多自由度系统非线性参数识别的灵敏度方法

为了识别多自由度系统的非线性参数（3次阻尼系数、3次刚度系数和干摩擦力），提出一种基于灵敏度分析用测量响应（位移、速度或加速度）识别非线性参数的方法。将结构抽象为由线性和非线性阻尼、刚度连接的集中质量系统，用四阶Runge—Kutta法求解多自由度非线性系统的振动响应和振动响应对非线性参数的灵敏度。假定非线性参数为零初值，根据计算响应与测试响应的差值，由基于正则化的阻尼最小二乘法迭代识别系统的非线性参数值。算例表明，该方法可以有效地识别多自由度系统的非线性参数。

Nonlinear Parameters Identification of Multi-Degree-of-Freedom Systems Using Sensitivity Analysis

A method is presented for identifying the nonlinear parameters, cubic damping, cubic stiffness and coulomb friction, of multi degree of freedoms system by using measured time responses (displacements, velocities or accelerations).The structure is modeled as equivalent lumped masses and connected by stiffness and damping elements. 4 th Runge-Kutta method is used to solve the responses of the system and response sensitivity respect to nonlinear parameters. Assuming initial values to the nonlinear parameters, the nonlinear parameter value is obtained by damping least square method based on the difference between the calculated and measured response. The validity and effectiveness of the method that identify nonlinear parameters of multi-degree-of-freedoms system are demonstrated by some numerical simulations.