The influence of random vibration on the design of mechanical components has been considered within the framework of the linear theory of small oscillations. However, in some important cases this theory is inadequate and fails to predict some complex response characteristics that have been observed experimentally and which can only be predicted by nonlinear analyses. This paper describes some recent developments in the theory of nonlinear random vibration based on Markov methods and related problems in the design of dynamical systems. Research efforts have been focused on stability/bifurcation conditions, response statistics and reliability problems. Significant progress has been made in developing new analytical methods and conducting experimental testing. These developments have helped to resolve some controversies, and to enhance our understanding of difficult issues. Experimental and numerical simulations have revealed new phenomena that were not predicted analytically. These include on-off intermittency, snap-through phenomena, and the dependence of the response bandwidth on the excitation level. The main results of studying the responses of nonlinear single-and two-degree-of-freedom systems to random excitations obtained by the author and others are discussed in this paper.
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June 1995
Research Papers
Recent Results in Random Vibrations of Nonlinear Mechanical Systems
R. A. Ibrahim
R. A. Ibrahim
Department of Mechanical Engineering, Wayne State University, Detroit, MI 48202
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R. A. Ibrahim
Department of Mechanical Engineering, Wayne State University, Detroit, MI 48202
J. Vib. Acoust. Jun 1995, 117(B): 222-233 (12 pages)
Published Online: June 1, 1995
Article history
Received:
October 1, 1995
Online:
February 26, 2008
Citation
Ibrahim, R. A. (June 1, 1995). "Recent Results in Random Vibrations of Nonlinear Mechanical Systems." ASME. J. Vib. Acoust. June 1995; 117(B): 222–233. https://doi.org/10.1115/1.2838667
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