Vibrational study of nonlinear euler beam
The chaotic vibrations of a simply supported slender beam is studied based on Euler Bernoulli theory. The partial differential equation is normalized and Galerkin procedure applied. Through forth order Runge Kutta numerical method, the vibratory effects are simulated. The resulting state responses,...
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| Other Authors: | |
| Format: | Final Year Project (FYP) |
| Language: | English |
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2015
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| Online Access: | http://hdl.handle.net/10356/61995 |
| _version_ | 1811681057103151104 |
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| author | Chen, Yaoji |
| author2 | Ng Teng Yong |
| author_facet | Ng Teng Yong Chen, Yaoji |
| author_sort | Chen, Yaoji |
| collection | NTU |
| description | The chaotic vibrations of a simply supported slender beam is studied based on Euler Bernoulli theory. The partial differential equation is normalized and Galerkin procedure applied. Through forth order Runge Kutta numerical method, the vibratory effects are simulated. The resulting state responses, bifurcation branch diagrams, Poincare maps and boundary basins are studied. The unpredictability of the outcome is discussed in details as the boundary basin evolves under increasing driving force. More specifically, eight basins of attraction are obtained under the simulated conditions. The patterns from these eight attractors under different initial conditions are exhibited to show how changes in initial conditions can result in drastically different response. |
| first_indexed | 2024-10-01T03:34:53Z |
| format | Final Year Project (FYP) |
| id | ntu-10356/61995 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:34:53Z |
| publishDate | 2015 |
| record_format | dspace |
| spelling | ntu-10356/619952023-03-04T19:36:24Z Vibrational study of nonlinear euler beam Chen, Yaoji Ng Teng Yong School of Mechanical and Aerospace Engineering DRNTU::Engineering::Mechanical engineering::Mechanics and dynamics The chaotic vibrations of a simply supported slender beam is studied based on Euler Bernoulli theory. The partial differential equation is normalized and Galerkin procedure applied. Through forth order Runge Kutta numerical method, the vibratory effects are simulated. The resulting state responses, bifurcation branch diagrams, Poincare maps and boundary basins are studied. The unpredictability of the outcome is discussed in details as the boundary basin evolves under increasing driving force. More specifically, eight basins of attraction are obtained under the simulated conditions. The patterns from these eight attractors under different initial conditions are exhibited to show how changes in initial conditions can result in drastically different response. Bachelor of Engineering (Aerospace Engineering) 2015-01-05T02:00:21Z 2015-01-05T02:00:21Z 2010 2010 Final Year Project (FYP) http://hdl.handle.net/10356/61995 en Nanyang Technological University 77 p. application/pdf |
| spellingShingle | DRNTU::Engineering::Mechanical engineering::Mechanics and dynamics Chen, Yaoji Vibrational study of nonlinear euler beam |
| title | Vibrational study of nonlinear euler beam |
| title_full | Vibrational study of nonlinear euler beam |
| title_fullStr | Vibrational study of nonlinear euler beam |
| title_full_unstemmed | Vibrational study of nonlinear euler beam |
| title_short | Vibrational study of nonlinear euler beam |
| title_sort | vibrational study of nonlinear euler beam |
| topic | DRNTU::Engineering::Mechanical engineering::Mechanics and dynamics |
| url | http://hdl.handle.net/10356/61995 |
| work_keys_str_mv | AT chenyaoji vibrationalstudyofnonlineareulerbeam |