Picard iteration scheme, we obtain the well-posednessof weak solutions to the initial boundary value problems for the vibration equations. More-over, we get an expression of the approximate solution by the Galerkin method. At last, bythe IHB method, we derive the diferential equations of frequencies and amplitudes of theapproximate solution, which will help to study some practical problems further.