Symmetry effect on the dynamic behaviors of sandwich beams with periodic face sheets

Abstract

We investigate theoretically and demonstrate experimentally, the effect of material and geometric periodicity in face sheets on the overall dynamics of sandwich beams. By treating the two face sheets and core as separate entities using the classical beam theory (CBT), in conjunction with Bloch’s theorem, and solving the governing equations with the transfer matrix method (TMM) and the generalized differential quadrature method (GDQM), we obtain a low-frequency total bandgap in which both transverse and longitudinal waves are blocked in sandwich beams with glide-reflected (GR) face sheets. On the other hand, only partial bandgaps blocking either transverse or longitudinal waves are present in the ones with mirror-reflected (MR) face sheets. Furthermore, a combination of full-scale finite element method (FEM) simulations and experimental characterization provide unequivocal evidence of these phenomenal wave features, as well as the accuracy of our theoretical results via defining separate displacement fields in comparison with effective periodic Timoshenko beam models. Our study indicates new mechanisms to suppress low-frequency elastic waves by tuning face sheet symmetry. Our explanation of wave behaviors from a structural symmetry point of view also provides a more comprehensive understanding of the symmetry effect on wave propagation in quasi-one-dimensional structures at large.