摘要
考虑连杆弹性的曲柄滑块机构为受约束刚弹耦合机械系统,采用Kane方程,将连杆弹性变形用伽辽金法离散成空间函数和广义坐标的乘积,计及轴向缩短对连杆角速度的影响,推导出弹性连杆多自由度线性参激振动方程组。应用多尺度法并结合笛卡尔坐标变换,分析连杆第一阶弯曲模态的主参激共振,获得平凡响应稳定性临界曲线,并讨论阻尼比和惯性比等参数的影响。
It builds the model of elastic link in a crank - slider mechanism, which is constrained with rigid - elastic coupled mechanical system. Adopting the Kane equation, the elastic deformation is diseretized into the serial product Of spatial functions and general coordinates. It derives the excited vibration system for the elastic link including the diverse angular velocity of link due to longitudinal shortening, the linear equations of multi- degree parametrically. Using the method of multiple scales and combining the Cartesian transformation, it analyzes the principal parametric resonance of the first order bending mode and obtains the transition curve of stability for the trivial response, discusses the effects of damping ratio and inertia ratio.
基金
国家自然科学基金资助项目(10572099)
苏州大学211工程建设项目(R2317038)
关键词
弹性连杆
KANE方程
伽辽金法
多尺度法
主参激共振
稳定性
Elastic Link
Kane Equation
Galerkin Method
Method of Multiple Scales
Principal Parametric Resonance
Stability
