Effect of Foam Faces and Butterfly Auxetic Core on Sandwich Nanoplate Vibration and Buckling

ABSTRACT

This research examines the thermomechanical vibration and buckling properties of a three‐layer sandwich nanoplate, which consists of foam face layers and a butterfly‐shaped auxetic core. The formulation is developed based on Hamilton's principle and higher‐order shear deformation theory (HSDT), utilizing an analytical Navier‐type solution to derive the governing responses. The proposed model integrates nonlocal elasticity to address size‐dependent effects at the nanoscale and considers temperature‐dependent behavior. A detailed parametric study is performed to assess the effects of butterfly core geometry, foam material properties, nonlocal parameters, and nanoplate thickness on vibration frequencies and critical buckling loads. The findings indicate that the configuration of the auxetic core and the thermomechanical properties of the foam layers are essential in shaping the structural response, especially at high temperatures. The interaction between nonlocal effects and geometric parameters results in significant deviations in stability behavior, underscoring the necessity of scale‐dependent modeling. The results show that temperature, nonlocal effects, material length scale, and Al ₂ O ₃ content significantly influence the vibration and thermal stability of the proposed sandwich nanoplate. The findings offer insights into the design of advanced sandwich nanoplates that exhibit improved thermal stability and mechanical performance, establishing a framework for future nano‐engineered structural applications.