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讨论了敷设阻尼材料的薄板结构考虑瞬态响应时阻尼材料层的最优布局问题。基于SIMP方法构造人工阻尼材料惩罚模型和结构拓扑优化模型,以阻尼材料的相对密度作为设计变量,在给定阻尼材料用量的条件下,最小化结构瞬态位移响应的时间积分。由于结构整体呈现非比例阻尼特性,采用逐步积分法对结构的振动方程进行求解。通过伴随变量法得到目标函数对设计变量的灵敏度表达式,在此基础上采用基于梯度的移动渐近线方法求解。数值算例验证了优化模型与算法的合理性和有效性。
The optimal layout of the damping material layer considering the transient response of the sheet structure of the damping material is discussed. Based on the SIMP method, the artificial damping material model and structural topology optimization model are constructed. With the relative density of the damping material as the design variable, the time integral of the transient response of the structure is minimized given the amount of damping material. Due to the non-proportional damping characteristic of the whole structure, the vibration integral equation of the structure is solved by the step-by-step integral method. The sensitivity expression of the objective function to the design variables is obtained by the method of concomitant variables. Based on this, a gradient-based moving asymptotic method is used to solve the problem. Numerical examples demonstrate the rationality and effectiveness of the optimization model and algorithm.