Residual vibration reduction for translation unconstrained or partially unconstrained structures by structural optimization

Abstract This paper studies residual vibration reduction in translation unconstrained or partially unconstrained structures by structural optimization. Suppression of elastic residual vibration is of great concern in many fields, and several approaches have been proposed to deal with it through structural optimization. However, these approaches are suitable for completely constrained structures, while unconstrained and partially unconstrained structures are not considered in particular. The dynamic responses of the latter include not only elastic responses but also rigid body responses. The rigid body responses make several effective structural optimization approaches inapplicable. This paper proposes two methods to solve the problem arising from the rigid body responses. Then the abovementioned effective approaches based on completely constrained models are applied to study the optimization of translation unconstrained or partially unconstrained structures to minimize the residual vibration. To reduce the computational burden of optimization, model reduction is further applied in this research. Finally, several numerical examples are presented to illustrate the effectiveness of the proposed approaches. The optimized results for residual vibration minimization show superiority over those obtained with classical objective functions.