Optimal Layout of Damping Material Using Homogenization Method.

Abstract

This paper shows an optimal layout algorithm of a damping material which is affixed on a vibrating surface of a structural component. This method is based on the generalized layout optimization method(1) where a prescribed amount of material is distributed in a design space so that an objective function may be minimum. The complex elastic moduli are employed to express the visco-elastic behaviours of a damping material under periodic loads. Two different objective functions are employed in numerical examples. One is dynamic mean compliance, which is useful in reducing the displacement at the loading points. The other is square product of the nodal displacement vector, which is effective to reduce the overall dynamic response of the structure. It is shown that both of the results show good convergence and give reasonable layout.