Vibration suppression in a cantilever beam using a string-type vibration absorber

Abstract

A string-type vibration absorber is proposed to suppress energy from a vibrating beam. A cantilever beam is considered with a harmonic force applied at its free end. The vibration absorber is a string attached to the beam at two different points. The string is rigidly connected to the fixed end of the beam and through a spring and damper to a second point on the beam. The finite element method is used to model the system and a reduced order model is obtained through modal reduction performed on both the string and the beam. The steady state amplitude of the transverse vibration of the beam is calculated using the first two modes of the beam-string system. It is found that the maximum amplitude at a given point of the beam occurs at a forcing frequency which is a root of a sixth order polynomial. The design of the vibration absorber is done in two steps. In the first, the spring stiffness, the position of the second attachment point of the string and a preliminary damping constant are calculated using a genetic algorithm approach where the objective function is the maximum displacement on the beam. Fine tuning is done in the second optimization step, by choosing an appropriate damping constant to further improve the design. To avoid buckling, the string tension is set to a value less than the lowest buckling force of the system. Numerical simulations of the beam’s maximum amplitude with and without absorber are shown to validate the proposed design