Journal of Theoretical
and Applied Mechanics

51, 2, pp. 287-296, Warsaw 2013

Application of higher order Hamiltonian approach to nonlinear vibrating systems

Hassan Askari, Zia Saadat Nia, Ahmet Yildirim, Mohammed K. Yazdi, Yasir Khan
The higher order Hamiltonian approach is utilized to elicit approximate solutions for two nonlinear oscillation systems. Frequency-amplitude relationships and the model of buckling of a column and mass-spring system are scrutinized in this paper. First, second and third approximate solutions of examples are achieved, and the frequency responses of the systems are verified by exact numerical solutions. According to the numerical results, we can conclude that the Hamiltonian approach is an applicable method for solving the nonlinear equations, and the accuracy of this method in the second and third approximates is very high and reliable. The achieved results of this paper demonstrate that this method is powerful and uncomplicated for solving of sophisticated nonlinear problems.
Keywords: higher order Hamiltonian approach; Duffing equation; analytical solutions