Residual vibration of a rotating flexible beam subject to prescribed motion

Abstract EN

In this paper, residual vibration of a servomotor driven rotating flexible beam is studied.

The beam is modeled as an Euler- Bernoulli beam ; it is rotated by a servomotor using triangular velocity profile (bang-bang trajectory).

Analytical solution is also obtained by using Fourier series expansion of the acceleration of the rotating beam.

Residual vibration amplitudes depend on the beam tip position at the end of the rotation, which is the function of rise time (the time to complete the rotation).

It is found that if the rise time is the odd multiple of the beam period 1, 3, 5 …, residual vibration amplitudes are maximized.

Residual vibration amplitude spectrum shows that for rise time to period ratios from 1.5 to 2.5, residual vibration amplitudes are lowered to less than 3 % of the maximum residual vibration amplitude, obtained for rise time, equal to the first natural period of the beam.