轴向运动屈曲梁非线性振动研究

Research on Nonlinear Vibration of Buckling Beam at Axial Motion

为解决屈曲梁在不同的激励条件下产生共振问题,基于哈密顿原理建立屈曲梁的振动模型以及非线性偏微分振动方程和边界条件,通过数值模拟分析了屈曲梁在相平面的动态特性.采用多模态伽辽金离散法预测静态弯曲参数,通过局部分析获得某一个弯曲附近处的非线性近似响应,并得出有效的非线性表达式和频率响应曲线.

T he nonlinear response phenomena of buckling beam ,w hich is clamped at one end and sliding at the other end to a harmonic axial excitation ,are studied .A vibration model of buckling beam and nonlinear partial differential equations and boundary conditions are established .T he static bending parameters are predicted by using multi-mode Galerkin method .The nonlinear approximative response is obtained in the vicinity of a certain beam bending through local analysis ,and the curve of frequency response and the effective nonlinear expressions are got .Through the numerical simulation ,the dynamic characteristics of buckling beam are analyzed in phase plane .For the nonlinear vibration system ,the result is much closer to the actual result of multi-mode vibration .This helps to understand the actual beam structure vibration in the working process ,and to determine the cause of structural vibration , reso nance f requency .