Free Vibration and Buckling Analysis of Sandwich Panels with Flexible Cores Using an Improved Higher Order Theory

In this paper, the behavior of free vibrations and buckling of the sandwich panel with a flexible core was investigated using a new improved ‎high-order sandwich panel theory. In this theory, equations of motion were formulated based on shear stresses in the core. First-order shear deformation theory was ‎applied for the procedures. In this theory, for the first time, incompatibility problem of velocity and acceleration field existing in Frostigʹs ‎first theory was solved using a simple analytical method. The main advantage of this theory is its simplicity and less number of equations than the ‎second method of Frostigʹs high-order theory. To extract dynamic equations of the core, three-dimensional elasticity theory was utilized. ‎Also, to extract the dynamic equations governing the whole system, Hamiltonʹs principle was used. In the analysis of free vibrations, the ‎panel underwent primary pressure plate forces. Results demonstrated that, as plate pre-loads got closer to the critical buckling loads, the natural frequency of the panel tended zero. The results obtained from the present theory were in good correspondence with the ‎results of the most recent papers.