弹性连接旋转柔性梁动力学分析

采用Chebyshev谱方法对考虑根部连接弹性的平面内旋转柔性梁动力学特性进行研究.基于Gauss--Lobatto节点与Chebyshev多项式方法对柔性梁变形场进行离散,通过投影矩阵法施加固定及弹性连接边界条件.利用Chebyshev谱方法获得了系统固有频率和模态振型数值解,通过与有限元方法及加权残余法的比较,验证了方法的有效性.分析了弹性连接刚度、角速度比率、系统径长比及梁的长细比等参数对系统固有频率及模态振型的影响.研究发现:由于系统弯曲模态、拉伸模态的频率随各参数的变化规律不一致,将出现频率转向与振型转换现象;随着弹性连接刚度、角速度比率及系统径长比的增大,低阶弯曲模态频率增大并超过高阶拉伸模态频率,随着梁的长细比的增大,低阶拉伸模态频率增大并超过高阶弯曲模态频率.

DYNAMIC ANALYSIS OF A ROTATING FLEXIBLE BEAM WITH ELASTIC BOUNDARY CONDITIONS

The dynamic characteristics of a flexible beam rotating in a plane with elastic boundary condition are investi-gated by the Chebyshev spectral method. The discrete equations of motion are obtained based on Gauss-Lobatto sampling and Chebyshev polynomials. Employing projection matrices, fixed and elastic boundary conditions are incorporated in the same form. Numerical solutions of natural frequencies and mode shapes are gained by Chebyshev spectral method and compared with the results of finite element and weighted residual methods to verify its correctness. The effects of various parameters, such as connection stiffness, angular velocity, hub radius ratio and slenderness ratio of the beam, on the vibration of the beam are analyzed. The results show that there is a veering phenomenon of natural frequencies loci accompanied by exchanges of the corresponding mode shape,due to the difference in sensitivity to system parameters between bending mode and strength mode. With the increasing of connection stiffness, angular velocity and hub radius ratio, a lower bending mode frequency will surpass its adjacent higher strength mode frequency. Similarly, strength mode frequencies will also surpass their adjacent higher bending mode frequencies with the increasing of slenderness ratio of the beam.