Vibration analysis of porous sandwich beam reinforced by graphene platelets/graphene origami auxetic metamaterials using sinusoidal shear deformation theories in thermal environment

The stiffness and vibration characteristics of the face sheets strongly influence the mechanical performance of sandwich beams. Reinforcing these layers with advanced nanomaterials has been demonstrated to enhance stiffness and effectively suppress vibrations. Recently, graphene-based metamaterials have attracted attention due to their exceptional mechanical properties and tunable behavior, enabling the design of lightweight, high-stiffness, and vibration-resistant structures for critical engineering applications. This work presents a benchmark study for the vibration behavior of a sandwich beam composed of composite face sheets reinforced with graphene platelets (GPL) and graphene origami auxetic metamaterials (GOAM), as well as porous or tetra-chiral aesthetic cores, in which it exhibits a zero Poisson’s ratio. The innovations of this work include the investigation of graphene origami auxetic metamaterials as reinforcement and a comparison of their effect with that of graphene platelets on the vibrations of a sandwich structure. Another innovation of this work is the investigation of two types of sinusoidal displacement fields and their comparison in terms of effect on the vibrations of sandwich structures. In addition, another novelty of the present study is the comparison of six sandwich structures with various cores and reinforcements in the face sheet. Hamilton’s principle is used to derive the governing equations of motion, which are then developed using displacement fields based on two types of sinusoidal shear deformation theories. Also, these equations are solved using trigonometric functions for various boundary conditions, such as clamped and simply supported at two ends. Various porosity patterns are considered in the study, although reinforcement is only used for the face sheets. A thorough parametric analysis shows how the Young’s modulus of the reinforcing material, wave number, length, and width of graphene platelets, temperature change, porosity type and distribution, core-to-face thickness ratio, and aspect ratio impact the natural frequencies. The findings show that fundamental natural frequencies decline as aspect ratio, porosity, and core-to-face thickness ratio increase. In contrast, distribution 2 of porous core generates greater frequencies than the 1 and 3 patterns. An increase in temperature and the folding degree (HGR) of graphene origami auxetic metamaterials reduces natural frequencies, while this result is observed for the weight% of GOAM nanoparticles (WGOAM ). Predicted frequencies are demonstrated to be significantly impacted by the difference between the two sinusoidal displacement fields. These findings indicate that graphene origami auxetic metamaterials, with their tunable Young’s modulus controlled by folding degree and temperature, can enable smart, adaptive, and high-performance sandwich structures, offering transformative potential for vibration-resistant and lightweight applications. These results demonstrate the importance of nanomaterial reinforcement and well-designed porosity in enhancing the dynamic performance of sandwich beams, providing valuable insights for creating lightweight, highly stiff, and vibration-resistant structures in civil, automotive, and aerospace engineering applications. Vibration analysis of a sandwich beam based on two types of sinusoidal shear deformation theories is studied. Based on a micromechanical model including Halpin-Tsai and the rule of mixture, GPL as reinforcement is considered. The GOAM as reinforcement by considering the folding degree (HGR), weight fraction, and temperature is investigated. Three types of porous core with distributions 1, 2, and 3 are employed. A tetra-chiral aesthetic material with zero Poisson’s ratio for the core of a sandwich beam is used.