Optimal design of laminated plate for minimizing frequency response based on discrete material model and mode reduction method

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.