摘 要：针对隔振器中普遍存在的非线性特性，以立方非线性恢复力作用的单自由度隔振系统为例，用谐波平衡法求解非线性隔振系统固有频率附近的主共振响应，根据Routh-Hurwitz稳定性判定定理，从理论上说明主共振响应的幅频特性曲线族上垂直切线点的轨迹曲线所包围的区域为不稳定区域。推导出了隔振系统跳跃频率和力传递率的计算公式。计算表明隔振系统力传递率出现跳跃、滞后、以及稳定和不稳定现象，且隔振传递力中的高频谐波分量的影响很小。隔振系统的阻尼、非线性恢复力系数和激励幅值对共振区域的力传递率有影响，对频率低于共振频率区域的力传递率没有影响，其中仅阻尼对频率高于共振频率区域的力传递率有影响。还给出了力传递率小于1的起始频率计算公式。

Abstract: In order to study the common nonlinear characteristics of the vibration isolator, a single degree of freedom system with cubic restoring force is introduced to describe the nonlinear vibration isolation system in the paper and the harmonic balance method was applied to investigate the primary resonance near the natural frequency of the system. Based on Routh–Hurwitz stability criterion, it was clarified theoretically that the region surrounded by the curve of the vertical tangential points in the curve cluster of the primary resonance amplitude frequency characteristics was instable. In addition, the equations of the jump frequency and force transmissibility were derived. The calculated results showed that the jump, hysteresis, stable and instable phenomena would take place for the force transmissibility of the isolator system and the effect of high frequency components of the transmitting force was limited; the damping, coefficient of nonlinear restoring force and the excitation amplitude had an influence on the force transmissibility whose frequencies were in the region of the resonance frequencies but not on those whose frequencies were lower than the resonance frequencies, and only the damping would affect the force transmissibility whose frequencies were higher than the resonance frequencies. Finally, the equation of the start frequency, on the condition that the force transmissibility was less than 1, was presented.