Stability of General Hill’s Equation With Three Independent Parameters

[+] Author and Article Information
K. Hamer

University of Newcastle Upon Tyne, Newcaste Upon Tyne, NEI, 7 RU, England

M. R. Smith

Department of Mechanical Engineering, University of Newcastle Upon Tyne, Newcastle Upon Tyne, NEI, 7 RU, England

J. Appl. Mech 39(1), 276-278 (Mar 01, 1972) (3 pages) doi:10.1115/1.3422628 History: Received December 31, 1970; Revised June 10, 1971; Online July 12, 2010


The stability of Hill’s equation with three independent parameters, two of which are small, is analyzed using a perturbation method. It is shown that, except for periodic terms of a special type, existing methods of determining stability boundaries fail. A new method, which works successfully to the first order of approximation, is described.

Copyright © 1972 by ASME
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