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.

摘要

在本文中，基于雅可比椭圆函数研究了经历大偏转和适度旋转的板的非线性自由/受迫振动。该公式是使用广义冯卡门应变建立的，其中同时包含偏转和旋转的非线性项。假设板受到椭圆型外力，利用扩展哈密顿原理推导了控制方程。证明基于单谐波假设的传统板非线性振动近似解不足以考虑高次谐波。而雅可比椭圆函数法考虑了高次谐波的影响，从而得到更精确的解。