Vibration reduction by natural frequency optimization for manipulation of a variable geometry truss

Abstract

This study investigates the optimization of motion plans for the two dimensional variable geometry trusses (VGTs) in order to semi-actively reduce the vibration amplitude while the VGTs move a target payload from one point to another. We assume that the payload such as a trouble satellites have a control moment gyro or reaction wheel; corresponding sinusoidal disturbance is generated by the payload and it probably cause the resonance vibration of the VGTs during the manipulation. The natural frequency during the manipulation of the VGTs is given as a function of the geometry; hence, the motion plan for the VGTs can be optimized by considering difference between the frequency of the disturbance applied by the payload and the natural frequency of the VGTs. In order to study the effect of the geometry changes on the structural vibration during the manipulation, a numerical, two-dimensional VGT model that has three variable length members in the trusses is constructed by finite element method. The numerical results show that resonant vibration can occur for the specific trajectory of the VGT to move the target payload. We assumed that the VGT changes their geometry as quasi-static way. We optimize the trajectory and the three variable length members of the VGT in order to prevent the resonance by using a sequential quadratic programming. As a result, the optimized manipulation effectively reduces the amplitude of vibration. Furthermore, the stress of the truss members and the total number of the motion steps for the manipulation are evaluated.