一类弹簧支撑系统非线性动力学特性实验研究

Experimental Study on Nonlinear Dynamic Characteristics of the Spring Supporting Model

以线性机械弹簧和斜支撑弹簧为元件,构建了支撑系统力学模型。在仿真计算的基础上,设计并制作与力学模型相对应的支撑系统。通过测试确定系统阻尼比、固有频率等力学参数,综合利用时频域分析、相轨迹分析和庞克莱分析等方法,对支撑系统在不同激励条件下的响应规律进行了实验分析。研究结果表明实验测试结果和数值仿真结果一致,该力学模型存在典型的非线性力学特性,如稳态周期解、暂态混沌、分岔、混沌等,为其进一步推广到工程实际提供了理论和实验支撑。

The mechanical model of supporting system was constructed consisting of linear mechanical springs and laterally supporting ones. Based on numerical simulation, the corresponding supporting system of the mechanical model was designed and built. Using time-frequency field analysis, phase trajectory and Poincaré map method, numerical simulation and experimental analysis were performed to study the responses of the supporting system. The results show the good consistency between numerical simulation and experimental analysis. Moreover, the nonlinear characteristics such as chaos, bifurcations, transient chaos, and steady-state periodic solution exist in this system, which provides theoretical and experimental basis for the application of the supporting system in vibration-reduction engineering.