Natural frequencies and critical loads of functionally graded single span beams resting on winkler’s elastic foundation

Abstract

Natural frequencies and critical loads of functionally graded single span beams resting on Winkler’s elastic foundation with general boundary conditions are presented in this paper. The analytical model of the beam is described by using the first order shear deformation theory, however, the transverse shear stress is derived from expression of the normal stress and equilibrium equation and thus, its shear correction factor is then obtained analytically. The effective material properties of the beam are assumed to follow simple power law form. The governing equation of motion of the beam is derived based on Lagrange’s equations with specific boundary conditions satisfied with the Lagrange’s multipliers. Comparisons between the results of present study with available results in the literature show a good agreement. In addition, parametric analysis is carried out, including material distribution, boundary conditions and axial load as well as foundation factor and slenderness ratio.