A Heuristic Method to Solve Nonlinear Vibration Problems
| Autor: | Somaraju Vempaty, Satyanarayana Badeti, Srinivas Suripeddi |
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| Rok vydání: | 2018 |
| Předmět: |
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Heuristic media_common.quotation_subject Mathematical analysis Frequency drift Zero (complex analysis) 02 engineering and technology 021001 nanoscience & nanotechnology 01 natural sciences Term (time) 010101 applied mathematics Amplitude Order (group theory) 0101 mathematics 0210 nano-technology Engineering (miscellaneous) Homotopy analysis method Mathematics media_common |
| Zdroj: | National Academy Science Letters. 41:225-231 |
| ISSN: | 2250-1754 0250-541X |
| DOI: | 10.1007/s40009-018-0646-x |
| Popis: | We propose a heuristic method to obtain the solutions, at least to the lowest order, for linear and nonlinear vibration problems governed by a small parameter ɛ. For a linear or nonlinear oscillator, we assume a perturbation expansion for the dependent variable u(t, ɛ) as in regular perturbation method, but choose a solution of the form a(t) cos (ω0t + β(t)) for the lowest order term u0 to take care of the frequency–amplitude interaction. It is then in general true that the frequency correction to lowest order is O(ɛ2) or O(ɛ) depending on whether a′(t) = O(ɛ) or zero respectively. This physical feature is made use of to obtain directly the secular terms in O(ɛ) and O(ɛ2) governing equations and hence obtain the amplitude a(t) and frequency drift β(t) to at least lowest order. The efficacy of the method is tested and illustrated with several examples. Also numerical values obtained using this method are compared with the numerical solution obtained with Differential transform method and Homotopy analysis method for one typical problem. |
| Databáze: | OpenAIRE |
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