Free vibration and flexural-torsional stability analyses of axially functionally graded tapered thin-walled beam resting on elastic foundation

The thin-walled beams are widely adopted in different structural components ranging from civil engineering to aeronautical applications due to their conspicuous characteristics. A slender thin-walled beam loaded initially in compression may buckle suddenly in flexural–torsional mode since its torsional strength is much smaller than bending resistance. In this paper, flexural-torsional stability and free vibration analyses of axially functionally graded tapered I-beam resting on Winkler elastic foundation are assessed. Considering the coupling between the flexural displacements and the twist angle, the motion equations are derived via Hamilton’s principle in association with Vlasov’s thin-walled beam theory. The differential quadrature method is applied to solve the system of differential equations and to acquire the critical buckling loads and natural frequencies. To validate the obtained results, at first, homogeneous tapered I-beam in the absence of elastic foundation was analyzed and compared with a finite element solution using ANSYS and other available benchmarks. Afterward, the numerical outcomes for axially graded non-prismatic I-beam resting on elastic foundation are reported in graphical form to find out the impacts of axial load position, beam’s length, end conditions, web and flanges tapering ratio, material gradient index, Winkler parameter and spring position on the non-dimensional buckling loads and vibration frequencies.