Analytical solution for imperfect functionally graded beams resting on viscoelastic foundation

Abstract

In this research the bending behavior and free vibration characteristics of imperfect functionally graded (IFG) beams are examined. The investigation incorporates cases where these beams are resting on both elastic and viscoelastic foundations. It is assumed that the IFG beam's material properties change continuously with thickness in accordance with the volume percentage of its constituent parts. The study employs a refined three-variable first-order shear deformation theory to consider kinematic relations. Hamilton's principle is employed to derive equations of motion. The development of the present theory is similar to the first-order simple shear deformation theory. With the assumption that the IFG beam is simply supported, this research presents the analytical solution. In order to showcase the precision of the developed theory, comparisons are conducted between the results derived from existing theories and present results of the proposed theory. Finally, a comprehensive discussion on the effects of span-to-depth ratio, porosity volume percentage, and viscoelastic foundations is provided.