Research on Damping Material Topological Layout of Constrained Damping Plate for Structural Anti-vibration

To lay foundations of anti-vibration design of structure, the optimization of constrained damping plates is studied. Based on mechanics constitutive relation of constrained damping structure and Hamilton principle, a differential dynamical equation for the constrained damping plates is derived. A mathematical model is built to maximize modal damping ratio with least damping material volume and structure modal frequency as constraint condition. Structural modal damping ratio formula is derived to give iteration direction for structural optimization. The sensitivity equation in frequency constraints is introduced. To verify evolutionary optimization algorithm for the model, a rectangular plate of numerical example is provided. After optimization, structural modal damping ratio of the plate increases, the modal frequency varies little, and according to the element number deleting damping materials of optimization methods, the damping ratio can show a trend of decline, the frequency increases dramatically. For single order modal optimization, specific order response peak are decreased. However, the composite vibration damping structure effect is better when the structure of compound multimodal optimization. The research shows that better comprehensive vibration effect can be obtained when maximizing structure composite modal damping ratio during the damping structural optimization iteration process.