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Shock and Vibration
Volume 16 (2009), Issue 3, Pages 261-271

Power Delivered to Mechanical Systems by Random Vibrations

Timothy S. Edwards

Analytical Structural Dynamics, Org.1523, Sandia National Laboratories, MS0557, P.O. Box 5800, Albuquerque, NM 87185, USA

Received 28 February 2008

Copyright © 2009 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper develops deformational response power descriptions of multiple degree-of-freedom systems due to stationary random vibration excitation. Two new concepts are developed. The deformational response power density (DRPD) can be computed when a structure's natural frequencies and modal masses are available. The DRPD shows the spectral content of the deformational power delivered to a specific structure by the stationary, random excitation. This function can be found through a weighted windowing of the power spectrum of the input acceleration excitation. Deformational response input power spectra (DRIPS), similar to the input energy spectrum and shock response spectrum, give the power delivered to single-degree-of-freedom systems as a function of natural frequency. It is shown that the DRIPS is simply a smoothed version of the power spectrum of the input acceleration excitation. The DRIPS gives rise to a useful power-based data smoothing operation.