Chaotic Dynamics of Structural Members Under Regular Periodic and White Noise Excitations; Lecture Notes in Computer Science; Vol. 10187 : Numerical Analysis and Its Applications
| Parent link: | Lecture Notes in Computer Science Vol. 10187 : Numerical Analysis and Its Applications.— 2017.— [P. 25-32] |
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| Autor corporatiu: | |
| Altres autors: | , , , , |
| Sumari: | Title screen In this work we study PDEs governing beam dynamics under the Timoshenko hypotheses as well as the initial and boundary conditions which are yielded by Hamilton's variational principle. The analysed beam is subjected to both uniform transversal harmonic load and additive white Gaussian noise. The PDEs are reduced to ODEs by means of the finite difference method employing the finite differences of the second-order accuracy, and then they are solved using the 4th and 6th order Runge-Kutta methods. The numerical results are validated with the applied nodes of the beam partition. The so-called charts of the beam vibration types are constructed versus the amplitude and frequency of harmonic excitation as well as the white noise intensity. The analysis of numerical results is carried out based on a theoretical background on non-linear dynamical systems with the help of time series, phase portraits, Poincar´e maps, power spectra, Lyapunov exponents as well as using different wavelet-based studies. A few novel non-linear phenomena are detected, illustrated and discussed. In particular, it has been detected that a transition from regular to chaotic beam vibrations without noise has been realised by the modified Ruelle-Takens-Newhouse scenario. Furthermore, it has been shown that in the studied cases, the additive white noise action has not qualitatively changed the mentioned route to chaotic dynamics. Режим доступа: по договору с организацией-держателем ресурса |
| Idioma: | anglès |
| Publicat: |
2017
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| Matèries: | |
| Accés en línia: | http://dx.doi.org/10.1007/978-3-319-57099-0_3 |
| Format: | Electrònic Capítol de llibre |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=655284 |
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| 200 | 1 | |a Chaotic Dynamics of Structural Members Under Regular Periodic and White Noise Excitations |f J. Awrejcewicz [et al.] | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 320 | |a [References: p. 32 (5 tit.)] | ||
| 330 | |a In this work we study PDEs governing beam dynamics under the Timoshenko hypotheses as well as the initial and boundary conditions which are yielded by Hamilton's variational principle. The analysed beam is subjected to both uniform transversal harmonic load and additive white Gaussian noise. The PDEs are reduced to ODEs by means of the finite difference method employing the finite differences of the second-order accuracy, and then they are solved using the 4th and 6th order Runge-Kutta methods. The numerical results are validated with the applied nodes of the beam partition. The so-called charts of the beam vibration types are constructed versus the amplitude and frequency of harmonic excitation as well as the white noise intensity. The analysis of numerical results is carried out based on a theoretical background on non-linear dynamical systems with the help of time series, phase portraits, Poincar´e maps, power spectra, Lyapunov exponents as well as using different wavelet-based studies. A few novel non-linear phenomena are detected, illustrated and discussed. In particular, it has been detected that a transition from regular to chaotic beam vibrations without noise has been realised by the modified Ruelle-Takens-Newhouse scenario. Furthermore, it has been shown that in the studied cases, the additive white noise action has not qualitatively changed the mentioned route to chaotic dynamics. | ||
| 333 | |a Режим доступа: по договору с организацией-держателем ресурса | ||
| 461 | |t Lecture Notes in Computer Science | ||
| 463 | |t Vol. 10187 : Numerical Analysis and Its Applications |o 6th International Conference, NAA 2016, Lozenetz, Bulgaria, June 15-22, 2016, Revised Selected Papers : proceedings |v [P. 25-32] |d 2017 | ||
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| 610 | 1 | |a нелинейная динамика | |
| 610 | 1 | |a пучок Тимошенко | |
| 610 | 1 | |a хаос | |
| 610 | 1 | |a бифуркации | |
| 610 | 1 | |a белый гауссовский шум | |
| 701 | 1 | |a Awrejcewicz |b J. |g Jan | |
| 701 | 1 | |a Krysko |b A. V. |c specialist in the field of Informatics and computer engineering |c programmer Tomsk Polytechnic University, Professor, doctor of physico-mathematical Sciences |f 1967- |g Anton Vadimovich |3 (RuTPU)RU\TPU\pers\36883 | |
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| 701 | 1 | |a Erofeev |b N. P. | |
| 701 | 1 | |a Krysko |b V. A. |g Vadim A. | |
| 712 | 0 | 2 | |a Национальный исследовательский Томский политехнический университет (ТПУ) |b Институт кибернетики (ИК) |b Кафедра инженерной графики и промышленного дизайна (ИГПД) |b Научно-учебная лаборатория 3D моделирования (НУЛ 3DМ) |3 (RuTPU)RU\TPU\col\20373 |
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