This paper builds an integrated optimization model for the laminated plate to suppress the structural frequency response in a given frequency band, where the objective is to minimize the dynamic compliance of the structure excited by an external sinusoidal mechanical load with given amplitude and frequency range. The dynamic response analysis of the laminated structure is performed via a finite element model based on the first-order shear deformation theory. Therein, the Heaviside penalization of the discrete material optimization method and the solid isotropic material with penalization scheme are separately employed to optimize the fiber orientation and the layout of the damping material. Meanwhile, mode reduction method and a decoupled sensitivity analysis are incorporated for efficient frequency and sensitivity analysis to reduce the heavy computational burden from many frequency steps in each iteration, a large number of freedom degrees and plenty of design variables as well as maintain high accuracy. And the method of moving asymptotes is used to solve the optimization problem. And three numerical examples including the efficiency and accuracy demonstration, single load and multi-load case with separate and integrated optimization are presented to verify the validity and advantage of the proposed model.

本文建立了层压板的集成优化模型，以抑制给定频带内的结构频率响应，其目标是最小化由具有给定幅度和频率范围的外部正弦机械载荷激发的结构的动态柔量。层合结构的动力响应分析是通过基于一阶剪切变形理论的有限元模型进行的。其中，分别采用离散材料优化方法的Heaviside惩罚和惩罚方案的固体各向同性材料来优化纤维取向和阻尼材料的布局。同时，结合模态缩减方法和解耦灵敏度分析进行高效的频率和灵敏度分析，以减少每次迭代中多个频率步长、大量自由度和大量设计变量的繁重计算负担，并保持较高的精度。并采用移动渐近线的方法求解优化问题。并给出了效率和精度论证、单载荷和多载荷情况下单独和集成优化的三个数值算例，以验证所提出模型的有效性和优势。