2016 International Symposium on Nanofluid Heat and Mass Transfer in Textile Engineering and 5th International Symposium on Nonlinear Dynamics

Journal: Nonlinear Science Letters A
(ISSN 2519-9072(Online), ISSN 2076-2275 (Print))          Vol. 2 No. 1
Free Vibration Analysis of Strongly Nonlinear Generalized Duffing Oscillators using He’s Variational Approach & Homotopy Perturbation Method
D. Younesian, H. Askari, Z. Saadatnia, M. K. Yazdi
School of Railway Engineering, Iran University of Science and Technology, Tehran- Iran
Abstract: Homogenous generalized Duffing equation is solved and discussed employing He’s Variational Approach (HVA) and He’s Homotopy Perturbation Method (HPM) in this paper. For any arbitrary odd-type exponential nonlinearity, natural frequency of the system is obtained as a function of the initial amplitude in an analytical form. Numerical simulations are then carried out and accuracy, validity and simplicity of the proposed techniques are verified by comparing the results obtained based on the HVA, HPM and Exact method. It is proved that first order approximate solutions based on HVA and HPM are of a high accuracy even for very strong nonlinearities.

Keywords: Nonlinear Vibration; Generalized Duffing Equation; He’s Variational Approach; He's Homotopy Perturbation.

Biographical Notes:


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