中文摘要：

同时包含二次的非线性的僵硬的许多重要颤动现象并且抑制在实际 circumstances.In 下面在复杂颤动系统存在这份报纸，我们建立了 2-degree-of-freedom ( DOF )为如此的一个系统的非线性的颤动模型，推出了管理它的动力学的运动的微分方程，并且基于杂木林的理论由非线性的正常模式( NLNM )的重叠的原则为管理方程得出了答案不变

英文摘要：

Many important vibration phenomena which simultaneously contain quadratic nonlinear stiffness and damping exist in the complicated vibrating systems under practical circumstances. In this paper, we established a 2-degree-of-freedom （DOF） nonlinear vibration model for such a system, deduced the differential equations of motion which govern its dynamics, and worked out the solutions for the governing equations by the principle of superposition of nonlinear normal modes （NLNM） based on Shaw＇s theory of invariant manifolds. We conducted numerical simulations with the established model, using superposition of nonlinear normal modes and direct numerical methods, respectively. The obtained results demonstrate the feasibility of the proposed method in that its calculated data varies in a similar tendency to that of the direct numerical solutions.