Riesz basis and exponential stability for Euler-bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity
This article concerns the Riesz basis property and the stability of a damped Euler-Bernoulli beam with nonuniform thickness or density, that is clamped at one end and is free at the other. To stabilize the system, we apply a linear boundary control force in position and velocity at the free end...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Texas State University
2015-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2015/54/abstr.html |
| _version_ | 1819095406220410880 |
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| author | K. Augustin Toure Adama Coulibaly Ayo A. Hermith Kouassi |
| author_facet | K. Augustin Toure Adama Coulibaly Ayo A. Hermith Kouassi |
| author_sort | K. Augustin Toure |
| collection | DOAJ |
| description | This article concerns the Riesz basis property and the stability of
a damped Euler-Bernoulli beam with nonuniform thickness or density,
that is clamped at one end and is free at the other.
To stabilize the system, we apply a linear boundary control
force in position and velocity at the free end of the beam.
We first put some basic properties for the closed-loop system and then
analyze the spectrum of the system. Using the modern spectral analysis
approach for two-points parameterized ordinary differential operators,
we obtain the Riesz basis property. The spectrum-determined growth condition
and the exponential stability are also concluded. |
| first_indexed | 2024-12-21T23:42:47Z |
| format | Article |
| id | doaj.art-76359625fa754d4bae4c0b754eaecd4e |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-21T23:42:47Z |
| publishDate | 2015-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-76359625fa754d4bae4c0b754eaecd4e2022-12-21T18:46:12ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912015-02-01201554,120Riesz basis and exponential stability for Euler-bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocityK. Augustin Toure0Adama Coulibaly1Ayo A. Hermith Kouassi2 Inst. National Polytech., Yamoussoukro, Cote d'Ivoire Univ. Felix Houphouet-Boigny, Cote d'Ivoire Univ. Felix Houphouet-Boigny, Cote d'Ivoire This article concerns the Riesz basis property and the stability of a damped Euler-Bernoulli beam with nonuniform thickness or density, that is clamped at one end and is free at the other. To stabilize the system, we apply a linear boundary control force in position and velocity at the free end of the beam. We first put some basic properties for the closed-loop system and then analyze the spectrum of the system. Using the modern spectral analysis approach for two-points parameterized ordinary differential operators, we obtain the Riesz basis property. The spectrum-determined growth condition and the exponential stability are also concluded.http://ejde.math.txstate.edu/Volumes/2015/54/abstr.htmlBeam equationasymptotic analysisRiesz basisexponential stability |
| spellingShingle | K. Augustin Toure Adama Coulibaly Ayo A. Hermith Kouassi Riesz basis and exponential stability for Euler-bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity Electronic Journal of Differential Equations Beam equation asymptotic analysis Riesz basis exponential stability |
| title | Riesz basis and exponential stability for Euler-bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity |
| title_full | Riesz basis and exponential stability for Euler-bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity |
| title_fullStr | Riesz basis and exponential stability for Euler-bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity |
| title_full_unstemmed | Riesz basis and exponential stability for Euler-bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity |
| title_short | Riesz basis and exponential stability for Euler-bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity |
| title_sort | riesz basis and exponential stability for euler bernoulli beams with variable coefficients and indefinite damping under a force control in position and velocity |
| topic | Beam equation asymptotic analysis Riesz basis exponential stability |
| url | http://ejde.math.txstate.edu/Volumes/2015/54/abstr.html |
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