A Stability Theorem for Hill’s Equation for Engineering Applications-Reference-Cited by-同舟云学术

A Stability Theorem for Hill’s Equation for Engineering Applications

Published:1995-07-01 Issue:3A Volume:117 Page:380-381
ISSN:1048-9002
Container-title:Journal of Vibration and Acoustics
language:en
Short-container-title:

Author:

Bhattacharyya R.¹

Affiliation:

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

Abstract

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.

Publisher

ASME International

Subject

General Engineering

Link

http://asmedigitalcollection.asme.org/vibrationacoustics/article-pdf/117/3A/380/5825197/380_1.pdf

Reference11 articles.

1. Beatty M. F. , and BhattacharyyaR., 1990, “Poynting Oscillations of a Rigid Disk Supported by a Neo-Hookean Rubber Shaft,” J. Elasticity, Vol. 24, pp. 135–186.

2. Bhattacharyya, R., 1993, “A Stability Criterion for the Mathieu-Hill Equation,” Proceedings, 14th Biennial ASME Vibration and Noise Conference, Albuquerque, DE-Vol. 56, pp. 369–376.

3. Goldberg W. , and HochstadtH., 1985, “On the Solvability of Hiil’s Equation by Quadrature,” J. Math. Anal. Appl, Vol. 112, pp. 411–416.

4. Keller J. B. , 1984, “Discriminant, Transmission Coefficient, and Stability Bands of Hill’s Equation,” J. Math. Phys., Vol. 25, pp. 2903–2904.

5. Magnus, W., and Winkler, S., 1979, Hill’s Equation, Dover Publications, New York.

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