Distributed Control of a Vibrating String in Response to Pointwise Force Application
The problem of controlling the vibrations of a string by a discrete applied force is considered. The vibrations of the string are modeled by the linear wave equation and the control is provided by an added force term. The wave equation is solved for controlled and uncontrolled cases with and without...
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| Language: | English |
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Sakarya University
2024-02-01
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| Series: | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/3390860 |
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| author | Mehmet Şirin Demir Şule Kapkın Erol Uzal |
| author_facet | Mehmet Şirin Demir Şule Kapkın Erol Uzal |
| author_sort | Mehmet Şirin Demir |
| collection | DOAJ |
| description | The problem of controlling the vibrations of a string by a discrete applied force is considered. The vibrations of the string are modeled by the linear wave equation and the control is provided by an added force term. The wave equation is solved for controlled and uncontrolled cases with and without control force term. The applied force is chosen to be proportional to string displacement at some specified point. In the controlled case; the wave equation involves a control parameter (gain) and related terms involving the value of the displcement at a single point and a delta function. This makes the equation quite different from the usual wave equation. The problem is solved analytically using a modified (compared to usual wave equation) solution procedure and an equation relating the string eigenfrequencies to the proportionality constant (gain) is derived. This allows the observation of the change in eigenfrequencies with the gain. Finally, examples of uncontrolled and controlled responses are presented, graphically. The results show that the resonances can be avoided by the applied control procedure. |
| format | Article |
| id | doaj-art-0364be2cd22f456b8045a09330444c93 |
| institution | Kabale University |
| issn | 2147-835X |
| language | English |
| publishDate | 2024-02-01 |
| publisher | Sakarya University |
| record_format | Article |
| series | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| spelling | doaj-art-0364be2cd22f456b8045a09330444c932024-12-23T08:16:41ZengSakarya UniversitySakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi2147-835X2024-02-0128116717310.16984/saufenbilder.135645328Distributed Control of a Vibrating String in Response to Pointwise Force ApplicationMehmet Şirin Demir0https://orcid.org/0000-0002-3965-4760Şule Kapkın1https://orcid.org/0000-0003-4951-7089Erol Uzal2https://orcid.org/0000-0003-0008-1376İSTANBUL ÜNİVERSİTESİ-CERRAHPAŞAİSTANBUL ÜNİVERSİTESİ-CERRAHPAŞAİSTANBUL ÜNİVERSİTESİ-CERRAHPAŞAThe problem of controlling the vibrations of a string by a discrete applied force is considered. The vibrations of the string are modeled by the linear wave equation and the control is provided by an added force term. The wave equation is solved for controlled and uncontrolled cases with and without control force term. The applied force is chosen to be proportional to string displacement at some specified point. In the controlled case; the wave equation involves a control parameter (gain) and related terms involving the value of the displcement at a single point and a delta function. This makes the equation quite different from the usual wave equation. The problem is solved analytically using a modified (compared to usual wave equation) solution procedure and an equation relating the string eigenfrequencies to the proportionality constant (gain) is derived. This allows the observation of the change in eigenfrequencies with the gain. Finally, examples of uncontrolled and controlled responses are presented, graphically. The results show that the resonances can be avoided by the applied control procedure.https://dergipark.org.tr/tr/download/article-file/3390860pointwise controlvibrationscontrol of partial differential equationsanalytical solution |
| spellingShingle | Mehmet Şirin Demir Şule Kapkın Erol Uzal Distributed Control of a Vibrating String in Response to Pointwise Force Application Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi pointwise control vibrations control of partial differential equations analytical solution |
| title | Distributed Control of a Vibrating String in Response to Pointwise Force Application |
| title_full | Distributed Control of a Vibrating String in Response to Pointwise Force Application |
| title_fullStr | Distributed Control of a Vibrating String in Response to Pointwise Force Application |
| title_full_unstemmed | Distributed Control of a Vibrating String in Response to Pointwise Force Application |
| title_short | Distributed Control of a Vibrating String in Response to Pointwise Force Application |
| title_sort | distributed control of a vibrating string in response to pointwise force application |
| topic | pointwise control vibrations control of partial differential equations analytical solution |
| url | https://dergipark.org.tr/tr/download/article-file/3390860 |
| work_keys_str_mv | AT mehmetsirindemir distributedcontrolofavibratingstringinresponsetopointwiseforceapplication AT sulekapkın distributedcontrolofavibratingstringinresponsetopointwiseforceapplication AT eroluzal distributedcontrolofavibratingstringinresponsetopointwiseforceapplication |