Auxetic honeycomb core layer effect on vibrations of annular plates based on shear deformation theory

Light composite materials such as auxetic honeycomb structures offer a unique combination of strength, lightweight, and durability, making them ideal for a wide range of industrial and structural applications. Consequently, it is crucial to study the effect of these materials on the dynamic behavior of structures. In this study, an analytical solution based on the multiple-scale method has been proposed to solve equations of motion of a multilayer axisymmetric annular plate. The plate includes two top and bottom isotropic layers and one auxetic honeycomb core layer. By considering both radial and transverse deflections, the governing equations are derived based on the first-order shear deformation theory. The radial and transverse frequencies of the plate are determined from the order zero of equations and a correction coefficient for each frequency has been extracted from the order one and solvability conditions. The response of the plate under harmonic transverse excitation has been determined analytically and by conducting a parametric study, the effect of different geometrical and mechanical parameters on the free and forced vibration responses has been studied. It is observed that employing a honeycomb core in the multilayer plate allows us to significantly decrease the plate weight while the dynamic response and the frequencies remain nearly the same or vary slightly. The results are validated by comparing them with the finite element method and some other references.