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dc.contributor.authorBelinskiy, Boris P. ( Orcid Icon 0000-0001-5146-1227 )
dc.contributor.authorKotval, David ( )
dc.date.accessioned2022-02-11T16:44:52Z
dc.date.available2022-02-11T16:44:52Z
dc.date.issued2018-05-17
dc.identifier.citationBelinskiy, B. P., & Kotval, D. H. (2018). Optimal design of minimum mass structures for a generalized Sturm-Liouville problem on an interval and a metric graph. Electronic Journal of Differential Equations, 2018(119), pp. 1-18.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15312
dc.description.abstractWe 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.en_US
dc.formatText
dc.format.extent18 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectSturm-Liouville Problemen_US
dc.subjectVibrating roden_US
dc.subjectCalculus of variationsen_US
dc.subjectOptimal designen_US
dc.subjectBoundary conditions with spectral parameteren_US
dc.subjectComplete bipartite graphen_US
dc.titleOptimal design of minimum mass structures for a generalized Sturm-Liouville problem on an interval and a metric graphen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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