非平稳激励下薄板结构减振附加阻尼层的拓扑优化

讨论了附加阻尼层的薄板结构在非平稳随机力作用下以减振为目标的阻尼材料层的拓扑优化问题。建立了以阻尼材料的相对密度为设计变量,以结构非平稳响应位移方差最小化为目标和阻尼材料用量为约束条件的拓扑优化模型。由于结构受到非平稳随机激励作用,其随机响应可以采用时域显式法快速求解;随机响应方差对设计变量的灵敏度采用了基于伴随变量法的时域显式法进行分析,并采用优化准则法求解优化问题。数值算例验证了所提方法在非平稳随机激励作用下进行动力拓扑优化减振的可行性与有效性。

Topology optimization of attached damping layers on thin plate structures for vibration attenuation under non-stationary stochastic excitations

This paper investigates the optimal distribution of damping material on thin-plate structures under non-stationary stochastic excitation.In the topology optimization model, the relative densities of the damping material were taken as design variables, and the design objective is to minimize the structural displacement variances at specified positions under a given volume constraint of damping material.Since the structure was subjected to non-stationary stochastic force, the stochastic responses were solved rapidly based on an explicit time domain method (ETDM).The analysis of the displacement variance sensitivity was implemented by using the ETDM based on an adjoint variable method.Then the topology optimization problem was solved with an optimal criteria (OC) method.Numerical examples illustrate the feasibility and effectiveness of the proposed method for vibration attenuation of structures through dynamic topology optimization of damping layer under non-stationary stochastic excitation.