Optimal design of minimum mass structures for a generalized Sturm-Liouville problem on an interval and a metric graph
Date
2018-05-17
Authors
Belinskiy, Boris P.
Kotval, David
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Sturm-Liouville Problem, Vibrating rod, Calculus of variations, Optimal design, Boundary conditions with spectral parameter, Complete bipartite graph
Citation
Belinskiy, 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.
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Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.