变滑动磨擦系数振动系统最优化计算方法研究

研究了两自由度滑动摩擦系数随相对速度变化的干摩擦振动系统简谐激励响应计算问题，通过将干摩擦力中的理想干摩擦力（Coulomb dry friction)部分进行Fourier级数展开，取级数展开的第一项作为近似，结合一次谐波平衡法，推导出了系统的非线性频响方程组，运用最优化理论中求解非线性方程组的梯度算法，给出非线性频响方程组的数值迭代格式，最后，通过一个数值例分析讨论了干摩擦力对系统响应的重要作用。

STUDY ON THE OPTIMUM METHOD OF RESPONSE COMPUTATION OF THE VIBRATION SYSTEM WITH VARIABLE COEFFICIENT OF SLIDING FRICTION

The response computation of a two degree of freedom dry friction damped system with velocity dependent variable coefficient of sliding friction under harmonic excitation was discussed. The dry friction model considered here consists of two parts,one can be described as a polynomial about relative velocity, another one actually is well known Coulomb dry friction. The Coulomb dry friction was expanded to the Fourier series, and the first order term in series was a approximate as the Coulomb dry friction. Although the response of the vibration system may contain some harmonic components, but the basic harmonic one operates significantly, so according to the basic harmonic balancing technique, the nonlinear amplitude frequency equations was derived. It is very difficult to get the analytical solution of the nonlinear amplitude frequency equations. To conquer this problem, the gradient arithmetic in the optimum theory was used to resolve the nonlinear amplitude frequency equations numerically. A conclution was obtained by a simple numerical sample that the Coulomb dry friction and dry friction with velocity dependent variable coefficient of sliding friction were very effective to reduce the response level of top device in the vibration system considered here comparing to the case with only linear viscous damp.