Free vibration analysis of elastically connected multiple-beams by using the Adomian modified decomposition method

The Adomian modified decomposition method (AMDM) is employed in this paper to investigate the free vibrations of N elastically connected parallel Euler–Bernoulli beams, which are continuously joined by a Winkler-type elastic layer. The proposed AMDM method can be used to analyze the vibration of beam system consisting of an arbitrary number of beams. By using boundary conditions the natural frequencies and corresponding mode shapes can be easily obtained simultaneously. The numerical results for different boundary conditions, beam numbers and the stiffness of the Winkler-type elastic layer are presented. It is shown that the AMDM offers an accurate and effective method of free vibration analysis of multiple-connected beams with arbitrary boundary conditions.

► A general solution for the free vibration problem of elastically connected beams is presented.
► Adomian modified decomposition method (AMDM) is used to analyze the free vibration problem.
► The proposed method can be used for general boundary conditions and arbitrary number of connected beams.
► The proposed approach proves to be computationally efficient and accurate.