简谐激励下一类干摩擦振子的响应计算

本文提出了计算简谐激励下一类干摩擦振子系统响应的解析方法,振子系统的摩擦力用含有限个Jenkins单元的Iwan模型描述。针对力-位移之间的分段线性关系,对振子运动逐段进行分析,并给出了各阶段内的系统的振动方程,最后通过变量代换,获得了方程的解析解. 由于每个阶段解的初值均由位移和速度的连续性条件得到,因此顺次求得各线性阶段中响应便获得了整个时域上的响应. 仿真结果表明,随着外激励量级的递增,接触面出现滑移,使得接触刚度减小,因而系统幅频曲线峰值明显左移；另一方面,系统的等效粘性阻尼会随着激励量级的递增而先增大后减小.

Calculation of the dynamic responses of a dry-friction oscillator under harmonic excitation

In this paper, an analytical method is presented to calculate the dynamic responses of a harmonic forced oscillator with dry friction. The friction of the oscillator is modeled by an Iwan model with finite Jenkins elements. As the force-displacement relationship of the oscillator is piecewise linear, the motion of the oscillator is analyzed interval by interval. The vibration equation in each linear interval is given and the corresponding analytical solution is derived by use of variable substitution. The initial values of each interval are obtained by the continuity condition of the displacement and velocity of the oscillator. Combining the dynamic responses of these intervals in sequence forms the dynamic responses of the model in the whole time history. The simulation results show that as the excitation amplitude level increases, slipping occurs in the contact surface which makes the contact stiffness decreased, thus results in obviously left shifted of the peak amplitude of the frequency response function curves. It is also found that the equivalent viscous damping first increases then decreases with the excitation amplitude level.