Residual Vibration of a Rotating Flexible Beam Subject to Prescribed Motion

In this paper, residual vibration of a servomotor drivenrotating flexible beam is studied. The beam is modeled as an Euler-Bernoulli beam; it is rotated by a servomotor using triangular velocityprofile (bang-bang trajectory). Analytical solution is also obtained byusing Fourier series expansion of the acceleration of the rotatingbeam. Residual vibration amplitudes depend on the beam tip positionat the end of the rotation, which is the function of rise time (the timeto complete the rotation). It is found that if the rise time is the oddmultiple of the beam period 1, 3, 5 …, residual vibration amplitudesare maximized. Residual vibration amplitude spectrum shows that forrise time to period ratios from 1.5 to 2.5, residual vibration amplitudesare lowered to less than 3% of the maximum residual vibrationamplitude, obtained for rise time, equal to the first natural period ofthe beam.