Geometrical design method of multi-degree-of-freedom dynamic vibration absorbers

This paper presents a new geometrical design method of multi-degree-of-freedom (mdof) dynamic vibration absorbers that reduce multiple modes of vibration. The design of an mdof vibration absorber involves, in general, the complexity of the equations and large numbers of design variables. For this reason, previous researches mainly focused on finding optimized stiffness and damping values that minimize the vibration responses. In this paper, we introduce a simple geometrical design method in which the sets of three mutually orthogonal line springs are used to first simplify the stiffness matrix. The dynamic equations of a main body and an absorber are then decoupled to obtain the geometric design rules for an mdof absorber. Numerical examples are used to illustrate the new design method.