Topology optimization for minimizing frequency response of constrained layer damping plates

This paper presents a topology optimization method to design the optimal layout of Constrained Layer Damping (CLD) material in structures subjected to harmonic excitations or stationary random excitations. A finite element model is used to describe the dynamic performances of the CLD structure. Since energy dissipation arises only from the viscoelastic (VEM) layer, the modulus of elasticity of the VEM layer is complex. The complex mode superposition method is employed to calculate the steady-state response of the CLD structure under harmonic excitations. According to Pseudo-Excitation Method (PEM), the vibration analysis of stationary stochastic excitations can be transformed to the analysis of harmonic excitations. The minimization of frequency response at specified one point or several points in structures are selected as optimization objective. The Solid Isotropic Material with Penalization (SIMP) method is adopted to interpolate the CLD material. The sensitivity is derived by means of the adjoint variable method which is more efficient than the direct variable method. The Method of Moving Asymptote (MMA) is used to search the optimal layout of CLD material on structures. Numerical examples are given to illustrate the efficiency and verification of the proposed approach.