Abstract This paper investigates the wave propagation characteristics of sandwich nanoplates with a novel butterfly‐shaped auxetic core and graphene‐reinforced functionally graded surface layers in a foam structure. Considering thermal effects and variations in the foam void ratio, the governing equations of motion are derived using sinusoidal higher‐order shear deformation theory and NSGT. A parametric study is carried out to determine the effects of the auxetic butterfly core topology, foam distribution modes, material grading index of the face layers, and nanoscale effects on the phase velocity, group velocity, and wave frequency. The results show that the auxetic core layer significantly affects the wave propagation properties in sandwich nanoplates and GRPL, foam, and FGM symmetric face layer structures. In particular, the emerging auxetic butterfly configuration as a metamaterial system addresses the fundamental performance of the structure where the flexural, longitudinal, and shear transmission properties of the sandwich nanoplate vary. The analysis also shows that face layers with different foam structures and material distribution properties affect the wave propagation properties of sandwich nanoplates.
Kafali et al. (Sun,) studied this question.