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

Boris P. Belinskiy

doi:10.3934/proc.2007.2007.85

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2007, Volume 2007: 85-91. Doi: 10.3934/proc.2007.2007.85 open access

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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

Received: July 31, 2006

Revised: April 30, 2007

Published: August 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 93B05; Secondary: 93C20, 35C20, 35L20.

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