Design of microstructures of viscoelastic composites for optimal damping characteristics

An inverse homogenization problem for two-phase viscoelastic composites is formulated as a topology optimization problem. The effective complex moduli are estimated by the numerical homogenization using the finite element met hod. Sensitivity analysis shows that the sensitivity calculations do not re quire the solution of any adjoint problem. The objective function is define d so that the topology optimization problem finds microstructures of viscoe lastic composites which exhibit improved stiffness/damping characteristics within the specified operating frequency range. Design constraints include volume fraction, effective complex moduli, geometric symmetry and material symmetry. Several numerical design examples are presented with discussions on the nature of the designed microstructures. From the designed microstruc tures, it is found that mechanism-like structures and wavy structures are f ormed to maximize damping while retaining stiffness at the desired level. ( C) 2000 Published by Elsevier Science Ltd. All rights reserved.