Non-linear transient vibration response of graphene origami enhanced metamaterial beams under spatially-varying temperature distributions

Abstract

Understanding the dynamic behavior of advanced materials under varying conditions is crucial for the development of resilient and efficient structural systems. This research investigates the non-linear transient response of auxetic metamaterial beams enhanced with graphene origami under spatially varying non-uniform thermal environment. Using Timoshenko beam theory with von-Kármánn type non-linear strain–displacement relations, graphene origami beams are modeled as layered structures. The equilibrium equations are solved using the Ritz method, with a focus on how different graphene origami distribution patterns, content levels, and folding degrees influence the transient response under various time-dependent forces. Non-linear motion equations are solved using the Newmark-Beta method. This study evaluates the impact of five distinct non-uniform temperature distributions, seven types of time-dependent loadings, three boundary conditions, and three configurations of graphene origami distribution on the vibration characteristics. Results indicate that parabolic temperature distributions with peak temperatures at the beam ends lead to substantially decreased dynamic deflections. This research provides valuable insights into the structural dynamics of graphene origami-enhanced metamaterial beams within complex thermal environments, highlighting the considerable influence of spatial temperature variations along the length of the beam. © 2025