各种边界条件下非线性弹性梁自由振动的响应分析

Response Analysis of Vibration on Nonlinear Elasticity Beam Under Various Boundary Conditions

针对轴向载荷作用下各种边界条件的非线性弹性矩形截面梁,考虑梁的非线性效应,运用Galerkin原理,林滋泰德—庞加莱法,对梁进行了研究。得到其动力响应解,并针对轴向静载N和非线性材料参数B对位移响应及频率响应的影响进行了讨论。

Galerkin principle and Linz Ted-Poincaré method are proposed for solving the nonlinear vibration problems of a rectangular beam with various boundary conditions. The efforts of material nonlinear and static deformation on the dynamic characteristics are taken into consideration. Then the dynamic response solution can be obtained. And the efforts of in-line static load and nonlinear elasticity parameter on the deflection response and frequency are discussed.