Multi-scale structural topology optimization of free-layer damping structures with damping composite materials

Damping performance of the free-layer damping structure mainly depends on the damping material layout and its material physical properties. This paper proposes a concurrent topology optimization method for the design of the multi-scale free-layer damping structures with damping composite materials. In order to maximize the structural damping performance, the density-based topology optimization method is adopted to find the optimal layout on both macro and micro scales. For this coupled system, the macrostructure is composed of periodic damping composite materials, a stiff damping material which is designed for maintaining the structural stiffness and a soft damping material which is used for improving structural damping. The homogenized effective complex elastic matrix is obtained by considering the two damping materials layout in the microstructure. Mathematical model is established and sensitivity analysis is deduced. Several numerical examples are presented to demonstrate the effectiveness of the proposed multi-scale optimization method. In-depth discussions are given for the effects of the volume fraction of soft damping material in the micro scale on the design results. The results show that there is an optimal volume ratio of the stiff and soft damping material to make the structure reach optimal vibration performance due to the effective competition of soft and stiff characteristics of different damping materials. The optimal microstructure has relatively great loss moduli and high material loss factor, and it also presents a negative Poisson's ratio. The structural vibration performance of the optimal multi-scale layer damping structure with damping composite materials is significantly improved.