受简谐激励弹簧测力机构的主参数共振研究  

STUDY ON PRIMARY PARAMETRIC RESONANCE OF A DYNAMOMETER SUBJECT TO HARMONIC EXCITATION

作　　者：杨志安[1] 

机构地区：[1]唐山学院唐山市结构与振动工程重点实验室,唐山063000

出　　处：《机械强度》2007年第5期708-712,共5页Journal of Mechanical Strength

摘　　要：应用拉格朗日方程得到有阻尼弹簧测力机构在简谐激励作用下的非线性运动微分方程Duffing-Mathieu方程;根据非线性振动的多尺度法求得系统满足主参数共振情况的一次近似解,并对其进行数值计算。分析激力、谐调值、阻尼等对系统主参数共振响应曲线的影响。随着阻尼的减小和参数激励幅值的增大,系统幅频响应曲线的峰值和共振区增大。其他参数相同时,硬刚度力幅响应曲线与软刚度力幅响应曲线关于谐调值反对称。The nonlinear mathematical model of a dynamometer subject to harmonic excitation is found to be a Duffing-Mathieu equation by the Lagrange＇ s formulation. By the method of multiple scales for nonlinear vibration analysis, the first approximation solution of primary parametric resonance of the Dtflfing-Mathieu system is obtained. Numerical analysis of the influence of excitation, detuning, and damping on the system response is carried out. With the reducing of damping and the increasing of parametric excitation, the resonant amplitudes, together with the resonant regions, of amplitude frequency response curves get enlarged. Under the same system parameters, the frequency response curves of the hardening stiffness system and those of the softening stiffness one are almost mirror images each other with respect to a neutral ordinate.

关 键 词：拉格朗日方程 测力机构 多尺度法 主参数共振 

分 类 号：O321[理学—一般力学与力学基础]