Nonlinear Vibration and Stability Analysis of Beam on the Variable Viscoelastic Foundation

Abstract

The aim of this study is the investigation of the large amplitude deflection of an Euler-Bernoulli beam subjected to an axial load on a viscoelastic foundation with the strong damping. In order to achieve this purpose, the beam nonlinear frequency has been calculated by homotopy perturbation method (HPM) and Hamilton Approach (HA) and it was compared by the exact solutions for the different boundary conditions such as simple-simple, clamped-simple and clamped-clamped which showed a good accuracy in results. In addition, to find the deflection of the nonlinear Euler-Bernoulli beam, the problem has been solved based on homotopy perturbation method and modified differential transform method (MDTM) and finally, the results were compared by Rung-Kutta exact solutions. The derived deflection results by two mentioned methods had a good agreement with the exact RK4 solutions. By considering the paper results, buckling force is increased for each case permanently by increase in the boundary rigidity for a constant value of system amplitude (A). As a final comparison, in based on paper results, the buckling force is arisen by increasing the system amplitude for each case.