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.%In order to study the common nonlinear characteristics of the vibration isolator, a single degree of freedom system with cubic restoring force was introduced 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 consisting of the vertical tangential points on the cluster of primary resonance amplitude frequency characteristics curves is instable. In addition, the equations for the jump frequency and force transmissibility were derived. The calculated results show 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 transmitted force is limited. The damping of the system, the coefficient of nonlinear restoring force and the excitation amplitude have influence on the force transmissibility only in the region of resonant frequencies, but no effect in the frequence range lower than the resonance frequencies. The damping would only affect the force transmissibility in the frequency range higher than the resonance frequencies. Finally, the equation of the start frequency, from which the force transmissibility becomes less than 1, was presented.
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