The characteristic frequency and bandwidth of the random response to parametric excitation may be influenced by the excitation processes. It is demonstrated that the effective stiffness and damping properties can be expressed as conditional mean values for given displacement and energy levels, respectively. These properties are used to describe the response in terms of its probability density function and its spectral density function. An example demonstrates the accuracy in predicting change of frequency and damping of a parametrically excited oscillator, and another example extends the method to a self-excited oscillator with domains of negative damping.
Effective System Properties and Special Density in Random Vibration With Parametric Excitation
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the Applied Mechanics Division, Jan. 22, 2001; final revision, Aug. 13, 2001. Associate Editor: N. C. Perkins. Discussion on the paper should be addressed to the Editor, Prof. Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
Krenk, S., Lin, Y. K., and Ru¨dinger, F. (August 13, 2001). "Effective System Properties and Special Density in Random Vibration With Parametric Excitation ." ASME. J. Appl. Mech. March 2002; 69(2): 161–170. https://doi.org/10.1115/1.1430665
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