Topology optimization of composite material with high broadband damping

Abstract

The optimization of damping composite material in a certain frequency range has become one of the critical issues in structural engineering applications due to the fact that the structures usually work in a wide vibration frequency range. This paper proposes a topology optimization method for designing the damping composite materials with high stiffness and high broadband damping. The broadband damping composite material is realized by the properly combing two phases of damping material, in which phase 1 has high loss factor in lower frequency range and phase 2 has high loss factor in higher frequency range. In order to maximize the material damping performance in a given frequency range, we suggest a new algorithm for finding the optimal two-phase damping materials layout in micro scales, while the homogenized effective complex elastic matrix is obtained by considering the two damping materials layout in the microstructure. The mathematical model with two different objective functions, which are K-S objective function and weighted objective function, has been established. The first is maximize the minimum material loss factor in the given frequency range and the second is maximize the sum of the material loss factor in the given frequency range. Several typical numerical examples are presented to demonstrate the effectiveness of the proposed optimization method. An in-depth analysis is conducted to reveal the effects of the weighting factor on the optimal solutions. The results show that the K-S function has the ability to maximize the minimum damping of composite material in the given frequency band. The material loss factor increases with the increase of weighting factor. All of the results show that the proposed method can get the optimal microstructure with clearly material layout, no matter the objective is K-S function or weighted function is used.