Electron. J. Differential Equations,
Vol. 2018 (2018), No. 119, pp. 118.
Optimal design of minimum mass structures for a generalized
SturmLiouville problem on an interval and a metric graph
Boris P. Belinskiy, David H. Kotval
Abstract:
We derive an optimal design of a structure that is described by a
SturmLiouville problem with boundary conditions that contain the
spectral parameter linearly. In terms of Mechanics, we determine necessary
conditions for a minimummass design with the specified natural frequency
for a rod of nonconstant crosssection 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.
Submitted December 4, 2017. Published May 17, 2018.
Math Subject Classifications: 34L15, 74P05, 49K15, 49S05, 49R05.
Key Words: SturmLiouville Problem; vibrating rod; calculus of variations;
optimal design; boundary conditions with spectral parameter;
complete bipartite graph.
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Boris P. Belinskiy
University of Tennessee at Chattanooga
Department of Mathematics
Dept 6956, 615 McCallie Ave.
Chattanooga TN 374032598, USA
email: borisbelinskiy@utc.edu


David H. Kotval
Middle Tennessee State University
Department of Mathematical Sciences
MTSU BOX 34, 1301 East Main Street
Murfreesboro TN 371320001, USA
email: dhk2e@mtmail.mtsu.edu

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