Effect of the tetra-chiral auxetic cell and layer geometries on the thermomechanical vibration response of magneto-electro-elastic smart sandwich nanoplates

Abstract This work investigates the thermomechanical vibration response of magneto-electro-elastic (MEE) smart sandwich nanoplates incorporating a tetra-chiral auxetic core. The analysis is performed within the framework of nonlocal strain-gradient elasticity combined with a four-variable refined shear deformation theory, enabling the simultaneous consideration of size-dependent effects, geometric chirality, and multi-field coupling. The studied configuration consists of a porous tetra-chiral auxetic core bonded to piezo-electro-magnetic face layers and subjected to thermal loading together with external electric and magnetic potentials. The effective elastic properties of the tetra-chiral auxetic core are evaluated by a unit-cell approach. The governing equations of motion are derived via Hamilton’s principle and solved analytically by Navier’s method. The model accuracy is verified through comparisons with the previously published results. A detailed parametric investigation is conducted to examine the effects of the auxetic geometric parameters, core-to-face thickness ratios, face-layer material composition, applied electric and magnetic fields, and nonlocal length-scale parameters on the fundamental vibration characteristics of the proposed smart sandwich nanoplates. The results indicate that the magnetic loading and strain-gradient effects enhance structural stiffness and stability, whereas the electric potential and nonlocal parameter introduce softening. Overall, the tetra-chiral auxetic cores provide an efficient mechanism for tuning and controlling the vibration behavior of smart sandwich nanoplates operating in coupled thermal and multi-field environments.