2026 Sarpangala Viscoelastic Energy Dissipation

Mechanical energy dissipation in networked materials is relevant for applications ranging from vibration isolation to impact protection. The objective of this study is to develop an efficient framework for analyzing viscoelastic truss networks, focusing on the architecture that optimizes energy dissipation. We introduce a graph Laplacian-based spectral method that retains the full continuum dynamics of each rod and scales with the number of joints, thus circumventing the computational limitations of conventional finite element methods. Our results reveal that redistributing cross-sectional areas within a truss network often reduces dissipation compared to a uniform distribution, while gradient-based optimization produces complex architectures guided by the intrinsic attenuation length of the material. This framework allows us to demonstrate that the optimal mass distribution decays from a driven joint in the network, adhering to the attenuation length scale, and that at small scales, the optimal designs are resilient to boundary conditions. These findings lay the groundwork for future investigations into dissipation length scale-based design principles for more intricate disordered structures, providing a robust computational tool for exploring such materials at a larger scale.