The effect of nonlinear elasticity on the large amplitude free vibration behavior of elastic plates at small scale

The effect of nonlinear elasticity on the free vibration behavior of elastic plates has been evaluated by employing continuum mechanics model. The second-order non-linear stress–strain relationship has been considered and the Kirchhoff’s hypothesis has been applied on the elastic plate. The large deformation during vibration has also been considered. By using the Hamilton principle, the governing equations of the free vibration of the plate under different boundary condition have been obtained. In order to get the explicit solutions of the governing equations, the Galerkin’s method and the harmonic balance method have been utilized. The relationship between the vibration frequency and the vibration amplitude has been discussed and the vibration frequencies of different shaped plate have been compared. It is perceived that the nonlinear elasticity has a distinct effect on the free vibration of the plate.