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

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


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