Topology optimization of periodic microstructures for enhanced dynamic properties of viscoelastic composite materials

We present a topology optimization method for the design of periodic composites with dissipative materials for maximizing the loss/attenuation of propagating waves. The computational model is based on a finite element discretization of the periodic unit cell and a complex eigenvalue problem with a prescribed wave frequency. The attenuation in the material is described by its complex wavenumber, and we demonstrate in several examples optimized distributions of a stiff low loss and a soft lossy material in order to maximize the attenuation. In the examples we cover different frequency ranges and relate the results to previous studies on composites with high damping and stiffness based on quasi-static conditions for low frequencies and the bandgap phenomenon for high frequencies. Additionally, we consider the issues of stiffness and connectivity constraints and finally present optimized composites with direction dependent loss properties.