Nonclassical thermo-electro-mechanical vibration of size-dependent auxetic smart microplates reinforced with graphene origami based on quasi-3D reddy’s and modified strain gradient theories
摘要
This study presents a comprehensive nonclassical thermo–electro–mechanical formulation for the free vibration analysis of size-dependent auxetic smart microplates reinforced with graphene origami (G-Ori) metamaterials. A quasi-three-dimensional kinematic model based on Reddy’s higher-order shear deformation theory is employed to accurately capture transverse shear deformation and thickness stretching effects. To incorporate small-scale phenomena, the governing equations are derived using Hamilton’s principle within the framework of the modified strain gradient theory. The microplate is integrated with surface-bonded piezoelectric layers to enable electromechanical coupling, while the temperature-dependent effective properties of the G-Ori auxetic metamaterial are modeled by considering the effects of folding degree, weighting percentage, and layer-wise distribution patterns. An analytical Navier-type solution is developed for fully simply supported boundary conditions to determine the normalized natural frequencies. The results demonstrate that the vibrational response of the structure can be effectively tuned through geometric parameters, material gradation, intrinsic length-scale parameters, and applied electric potential, highlighting the strong interplay between mechanical, electrical, and thermal fields at micro-scales. The proposed framework provides a robust theoretical foundation for the design and optimization of advanced smart microstructures, particularly in applications such as MEMS/NEMS devices, adaptive micro-actuators, energy harvesting systems, structural health monitoring, and biomedical microsensors. Overall, the synergy between auxetic graphene origami architectures and nonclassical size-dependent mechanics offers a promising pathway toward the development of high-performance multifunctional micro-scale systems.