This study develops a modified elliptic harmonic balance method (EHBM) and uses it to solve the force and displacement transmissibility of a two-stage geometrically nonlinear vibration isolation system. Geometric damping and stiffness nonlinearities are incorporated in both the upper and lower stages of the isolator. After using the relative displacement of the nonlinear isolator, we can numerically obtain the steady-state response using the first-order harmonic balance method (HBM1). The steady-state harmonic components of the stiffness and damping force are modified using the Jacobi elliptic functions. The developed EHBM can reduce the truncation error in the HBM1. Compared with the HBM1, the EHBM can improve the accuracy of the resonance regimes of the amplitude-frequency curve and transmissibility. The EHBM is simple and straightforward. It can maintain the same form as the balancing equations of the HBM1 but performs better than it.

中文翻译：

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具有几何非线性的两阶段隔振系统性能分析的椭圆谐波平衡法

本研究开发了一种改进的椭圆谐波平衡方法（EHBM），并将其用于解决两阶段几何非线性隔振系统的力和位移传递率。隔离器的上，下级都包含了几何阻尼和刚度非线性。使用非线性隔离器的相对位移后，我们可以使用一阶谐波平衡法（HBM1）数值获得稳态响应。使用雅可比椭圆函数修改刚度和阻尼力的稳态谐波分量。开发的EHBM可以减少HBM1中的截断错误。与HBM1相比，EHBM可以提高振幅-频率曲线和传输率的共振方式的准确性。EHBM简单明了。