This study presents a modified harmonic balance method, which is used to solve the force and displacement transmissibilities of a vibration isolator with both the quasi-zero-stiffness and geometrically nonlinear damping. The steady-state response of the nonlinear isolation system is obtained by Jacobi elliptic functions, and is used to modify the harmonic components of stiffness and damping force in the harmonic balance method, which can reduce the truncation error produced by the trigonometric Fourier series. When the modified harmonic components are combined based on the orthogonality condition, the elliptic harmonic balance method (EHBM) is obtained. The results show that the amplitude–frequency response curve, and force and displacement transmissibilities obtained by using the EHBM can be compared well with those obtained by using the fourth order Runge–Kutta method. The EHBM can be used to improve the accuracy of the results at the resonance and high frequency regimes. The EHBM is simple and straightforward for the detailed study of the vibration isolation characteristics of the geometrically nonlinear isolator.

这项研究提出了一种改进的谐波平衡方法，该方法用于解决具有准零刚度和几何非线性阻尼的隔振器的力和位移传递率。非线性隔离系统的稳态响应是通过雅可比椭圆函数获得的，并通过谐波平衡法来修改刚度和阻尼力的谐波分量，从而减少三角傅里叶级数所产生的截断误差。当基于正交条件组合修改后的谐波分量时，可获得椭圆谐波平衡法（EHBM）。结果表明，幅频响应曲线 使用EHBM获得的力和位移传递率可以与使用四阶Runge-Kutta方法获得的力和位移传递率很好地比较。EHBM可用于提高共振和高频状态下结果的准确性。对于详细研究几何非线性隔离器的隔振特性，EHBM简单明了。