Design principles for energy dissipation in viscoelastic network metamaterials

Mechanical energy dissipation in networked materials is crucial for applications such as vibration isolation and impact protection, yet identifying optimal dissipative architectures in large disordered truss networks is computationally demanding with conventional methods. This study presents an efficient graph Laplacian-based spectral framework for viscoelastic truss networks, which accurately retains the full continuum dynamics of each rod and scales the problem size with the number of joints. The research investigates how the redistribution of cross-sectional areas within a network influences energy dissipation, revealing that random redistribution generally lowers dissipation compared to a uniform baseline, while gradient-based optimization produces complex architectures determined by the attenuation length of the material. The findings show that the optimal mass distribution near the driving frequencies relates to the attenuation length scale and remains consistent independently of boundary conditions at small attenuation lengths. These results encourage further exploration of design principles based on dissipation length scales in more intricate disordered architectures and establish an efficient computational framework for large-scale structural investigations.