Vibration and stability of a double-beam system interconnected by an elastic foundation under conservative and nonconservative axial forces

• The flutter and divergence instability of the double-beam system are investigated.
• Adomian modified decomposition method is used to analyze the stability problem.
• The influence of nonconservative parameters on the critical loads is discussed.
• The boundary conditions effect on the dynamic stability is graphically represented.

The Adomian modified decomposition method (AMDM) is employed in this study to investigate the free vibration and stability of a cantilever double-beam system, which is continuously joined by a Winkler-type elastic layer. The free end of each beam is restrained by a translational spring and subjected to a combination of compressive axial and follower loads. Based on the AMDM, the governing differential equations for the double-beam system are represented as a recursive algebraic equation. By using boundary condition equations, the natural frequencies and corresponding mode shapes can be easily obtained simultaneously. The double-beam system becomes unstable in the form of either divergence or flutter with the increasing loads. Then the critical loads are discussed under different boundary conditions and the nonconservative parameters. Furthermore, the effect of the value of the spring stiffness on the critical loads for either flutter or divergence instability of the double-beam systems is studied.