mehdi akbarzade - PHD Student, Mechanical Engineering, Ferdowsi University of Mashhad, Iran
anoushirvan farshidianfar - Professor, Department of Mechanical Engineering, Ferdowsi University of Mashhad, Iran
hojat nadaf shargh - MSC Student, Aerospace Structure Engineering, Ferdowsi University of Mashhad, Iran

Nonlinear oscillator models have been widely used in many areas of physics and engineering such as mechanical and structural problems. In this paper, different analytical methods are applied to the strongly nonlinear oscillator with high nonlinearity. Periodic solutions are analytically verified and consequently the relationship between the natural frequency and the initial amplitude is obtained in an analytical form. According to this article on comparative study of four analytical method to solve the equations of ordinary differential equation vibration beam is focused. The obtained results are compared with each other and exact solution. Accuracy and validity of the proposed techniques are then verified by comparing the numerical results obtained based on these methods and exact integration method. These methods are Coupled Homotopy Variational Formulation, Integral Iteration Method, Amplitude Frequency Formulation and Variational Approach. Finally, present analytical procedures is evaluated in comparison with numerical calculation methods

Analytical Methods, Nonlinear Oscillation, Periodic Solution, Natural Frequency