Assessment of nonlinear vibrations of thin plates undergoing large deflection and moderate rotation using Jacobi elliptic functions

In this article, nonlinear free/forced vibrations of a plate undergoing large deflection and moderate rotation have been investigated based on Jacobi elliptic functions. The formulation has been established using a generalized von-Karman's strain in which nonlinear terms of deflection and rotations are simultaneously included. The governing equations have been derived with the use of extended Hamilton's principle assuming that the plate is under an external force of elliptic type. It is proved that conventional approximate solutions of nonlinear vibrations of plates based on single-harmonic assumption are inadequate to consider higher harmonics. Whereas, Jacobi elliptic function method considers the effects of higher-order harmonic leading to a more exact solution. This becomes more important when extra nonlinearity due to nonlinear rotations is included in the calculations.

Automated summary

In this article, the nonlinear free/forced vibrations of a plate undergoing large deflection and moderate rotation were investigated using Jacobi elliptic functions. The results showed that the conventional approximate solutions based on single-harmonic assumption were inadequate, while the Jacobi elliptic function method considered higher-order harmonics and provided a more accurate solution.