Vibration of two cantilever beams clamped at one end and connected by a rigid body at the other

Abstract

This study presents the pure bending and coupled bending-torsional vibration characteristics of a beam structure which consists of two cantilever beams and a rigid body at their free ends. This structure is available in many mechanical structures such as robots, space constructions, and optical pickup actuators in optical disc drives (ODDs). In order to depict the vibration of the beam structure originating from the deflection and torsion of two beams, the motion equations and continuity conditions are analytically induced by using energy conservation. In the process that the free vibration problem is solved, two independent characteristic equations are obtained. The former is an equation for the pure bending vibration of two beams, and the latter is for their coupled bending-torsional vibration. It is proved that these characteristic equations are exact by comparing natural frequencies obtained from FEM. As natural frequencies are described in many dimensional variations, the relation between vibration characteristics and the dimensions of the given system is also investigated. Finally, resonant frequencies from test results are presented to confirm the validation of this study for a new type optical pickup actuator.