Boris P. Belinskiy, David H. Kotval
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.
Submitted December 4, 2017. Published May 17, 2018.
Math Subject Classifications: 34L15, 74P05, 49K15, 49S05, 49R05.
Key Words: Sturm-Liouville Problem; vibrating rod; calculus of variations;
optimal design; boundary conditions with spectral parameter;
complete bipartite graph.
Show me the PDF file (294 KB), TEX file for this article.
 |
Boris P. Belinskiy University of Tennessee at Chattanooga Department of Mathematics Dept 6956, 615 McCallie Ave. Chattanooga TN 37403-2598, USA email: boris-belinskiy@utc.edu |
|---|---|
 |
David H. Kotval Middle Tennessee State University Department of Mathematical Sciences MTSU BOX 34, 1301 East Main Street Murfreesboro TN 37132-0001, USA email: dhk2e@mtmail.mtsu.edu |
Return to the EJDE web page