Grazing Orbits and Related Local Bifurcations of an Oscillator with Continuous and Piecewise-Linear Restoring Force
One critical case for the motion of a periodically excited oscillator with continuous and piecewise-linear restoring force is that the motion happens to graze a switching plane between two linear regions of the restoring force. This article presents a numerical scheme for locating the periodic grazi...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1996-01-01
|
| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.3233/SAV-1996-3103 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832555851919917056 |
|---|---|
| author | Haiyan Hu |
| author_facet | Haiyan Hu |
| author_sort | Haiyan Hu |
| collection | DOAJ |
| description | One critical case for the motion of a periodically excited oscillator with continuous and piecewise-linear restoring force is that the motion happens to graze a switching plane between two linear regions of the restoring force. This article presents a numerical scheme for locating the periodic grazing orbit first. Then, through a brief analysis, the article shows that the grazing phenomenon turns the stability trend of the periodic orbit so abruptly that it may be impossible to predict an incident local bifurcation with the variation of a control parameter from the concept of smooth dynamic systems. The numerical simulation in the article well supports the scheme and the analysis, and shows an abundance of grazing phenomena in an engineering range of the excitation frequency. |
| format | Article |
| id | doaj-art-35887395e7a74e56830f6e4770a6ae64 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-35887395e7a74e56830f6e4770a6ae642025-02-03T05:47:02ZengWileyShock and Vibration1070-96221875-92031996-01-0131111610.3233/SAV-1996-3103Grazing Orbits and Related Local Bifurcations of an Oscillator with Continuous and Piecewise-Linear Restoring ForceHaiyan Hu0Institute of Vibration Engineering, Nanjing University of Aeronautics and Astronautics, 210016, Nanjing, ChinaOne critical case for the motion of a periodically excited oscillator with continuous and piecewise-linear restoring force is that the motion happens to graze a switching plane between two linear regions of the restoring force. This article presents a numerical scheme for locating the periodic grazing orbit first. Then, through a brief analysis, the article shows that the grazing phenomenon turns the stability trend of the periodic orbit so abruptly that it may be impossible to predict an incident local bifurcation with the variation of a control parameter from the concept of smooth dynamic systems. The numerical simulation in the article well supports the scheme and the analysis, and shows an abundance of grazing phenomena in an engineering range of the excitation frequency.http://dx.doi.org/10.3233/SAV-1996-3103 |
| spellingShingle | Haiyan Hu Grazing Orbits and Related Local Bifurcations of an Oscillator with Continuous and Piecewise-Linear Restoring Force Shock and Vibration |
| title | Grazing Orbits and Related Local Bifurcations of an Oscillator with Continuous and Piecewise-Linear Restoring Force |
| title_full | Grazing Orbits and Related Local Bifurcations of an Oscillator with Continuous and Piecewise-Linear Restoring Force |
| title_fullStr | Grazing Orbits and Related Local Bifurcations of an Oscillator with Continuous and Piecewise-Linear Restoring Force |
| title_full_unstemmed | Grazing Orbits and Related Local Bifurcations of an Oscillator with Continuous and Piecewise-Linear Restoring Force |
| title_short | Grazing Orbits and Related Local Bifurcations of an Oscillator with Continuous and Piecewise-Linear Restoring Force |
| title_sort | grazing orbits and related local bifurcations of an oscillator with continuous and piecewise linear restoring force |
| url | http://dx.doi.org/10.3233/SAV-1996-3103 |
| work_keys_str_mv | AT haiyanhu grazingorbitsandrelatedlocalbifurcationsofanoscillatorwithcontinuousandpiecewiselinearrestoringforce |