硬弹簧Duffing系统在同一简谐激励下有时有多个周期解，并且系统能在这几个解之间来回跳动，也就是突跳。为精确找到系统随参数变化时产生跳跃的区间，先运用谐波平衡法分析系统的频率—振幅响应曲线和激励力幅值—振幅响应曲线，再通过预估—校正算法准确找到了系统随激励频率和激励力变化的跳跃区间，最后分别采用PMUCR胞映射方法和范德玻尔平面分析对所求得的区间加以验证，验证了所求得跳跃区间的精确性。%Hard Duffing vibration isolation system sometimes has several periodic solutions under the same harmonic excitation, and the system can bounce back and forth among the several solutions, which is known as snap-through. In order to find the snap-through regions accurately, the amplitude against frequency curve of the system and system amplitude against excitation amplitude curve are plotted by the harmonic balance method. Then, the snap-through regions of the system for different frequencies and excitations are obtained by trial and error method. Finally, the regions are verified to be accurate by PMUCR cell mapping method and Vandel pol plane analysis method.
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