Concurrent design of the free damping structure for minimizing the frequency response in a broad frequency band

This article develops a multiscale topology optimization model for the free damping structure to optimize the microstructure of the damping material and its macro layout. The objective is to minimize structural response in a broad frequency gap subject to volume constraints on both macro and micro levels. To overcome the convergence difficulty caused by the sharp jumping of the harmonic response around structural eigenfrequencies and maintain high-precision integral, the Gauss Legendre integration method is adopted to calculate the integration of objective function. Based on the density-based method, the sensitivity analysis of the objective function and the constraint is deduced. The mode acceleration method is used to reduce computational cost and a modified threshold Heaviside projection method is used to obtain the clear black-and-white designs. Several numerical examples are investigated to demonstrate the validity of the proposed model.