Optimal design of minimum mass structures for a generalized Sturm-Liouville problem on an interval and a metric graph
We derive an optimal design of a structure that is described by a Sturm-Liouville problem with boundary conditions that contain the spectral parameter linearly. In terms of Mechanics, we determine necessary conditions for a minimum-mass design with the specified natural frequency for a rod of no...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2018-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2018/119/abstr.html |
| _version_ | 1819174998347087872 |
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| author | Boris P. Belinskiy David H. Kotval |
| author_facet | Boris P. Belinskiy David H. Kotval |
| author_sort | Boris P. Belinskiy |
| collection | DOAJ |
| description | We derive an optimal design of a structure that is described by a
Sturm-Liouville problem with boundary conditions that contain the
spectral parameter linearly. In terms of Mechanics, we determine necessary
conditions for a minimum-mass design with the specified natural frequency
for a rod of non-constant cross-section and density subject to the boundary
conditions in which the frequency (squared) occurs linearly. By virtue of
the generality in which the problem is considered other applications are
possible. We also consider a similar optimization problem on a complete
bipartite metric graph including the limiting case when the number of
leafs is increasing indefinitely. |
| first_indexed | 2024-12-22T20:47:52Z |
| format | Article |
| id | doaj.art-07a827dfc14f4db1b7566b940bafbc2b |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-22T20:47:52Z |
| publishDate | 2018-05-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-07a827dfc14f4db1b7566b940bafbc2b2022-12-21T18:13:10ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912018-05-012018119,118Optimal design of minimum mass structures for a generalized Sturm-Liouville problem on an interval and a metric graphBoris P. Belinskiy0David H. Kotval1 Univ.of Tennessee, Chattanooga, TN, USA Middle Tennessee State Univ., Murfreesboro TN, USA We derive an optimal design of a structure that is described by a Sturm-Liouville problem with boundary conditions that contain the spectral parameter linearly. In terms of Mechanics, we determine necessary conditions for a minimum-mass design with the specified natural frequency for a rod of non-constant cross-section and density subject to the boundary conditions in which the frequency (squared) occurs linearly. By virtue of the generality in which the problem is considered other applications are possible. We also consider a similar optimization problem on a complete bipartite metric graph including the limiting case when the number of leafs is increasing indefinitely.http://ejde.math.txstate.edu/Volumes/2018/119/abstr.htmlSturm-Liouville Problemvibrating rodcalculus of variationsoptimal designboundary conditions with spectral parametercomplete bipartite graph |
| spellingShingle | Boris P. Belinskiy David H. Kotval Optimal design of minimum mass structures for a generalized Sturm-Liouville problem on an interval and a metric graph Electronic Journal of Differential Equations Sturm-Liouville Problem vibrating rod calculus of variations optimal design boundary conditions with spectral parameter complete bipartite graph |
| title | Optimal design of minimum mass structures for a generalized Sturm-Liouville problem on an interval and a metric graph |
| title_full | Optimal design of minimum mass structures for a generalized Sturm-Liouville problem on an interval and a metric graph |
| title_fullStr | Optimal design of minimum mass structures for a generalized Sturm-Liouville problem on an interval and a metric graph |
| title_full_unstemmed | Optimal design of minimum mass structures for a generalized Sturm-Liouville problem on an interval and a metric graph |
| title_short | Optimal design of minimum mass structures for a generalized Sturm-Liouville problem on an interval and a metric graph |
| title_sort | optimal design of minimum mass structures for a generalized sturm liouville problem on an interval and a metric graph |
| topic | Sturm-Liouville Problem vibrating rod calculus of variations optimal design boundary conditions with spectral parameter complete bipartite graph |
| url | http://ejde.math.txstate.edu/Volumes/2018/119/abstr.html |
| work_keys_str_mv | AT borispbelinskiy optimaldesignofminimummassstructuresforageneralizedsturmliouvilleproblemonanintervalandametricgraph AT davidhkotval optimaldesignofminimummassstructuresforageneralizedsturmliouvilleproblemonanintervalandametricgraph |