Solution of the Characteristic Frequency Equations of Levy-type Sandwich Panels with Auxetic Honeycomb Core based on the Improved Reddy’s Third-order Theory

In this paper, the equations of motion are derived based on the improved third-order shear deformation theory with shear correction factors to investigate the free transverse vibration of rectangular sandwich panels having Levy boundary conditions. Reddy’s third-order theory devote a parabolic distribution for transverse shear stress along the thickness of plate and is suitable for thin to relatively thick single-layer plates. However, for the case of sandwich panels, in Reddy’s theory, the continuity condition of inter-laminar surfaces is not satisfied. This defect is improved by adding shear correction factors only in the energy viewpoint. Sandwich panel consist of isotropic facesheets and an auxetic honeycomb core making from the same facesheet’s material. The effective properties of honeycomb core were derived from the newest revised Gibson model based on Timoshenko beam theory. For validation, some comparison study is carried out to compare the current solution with the results reported in literature and also finite element ANSYS software.The results of validation indicates the important effect of suitable shear correction factors to decrease error percentage. Finally, the effect of boundary conditions, panel thickness to length ratio, core thickness to panel thickness ratio and geometrical parameters of the reentrant hexagon cell on the non-dimensional natural frequencies were investigated and the results were presented in some graphs.