Abstract:

A cantilever beam with unilateral collision under base excitation is investigated experimentally. The response of the free end of the cantilever beam and the impact force were measured in the experiment. From the experimental results, it can be seen that the system response will exhibit periodic motion and chaotic motion under different excitation frequency. The high order modal frequencies of the cantilever beam are found in the power spectrum of the chaotic motion. This phenomenon is not obvious in periodic motion. The dynamic equation of the system is established with method of lumped mass and impact rule, and the dynamical response of the system is studied by using Runge-Kutta method. The numerical results coincide with the experimental results not only in time domain but also in frequency domain.

摘要：

针对基础激励下单边碰撞悬臂梁系统进行详细的实验研究。在实验中，测量悬臂梁自由端的响应信号以及碰撞力信号。从实验结果中可以看到在不同的激励频率下，系统响应会表现出周期运动和混沌运动。在混沌运动的功率谱中发现悬臂梁的高阶模态频率，而在周期运动时这一特征并不明显。利用集中质量法和碰撞条件建立该系统的动力学方程，并运用 Runge-Kutta法直接积分得到系统的动力学响应。从时域和频域两方面分析比较仿真结果与实验结果，两者有较好的吻合度。

关键词: 振动与波, 混沌运动, 响应特性, 单边碰撞, 悬臂梁