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RESEARCH PAPERS: Mechanisms Papers

Parametric Stability of a Two-Degree-of-Freedom Machine System: Part I—Equations of Motion and Stability

[+] Author and Article Information
R. I. Zadoks, A. Midha

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907

J. Mech., Trans., and Automation 109(2), 210-215 (Jun 01, 1987) (6 pages) doi:10.1115/1.3267440 History: Received July 01, 1986; Online November 19, 2009

Abstract

An important question facing a designer is whether a certain machine system will have a stable operating condition. To date, the investigations which deal with this question have been scarce. This study treats an elastic two-degree-of-freedom system with position-dependent inertia and external forcing. In Part I, the nonlinear equations of motion are derived and linearized about the system’s steady-state rigid-body response. The stability of the linearized equations is examined using Floquet theory, and a computationally efficient method for approximating the monodromy matrix is presented. A specific example is proposed and the results are presented in Part II of this paper.

Copyright © 1987 by ASME
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