On the free vibration of sandwich panels with a transversely flexible and temperature-dependent core material – Part I: Mathematical formulation

The free vibration analysis of sandwich panels with a core that is flexible and compliant in the vertical direction and with temperature-dependent mechanical properties is presented in two parts. The first part presents the mathematical formulation while the second deals numerically with the effects of the degrading properties of the core on the free vibration response. The analysis is based on the high-order sandwich panel theory approach (HSAPT), and the equations of motions along with the appropriate boundary conditions are derived using the Hamilton’s principle. The study investigates the role of increasing temperature, through the degradation of the mechanical properties of the core, on the free vibration response of structural sandwich panels. The mathematical formulation uses two types of computational models. At first, following the HSAPT approach, the unknowns include the displacements of the face sheets as well as the shear stress in the core. Secondly, it is assumed that the through-thickness distributions of the vertical and horizontal core displacements can be represented as polynomials, following the results of the HSAPT static case, and the effect of the variable mechanical properties are implemented directly.