Vibration analysis of FG beams with a new type of gradient variation reposed on elastic foundations

This paper presents a study on the free vibrations of a new concept of functionally graded beams (FGM) resting on an elastic foundation under various boundary conditions employing the higher-order shear deformation theory (HDT). In classical FGM beam models, the variation of mechanical properties typically occurs from the top to the bottom surface. However, in this new concept, a novel variation has been proposed where the mechanical properties evolve from the exterior to the interior of the beam. This new variation is accounted for using a novel power-law mixing rule based on the constituents' volume fractions. The theoretical approach relies on the application of Hamilton's principle to derive the governing equations, which are solved using the state-space method. A parametric analysis is carried out to examine the influence of several parameters on the natural frequencies, including the power-law index, the slenderness ratio, and the Winkler and Pasternak parameters associated with the elastic foundation.