STUDY ON FREE VIBRATION OF A ۲-D STRUCTURALFRAME CONNECTED TO THE NONLINEAR SPRINGSUSING MODIFIED HOMOTOPY PERTURBATION METHOD

In this paper, we investigate and apply the Homotopy Perturbation Method as one of theapproximate analytical techniques to solve the equation of free vibration of a ۲-D structural frameconnected to the nonlinear springs. In nonlinear dynamical systems, for large values of time andvibration amplitude, the results of homotopy perturbation method are not convergent. The homotopyperturbation method can be modified for nonlinear dynamical systems. In order to solve thisproblem, we introduce a new variable and we found the convergent approximate analytical solutionfor large values of time and vibration amplitude. This modified homotopy perturbationmethod utilizes an alternative framework to capture the periodic behavior of the solution, which ischaracteristic of oscillator equations, and to give a good approximation to the true solution in a verylarge region. The current results are compared with those derived from the Hamiltonian approach inorder to verify the accuracy of the modified homotopy perturbation method. It is shown that there isexcellent agreement between the two sets of results. The modified homotopy perturbationmethod suggested in this paper is an efficient tool for calculating periodic solutions tononlinear oscillatory systems and can be extended to the other nonlinear dynamical systems andcan therefore be found widely applicable in engineering and other sciences.

کلیدواژه ها:

Free Vibration ، ۲-D Structural Frame ، Nonlinear Spring ، Approximate AnalyticalMethod ، Homotopy Perturbation Method