Parametric vibration control of a flexible arm

Abstract

This paper proposes a vibration attenuation method of a flexible arm utilizing parametric vibration control. Parametric vibration, which is usually discussed in terms of exciting a vibration by changing parameters of a vibration system, can be utilized for attenuating vibration by changing parameters opposite to excitation. A rectangular beam is inserted in a flexible arm and suspended by bearings to allow rotation about its longitudinal axis. Since bending stiffness of a rectangular beam is larger in the direction in which the cross section of the beam is thicker, rotation of the beam changes the direction of bending stiffness of the flexible arm. Controlling the rotational angle of the inner beam attenuates two-dimensional vibration of the flexible arm. Parametric vibration attenuation algorithm is derived theoretically and verified by experiments.