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

Pages: 85 - 91, Issue Special, September 2007

 Abstract        Full Text (158.0K)              

Boris P. Belinskiy - Department of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403-2598, United States (email)

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.

Keywords:  rod equation, exact controllability, optimal design.
Mathematics Subject Classification:  Primary: 93B05; Secondary: 93C20, 35C20, 35L20.

Received: August 2006;      Revised: May 2007;      Published: September 2007.