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 investigated 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.