A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches |
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| Institution: | 1. Freiburg Materials Research Center FMF, Stefan-Meier-Str. 21, D-79104 Freiburg, Germany;2. Institute for Macromolecular Chemistry of the University of Freiburg, Stefan-Meier-Str. 31, D-79104 Freiburg, Germany;1. Nanomedicine and Nanobiology Research Center, Shiraz University of Medical Sciences, Shiraz, Iran;2. Department of Nanomedicine, School of Advanced Medical Sciences and Technologies, Shiraz University of Medical Sciences, Shiraz, Iran;3. Department of Medical Physics, School of Medicine, Shiraz University of Medical Sciences, Shiraz, Iran;1. Key Laboratory of Coal Science and Technology of Shanxi Province and Ministry of Education, Taiyuan University of Technology, Taiyuan 030024, China;2. College of Environmental Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China |
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| Abstract: | This paper intends to promote the application of modern analytical approaches to the governing equation of transversely vibrating quintic nonlinear beams. Four new studied methods are Stiffness analytical approximation method, Homotopy Perturbation Method with an Auxiliary Term, Max–Min Approach (MMA) and Iteration Perturbation Method (IPM). The powerful analytical approaches are used to obtain the nonlinear frequency–amplitude relationship for dynamic behavior of vibrating beams with quintic nonlinearity. It is demonstrated that the first terms in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a numerical example is conducted to verify the integrity of the asymptotic methods. |
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| Keywords: | Iteration perturbation method Stiffness analytical approximation method Homotopy perturbation method with an auxiliary term Max–min approach Quintic non-linear beam |
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