TY - JOUR ID - 3403 TI - An Efficient Concept for Non-dimensionalizing the Duffing Equations Based on the Parameterized Perturbation Method JO - Scientia Iranica JA - SCI LA - en SN - 1026-3098 AU - Afsharfard, Aref AU - Farshidianfar, Anooshiravan AD - Department of Mechanical Engineering, University of Torbat-e-Heydarieh, Torbat-e-Heydarieh, Iran AD - Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran Y1 - 2013 PY - 2013 VL - 20 IS - 5 SP - 1455 EP - 1463 KW - Nonlinear ordinary differential equation KW - Perturbation method KW - Characteristic distance KW - Non-dimensionalization DO - N2 - In this paper, ongoing studies to investigate nonlinear ordinary differential equations (ODE) are extended by presenting a new concept in non-dimensionalization process. This concept is illustrated with a practical example of nonlinear ODEs, which cannot reliably solve using the numerical methods. In this paper, two perturbation techniques are used to solve the problem. Effect of varying the dimensionless initial displacement on the accuracy of solution is investigated. It is shown that if the process of non-dimensionalizing is done appropriately, the calculated results will be extremely accurate. Moreover, a new concept called ″behavior of results″ is proposed to find accurate results. UR - https://scientiairanica.sharif.edu/article_3403.html L1 - https://scientiairanica.sharif.edu/article_3403_0dcba553b29e8ac00054ee58fa443664.pdf ER -