A Stability Theorem for Hill’s Equation for Engineering Applications

[+] Author and Article Information
R. Bhattacharyya

Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur-721302, India

J. Vib. Acoust 117(3A), 380-381 (Jul 01, 1995) (2 pages) doi:10.1115/1.2874465 History: Received July 01, 1993; Revised February 01, 1994; Online February 26, 2008


A criterion for determining the stability of solutions of Hill’s equation containing even periodic potential is developed based on Hill’s method of solution. In the special case of the Mathieu equation, the theorem is applied to generate stability maps that compares well with those obtained by existing methods. Finally, stability of Poynting oscillations of a rigid disk attached to a neo-Hookean rubber rod is briefly discussed.

Copyright © 1995 by The American Society of Mechanical Engineers
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