A conditional stochastic projection method applied to a parametric vibrations problem
Parametric vibrations can be observed in cable-stayed bridges due to periodic excitations caused by a deck or a pylon. The vibrations are described by an ordinary differential equation with periodic coefficients. The paper focuses on random excitations, i.e. on the excitation amplitude and the excit...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Vilnius Gediminas Technical University
2014-07-01
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| Series: | Journal of Civil Engineering and Management |
| Subjects: | |
| Online Access: | http://journals.vgtu.lt/index.php/JCEM/article/view/3174 |
| _version_ | 1818570205502111744 |
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| author | Wlodzimierz Brzakala Aneta Herbut |
| author_facet | Wlodzimierz Brzakala Aneta Herbut |
| author_sort | Wlodzimierz Brzakala |
| collection | DOAJ |
| description | Parametric vibrations can be observed in cable-stayed bridges due to periodic excitations caused by a deck or a pylon. The vibrations are described by an ordinary differential equation with periodic coefficients. The paper focuses on random excitations, i.e. on the excitation amplitude and the excitation frequency which are two random variables. The excitation frequency ωL is discretized to a finite sequence of representative points, ωL,i Therefore, the problem is (conditionally) formulated and solved as a one-dimensional polynomial chaos expansion generated by the random excitation amplitude. The presented numerical analysis is focused on a real situation for which the problem of parametric resonance was observed (a cable of the Ben-Ahin bridge). The results obtained by the use of the conditional polynomial chaos approximations are compared with the ones based on the Monte Carlo simulation (truly two-dimensional, not conditional one). The convergence of both methods is discussed. It is found that the conditional polynomial chaos can yield a better convergence then the Monte Carlo simulation, especially if resonant vibrations are probable. |
| first_indexed | 2024-12-14T06:57:36Z |
| format | Article |
| id | doaj.art-69a44fb925df46d7b93a1fa027857784 |
| institution | Directory Open Access Journal |
| issn | 1392-3730 1822-3605 |
| language | English |
| last_indexed | 2024-12-14T06:57:36Z |
| publishDate | 2014-07-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Journal of Civil Engineering and Management |
| spelling | doaj.art-69a44fb925df46d7b93a1fa0278577842022-12-21T23:12:35ZengVilnius Gediminas Technical UniversityJournal of Civil Engineering and Management1392-37301822-36052014-07-0120610.3846/13923730.2014.914105A conditional stochastic projection method applied to a parametric vibrations problemWlodzimierz Brzakala0Aneta Herbut1Faculty of Civil Engineering, Wroclaw University of Technology, PolandFaculty of Civil Engineering, Wroclaw University of Technology, PolandParametric vibrations can be observed in cable-stayed bridges due to periodic excitations caused by a deck or a pylon. The vibrations are described by an ordinary differential equation with periodic coefficients. The paper focuses on random excitations, i.e. on the excitation amplitude and the excitation frequency which are two random variables. The excitation frequency ωL is discretized to a finite sequence of representative points, ωL,i Therefore, the problem is (conditionally) formulated and solved as a one-dimensional polynomial chaos expansion generated by the random excitation amplitude. The presented numerical analysis is focused on a real situation for which the problem of parametric resonance was observed (a cable of the Ben-Ahin bridge). The results obtained by the use of the conditional polynomial chaos approximations are compared with the ones based on the Monte Carlo simulation (truly two-dimensional, not conditional one). The convergence of both methods is discussed. It is found that the conditional polynomial chaos can yield a better convergence then the Monte Carlo simulation, especially if resonant vibrations are probable.http://journals.vgtu.lt/index.php/JCEM/article/view/3174stochastic dynamicsparametric vibrationsHermite’s polynomial chaosMonte Carlo simulation |
| spellingShingle | Wlodzimierz Brzakala Aneta Herbut A conditional stochastic projection method applied to a parametric vibrations problem Journal of Civil Engineering and Management stochastic dynamics parametric vibrations Hermite’s polynomial chaos Monte Carlo simulation |
| title | A conditional stochastic projection method applied to a parametric vibrations problem |
| title_full | A conditional stochastic projection method applied to a parametric vibrations problem |
| title_fullStr | A conditional stochastic projection method applied to a parametric vibrations problem |
| title_full_unstemmed | A conditional stochastic projection method applied to a parametric vibrations problem |
| title_short | A conditional stochastic projection method applied to a parametric vibrations problem |
| title_sort | conditional stochastic projection method applied to a parametric vibrations problem |
| topic | stochastic dynamics parametric vibrations Hermite’s polynomial chaos Monte Carlo simulation |
| url | http://journals.vgtu.lt/index.php/JCEM/article/view/3174 |
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