分段线性减振系统的防跳跃及减振性能

摘要

The damping performance of a single DOF system with piecewise linear terms under primary resonance excitation is studied. Employing the averaging method, an implicit function of the amplitude-frequency response equation under the primary resonance excitation is obtained. The transition sets can be calculated from this function on the basis of constraint bifurcation theory. The parametric critical condition to avoid jumping is calculated by qualitative analysis of the amplitude-frequency response equation in the sub-regions of the transition sets. Numerical calculation verifies the feasibility of this method. In addition, the influence of damping ratio and external excitation amplitude within the jump-free region on the global force transmissibility and the force transmissibility at the peak point of the amplitude-frequency response curve is discussed. The results show that under small excitation, large damping ratio can enhance the vibration resistance effect of the system.%为分析一类单自由度分段线性减振系统性能。先用平均法求得系统在主共振激励下的幅频响应方程，并基于约束分岔理论计算转迁集。再定性地分析转迁集各区域系统的幅频响应类型，得到避免跳跃的参数临界条件。数值计算验证了理论分析的可靠性。此外还讨论了阻尼比和激励幅值在非跳跃参数区域变化时，对系统力传递率及系统幅频响应峰值点力传递率的影响。研究结果证明较小激励情况下，阻尼比越大，减振系统的抗振动性能越好。