摘要
本文对变化角度(0°～90°)的复合悬臂梁振动的各阶模态频率进行了研究。连续悬臂梁弯折成某一角度时,由于梁的两段在连接点上的位移耦合作用使系统成为非线性的。作者推导了该非线性系统的运动微分方程,并用大量的实验对理论计算结果进行了验证;创造了一种借助计算机解析图解研究当角度变化时各阶模态频率的变化规律的方法;同时,提出了一种基于特征值问题的频率轨迹曲线解的模态频率稳定性判据。据知,这种变角度复合梁的模态频率稳定性被观察注意到,并在物理结构上认真进行研究,至今,还是第一次。
The mode frequencies of a cantilever beant(bent angle 0—90)have been investigated. When the beam is bent to an angle,due to displacement coupling between the two sections of the beam at the point a non-linear system is developed. The differential equations of motion of the nonlinear system was derived and extensive experiments were conducted to verify the theoretical results. A new analytical-computer-aided-graphical method for studying the mode frequencies of the beam with varying bent angles has been deve loped also,stability critria of mode frequencies based on the frequency locus curves solution of the eigen-value problem was created. As far as is known this is the first time that stability of mode frequencies of the compound cantilever beam has been observed and studied in detail in a physical structure.
