单侧限位悬臂梁碰撞系统的动力学实验研究

摘要

对构造的单边碰撞悬臂梁系统进行实验的定性研究,在基础激励实验中,变换多次激励频率,通过加速度传感器测量悬臂梁测点的响应信号,并通过力传感器测量得到限位器与柔性悬臂梁之间的碰撞力.通过Matlab软件对实测响应的时、频域分析处理,观察到系统复杂的周期、概周期、混沌等多种运动形式,并发现其中运动形式变化的区间存在突变.尝试对实验时域数据计算最大Lyapunov指数,以进一步验证其中混沌的存在,进一步发现了混沌响应下末端加速度响应与碰撞力的传递函数具有频响函数特征.实验研究体现了非线性动力学现象,也对分析应用混沌运动的实验结果提供了一个新视角.%Based on a simple model of a cantilever beam with unilateral collision,the nonlinear dynamics of the beam under different frequencies of sinusoidal excitation is studied.The acceleration response of the free end of the cantilever beam and the impact force are measured by accelerometers and forcing transducer,respectively.Periodic,chaotic motions are also observed through the analysis of experimental results in time and frequency domain by Matlab software.It is also found of the mutation between different kinds of motions under different frequencies excitation.The largest Lyapunov exponent is also calculated by the time data of chaotic motions response.Furthermore,the transfer function between the the acceleration of the end of the cantilever beam and the impact force in the chaotic responses are found to be similar with the frequency response function in the modal test.The observation and results of this paper demonstrate the nonlinear dynamics motions,and provide a new horizon for the understanding of chaotic experimental results.