Response spectrum of a coupled flexible shaft-flexible beam system for cycloidal input motion

In this study, flexible Euler-Bernoulli type beam attached to a flexible shaft-rigid disk system which is driven by a servomotor is considered. A cycloidal rise motion is assumed for disk rotation. Equation of motion for the flexible shaft-rigid disk system is developed and the disk motion for the cycloidal input motion is obtained. In the second step, elastic beam which is attached to the rigid disk is modeled with the boundary conditions of flexible root-free end. Mode summation technique is assumed for the solution of the equations. Analytical solutions are obtained and spectrum of beam tip vibration amplitudes with respect to frequency ratio is obtained. Frequency ratio is defined as the elastic beam first natural frequency divided by the cycloidal rise frequency. Results show that at frequency ratios of 2, 3, 4, … beam tip vibration amplitudes become zero. With the proper selection of either first natural frequency of elastic beam or the cycloidal rise frequency, it is possible to drive elastic shaft-rigid disk-elastic beam system without exciting vibrational motion.