摘要
应用拉格朗日方程,得到带平方和立方非线性的皮带驱动机构的非线性振动微分方程,根据非线性振动的多尺度解法,求得系统满足主共振情况的近似解,分析系统的稳定性,并对其进行数值计算。分析带的长度和横截面积、外激力、谐调值、系统阻尼等对系统的影响。分析一次近似解、二次近似解的特点,指出系统主共振的一次近似解的幅频响应曲线表现为硬刚度特性;二次近似解的幅频响应曲线表现为软刚度特性。
The nonlinear differential vibration equation with quadratic and cubic nonlinearities of the belt driver mechanism is derived by means of Lagrange equation. By means of the method of multiple scales, for nonlinear vibration the primary resonance approximate solution of the system is obtained. Numerical results on the influences of length, cross section area of the belt, excitation, detuning and damping on the system are carried out. The first approximate solution for amplitude frequency response curve of the primary resonance of the system has hardening characteristic. It compares the difference between the first and the second approximate solution, and points out the second approximate solution for amplitude frequency response curve of the primary resonance of the system has softening stiffness characteristic.
出处
《机械强度》
CAS
CSCD
北大核心
2009年第5期697-701,共5页
Journal of Mechanical Strength
关键词
皮带
非线性
多尺度法
主共振
Belt
Nnonlinear vibration
The method of multiple scales
Primary resonance
