关键词: 阻尼板, 差值型目标函数, 双线性材料插值, 拓扑优化

Abstract: Aimed to reduce vibrations and weights， a dynamics optimization method of damping plates was proposed. An optimization model of damping plates was presented taking the difference between a moving constant and the modal loss factor as objective function， density of damping layers elements as design variables， the volume usage of damping materials and the modal frequencies as constraints. A convex approximation function for objective function was provided with sequential convex programming method， and the Lagrange multiplier method was employed to solve the function so that a globally optimized damping layer layout was obtained. The sensitivity of objective function to design variables was derived using the relation of the modal loss factor and modal strain energy， and the iterative formulas of these variables were derived from K-T condition. The bilinear interpolation functions were used to punish the variables to make them converge to 0 or 1. The optimization programs were programmed and implemented for a cantilever damping plate. It is shown that the 1st order modal loss factor increases 52.29% and the proportion of gray element is as 1.78%， when the volume usage of damping materials is limited to 50%. Better vibration suppression property of the optimized plates is demonstrated by harmonic response analysis. The optimized damping layout from bilinear interpolation may make full use of the energy dissipation of damping materials and reduce the number of gray damping elements largely. 

Key words:  , damping plate, differential target function, bilinear material interpolation, topological optimization