Free Vibration Analysis of Sandwich Beams with Functionally-Graded-Cores by Complementary Functions Method

A plane vibration study of a sandwich thermal protection system insulation panel with a functionally graded core is conducted. The panel is assumed to be under plane-stress conditions and subjected to simply supported boundary conditions. The two-dimensional elasticity formulations are used to derive the equations of motion for each layer. The effects of the in-plane normal stresses as well as the shear stress are taken into consideration for all layers. Material properties of layers may vary through the transverse coordinate resulting in a pair of second-order coupled variable- coefficient governing differential equations. The governing equations are reduced to an uncoupled fourth-order differential equation, which is solved by the complementary functions method (CFM). The novelty of the present study includes the vibration analysis of functionally graded core sandwich beam using plane elasticity and implementation of CFM as the solution procedure. The influences of face sheets and core materials and the grading model on the free vibration behavior are studied. The solutions are compared with results available in the literature and those obtained from finite element software (ANSYS) for a three-layered isotropic panel to display the accuracy and efficiency of the presented method. The mode shapes dominated by vertical and horizontal displacements are also depicted. The method that is applicable for both symmetric and unsymmetric beams is shown to be accurate and efficient in the analysis of sandwich panels with a core graded in the thickness direction.