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

Abstract

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.

Keywords:

• Nonlinear vibration
• thin plate
• forced vibration
• Jacobi elliptic function
• Galerkin’s method