【摘要】 采用符号函数和分段线性方法,推导干滑动摩擦力作用下单自由度系统的自由振动通解,分析了滑块的运动特性,运用动能定理对解析解进行了严格证明,然后通过Matlab数值仿真和滑块在花岗岩上的滑动试验进行验证。结果表明,干滑动摩擦单自由度系统中的滑块运动是一个具有线性衰减振幅的简谐运动;理论计算得出的滑块位移曲线中所有较高点形成上包络直线,所有较低点形成下包络直线;数值仿真和滑动试验结果与理论值非常接近,验证了所推导的位移解析解的有效性。干滑动摩擦单自由度系统自由振动通解的构建有助于求解该类系统的强迫振动通解。更多还原

【Abstract】 The general solution of free vibration of a single-degree-of-freedom system with dry sliding friction was derived by adopting sign function and piecewise linear method. The kinematic characteristics of the slider were analyzed. The analytical solution was proved strictly by kinetic energy theorem, and validated by Matlab numerical simulation and sliding test of the slider on granite. The results show that the slider’s motion in single-degree-of-freedom system with dry sliding friction is the simple harmonic motion with linear attenuation amplitude. All higher points in the slider’s displacement curve via theoretical calculation form an upper envelope line, and all lower points form a lower one. The numerical simulation and sliding test results are very close to the theoretical values, which verify the validity of the displacement’s analytical solution. The construction of the free vibration general solution is helpful to deduce the forced vibration general solution of the studied system.更多还原