Dynamic Topology Optimization of Constrained Damping Plates considering Frequency and Temperature Characteristics Based on an Efficient Strategy

The frequency- and temperature-dependent characteristics of viscoelastic materials significantly affect the vibration response of the damped composite structures. In this paper, an efficient strategy of hybrid expansion combined with dynamic reduction is developed to solve the steady-state response of the frequency- and temperature-dependent viscoelastic structure characterized by nonproportional system, and the sensitivity analysis is carried out based on the adjoint variable method. The similarity index is defined to distinguish the correlation among different design layouts. Two instances demonstrated the validity of the proposed approach. The findings indicated that a positive compromise between accuracy and efficiency can be achieved, and the computational time can be significantly reduced while ensuring the accuracy of the results. Furthermore, it has been discovered that the excitation frequency and temperature significantly impact the optimal configuration of damping material. The effects of layer thicknesses and volume fractions on optimization designs are also further investigated.