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Free and Forced Vibrations of the Strongly Nonlinear Cubic-Quintic Duffing Oscillators
| Content Provider | Scilit |
|---|---|
| Author | Karahan, M. M. Fatih Pakdemirli, Mehmet |
| Copyright Year | 2016 |
| Abstract | Strongly nonlinear cubic-quintic Duffing oscillatoris considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions. |
| Related Links | http://www.degruyter.com/downloadpdf/j/zna.2017.72.issue-1/zna-2016-0263/zna-2016-0263.xml |
| Ending Page | 69 |
| Page Count | 11 |
| Starting Page | 59 |
| ISSN | 18657109 |
| DOI | 10.1515/zna-2016-0263 |
| Journal | Zeitschrift für Naturforschung A |
| Issue Number | 1 |
| Volume Number | 72 |
| Language | English |
| Publisher | Walter de Gruyter GmbH |
| Publisher Date | 2017-01-01 |
| Access Restriction | Open |
| Subject Keyword | Zeitschrift Für Naturforschung A Mechanical Engineering Cubic-quintic Duffing Oscillator Forced Vibrations Multiple Scales Lindstedt Poincare (mslp) Method Multiple Scales Method Perturbation Methods Strongly Nonlinear Systems Journal: Zeitschrift für Naturforschung A, Issue- 4 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Physics and Astronomy Physical and Theoretical Chemistry Mathematical Physics |
