Une Nouvelle théorie pour l’analyse vibratoire en flexion des poutres epaisses

Abstract

This paper presents an improved beam-theory for the bending vibratory behavior analysis of thick functionally graded (FG) beams those accounts for thickness-stretching. The number of unknowns in this theory is four, as opposed to five in the other methods. The transverse displacement can be separated into thickness-stretching, bending, and shear components using a hyperbolic function as an expression. There is a decrease in the number of governing equations as a result of the reduction in unknowns. Without the need for a shear correction factor, the boundary conditions at the top and bottom of the FG beam faces are satisfied. Effective properties of FG beam material vary constantly in the thickness direction based on the volume percentage of the constituent, as per a distribution law. The equations of motion for a supported FG beam under transverse load are derived from Hamilton's principle and are solved by assuming the Navier's solution type. The obtained numerical results are exposed and thoroughly analyzed to confirm the validity of the current theory and demonstrate the impact of normal deformation, which is largely ignored in beam theories, on the vibratory responses of FG beams. It also proves the influence of material composition, geometry, and shear deformation on these responses. We compare the reported results with various beam theories' predictions. We find that the current theory for predicting the bending and free vibration responses of FG beams is straightforward and accurate