Optimal design of minimum mass structures for a generalized Sturm-Liouville problem on an interval and a metric graph

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dc.contributor.authorBelinskiy, Boris P.
dc.contributor.authorKotval, David
dc.date.accessioned2022-02-11T16:44:52Z
dc.date.available2022-02-11T16:44:52Z
dc.date.issued2018-05-17
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.
dc.description.departmentMathematics
dc.formatText
dc.format.extent18 pages
dc.format.medium1 file (.pdf)
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. <i>Electronic Journal of Differential Equations, 2018</i>(119), pp. 1-18.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15312
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectSturm-Liouville Problem
dc.subjectVibrating rod
dc.subjectCalculus of variations
dc.subjectOptimal design
dc.subjectBoundary conditions with spectral parameter
dc.subjectComplete bipartite graph
dc.titleOptimal design of minimum mass structures for a generalized Sturm-Liouville problem on an interval and a metric graph
dc.typeArticle

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