Vibration and buckling analysis of double-functionally graded Timoshenko beam system on Winkler-Pasternak elastic foundation

Abstract

To acquire exact solutions of double-functionally graded Timoshenko beam system on Winkler-Pasternk elastic foundation, which are benchmarks of double-beam systems in the field of engineering, motion differential equations of double-beam system are derived using Hamilton’s principle. In this paper, the exact dynamic stiffness matrix of double-functionally graded Timoshenko beam system on Winkler-Pasternak under axial loading are established and the damping of the connecting layer is also taken into consideration. The exact natural frequency and buckling load are obtained using Wittrick-William algorithm. To comprehensively analyze dynamic characteristics of double beam system, the effect of gradient parameter, foundation parameters, axial loading and connecting stiffness on the frequency and buckling load is compared, and the influence of damping factor is also investigated. Finally, dynamic response of double-beam system is studied using Fourier transformation.