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A two-level procedure for the global optimization of the damping behavior of composite laminated plates with elastomer patches

This work concerns a two-level procedure for the global optimum design of hybrid elastomer/composite modular structures. The goal of the procedure is the maximization of the first Nf modal loss factors of the structure, satisfying mechanical constraints on the weight and on the bending stiffness, feasibility constraints on the admissible moduli for the constitutive laminates, along with geometric constraints on the positions of the viscoelastic patches. At the first level of the procedure, the optimization of the damping behavior of the structure is carried out: the optimization variables at this stage are the number of elastomer patches (modules), as well as their geometrical parameters (position, thickness and diameter), along with the material and geometric parameters of the composite laminated structure (elastic moduli, thickness of the laminate). The composite structure supporting the elastomer patches is thus optimized using a free-material approach, via the polar representation of 2D elasticity, and the second level of the optimization consists in finding the laminate stacking sequence satisfying the optimal elastic moduli and thickness issued from the first step. The method is able to automatically determine the optimal number of modules and it does not need the introduction of any simplifying assumption. The proposed approach relies on one hand, on the application of the well-known Iterative Modal Strain Energy (IMSE) method for the evaluation of the dynamic response of the structure, and on the other hand on the use of the polar formalism for the representation of the elastic anisotropic behavior of composite laminates as well as of a genetic algorithm as optimization tool to perform the solution search. We will illustrate the application of our approach to the optimization of the damping behavior of a rectangular composite plate with a discontinuous aperiodic distribution of viscoelastic material. The numerical results show the effectiveness of the proposed strategy.