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2007, 2007(Special): 85-91. doi: 10.3934/proc.2007.2007.85

Optimal design of an optical length of a rod with the given mass

Boris P. Belinskiy 1,

1. 

Department of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403-2598, United States

Received  August 2006 Revised  May 2007 Published  September 2007

The optical length of an elastic rod appears to be important in problems of control of its longitudinal vibrations. We consider the problem of optimal design (optimal density distribution) of an elastic rod of a given variable modulus of elasticity with the optical length as a criterion and assuming that the total mass of the rod is given. The results provide some bounds on the optical length.
Keywords: exact controllability, rod equation, optimal design..
Mathematics Subject Classification: Primary: 93B05; Secondary: 93C20, 35C20, 35L2.
Citation: Boris P. Belinskiy. Optimal design of an optical length of a rod with the given mass. Conference Publications, 2007, 2007 (Special) : 85-91. doi: 10.3934/proc.2007.2007.85
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