Coupled magneto-electro-thermal buckling and vibration analysis of TPMS-based auxetic core sandwich nanoplates within the framework of HSDT and NSGT

This study examines buckling in a sandwich nanoplate. The top and bottom layers are made of piezoelectric Barium Titanate (BaTiO3) and Cobalt Ferrite (CoFe2O4), while the central core consists of a metallic TPMS-based auxetic lattice structure constructed from SUS304. The implementation of nonlocal strain gradient elasticity, in conjunction with sinusoidal higher-order deformation theories, was carried out. The equations regulating the motion of the nanosensor sandwich nanoplate were calculated using Hamilton’s principle, considering the magnetostrictive, electroelastic, and thermal properties of the piezoelectric surface plates. After that, Navier equations were solved. The sandwich nanoplate’s TPMS-based auxetic core’s geometric, nonlocal, temperature, and electric and magnetic potentials were studied. Dimensionless natural frequencies of the sandwich nanoplate were the study’s main focus. Topology, porosity, size effects, and external fields can alter auxetic TPMS-cored sandwich nanoplates’ buckling and vibration responses, according to this study. Increasing porosity (V = 0.10–0.75) lowers fundamental frequency by 52% (λ(1,1)≈8.0→3.8) and raises critical buckling temperature (ΔT ≈ 2000→2110 K), with Type II cores having the strongest thermal resistance. Nonlocal effects reduce λ(1,1) by 22% and ΔT by 30 K, whereas strain-gradient effects increase it by 38%, indicating opposing nanoscale mechanisms. High-temperature nanosensors, transducers, and nanoelectromechanical systems will be developed and deployed.