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 e€ective complex moduli are estimated by the numerical homogenization using the ®nite element method. Sensitivity analysis shows that the sensitivity calculations do not require the solution of any adjoint problem. The objective function is de®ned so that the topology optimization problem ®nds microstructures of viscoelastic composites which exhibit improved sti€ness/damping characteristics within the speci®ed operating frequency range. Design constraints include volume fraction, e€ective 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 microstructures, it is found that mechanism-like structures and wavy structures are formed to maximize damping while retaining sti€ness at the desired level.