Layout optimization of multi-type resonators using frequency-dependent fictitious grounded spring

In this study, the layouts of multiple types of resonators are optimized within a multi-material topology optimization framework to maximize damping performance in multiple vibration modes of thin plates. The optimized configurations are validated experimentally. Each resonator consists of a metallic mass embedded at the tip of a rubber cylinder. To maximize resonator damping, two conditions must be satisfied. The resonators must be placed at vibration antinodes, and their natural frequencies must be tuned to those of the entire system, namely the combined system of the thin plate and the attached resonators. Because thin plates are lightweight, modifications in resonator layout readily alter both the mode shapes and the natural frequencies of the entire system. Consequently, identifying a layout that simultaneously satisfies displacement and frequency tuning requirements is nontrivial. To overcome this difficulty, a novel fictitious grounded spring element is introduced to represent the damping of the resonators. Displacement dependence is modeled by grounded springs. Frequency dependence is incorporated into the spring modulus to capture the resonators’ resonance. In the optimized layouts, resonators associated with each target mode are distributed at the corresponding antinodes, and the natural frequencies of the entire system are tuned accordingly. Experimental results confirm substantial improvements in damping performance for all targeted modes. By maximizing the system damping represented through the grounded springs, both displacement and frequency tuning requirements are satisfied without explicitly incorporating them into the objective function. The satisfaction of these conditions through an implicit procedure indicates the high generality of the proposed method.