非线性隔振系统物理参数空间局部分岔分析

摘要

In order to reveal the bifurcation mechanism and optimize the system design for nonlinear vibration isolation system ,the local bifurcation analysis in physical parameter space is carried out . Firstly ,this paper formulates the equations of motion for a high-dimensional nonlinear vibration isola-tion system (VIS) to transform the system into a standard form and used the averaging method to ob-tain the bifurcation equation for the system of quadratic nonlinear stiffness in the case of 1∶2 internal resonances .Secondly ,the application of singularity theory to analyzing the local bifurcation of the system derives the high-codimensional universal unfolding and results in the transition sets and bifur-cation diagrams .Finally ,for the engineering application ,the transition sets are transferred back to the physical parameter space ,thus to obtain the bifurcation diagrams of the amplitude with respect to the external force .The results show that the necessary condition of multiple solutions lies in the tu-ning parameters required to be larger than some thresholds .%为揭示非线性隔振系统分岔机理、优化系统设计，开展了非线性隔振系统物理参数空间局部分岔研究。首先，建立了高维非线性隔振系统动力学方程，并将其化为标准形式，利用平均法得到含平方非线性刚度系统在1∶2内共振情况下的单变量分岔方程；然后，根据奇异性理论对系统局部分岔进行了分析，得到了高余维的普适开折，给出了转迁集和静态分岔图；最后，针对工程开折问题进行了研究，将转迁集从开折参数平面转换至物理参数空间，给出了具有工程应用价值的局部分岔图。计算分析表明：系统存在多解的必要条件是调谐参数需大于某些阈值。