Topology Optimization of Constrained Layer Damping Treatment Plate Under Harmonic Excitations

The constrained layer damping (CLD) treatment is widely used to suppress the vibration and noise of thin-walled structures. However, the complete coverage of the constrained damping layer will increase the unnecessary additional mass, lead to material waste and can not effectively improve the damping performance of the composite structure. In this paper, the evolutionary topology optimization (ETO) method is used to investigate the optimal distribution of damping materials of CLD structures under harmonic excitation. The design objective is to minimize the vibration of the structure at the specified location by allocating a given amount of damping materials. The projection relationship between the design model and the finite element analysis (FEA) model is established. Based on a modified modal superposition method, the sensitivities of the objective function with respect to the design variables are obtained. The implicit smooth structure topology of constrained damping layer is determined by the level set function (LSF) constructed by node sensitivity. The analysis of the design model is replaced by the FEA model with various elemental volume fractions, which are determined by the auxiliary LSF. Numerical examples show the effectiveness and efficiency of the method. The research shows that the proposed method can not only make the objective function converge to the optimal value stably, but also obtain smooth and clear boundary.