In
mechanical engineering
Mechanical engineering is the study of physical machines that may involve force and movement. It is an engineering branch that combines engineering physics and mathematics principles with materials science, to design, analyze, manufacture, an ...
, random vibration is motion which is non-deterministic, meaning that future behavior cannot be precisely predicted. The randomness is a characteristic of the excitation or input, not the
mode shapes or natural frequencies. Some common examples include an automobile riding on a rough road, wave height on the water, or the load induced on an airplane wing during flight. Structural response to random vibration is usually treated using statistical or probabilistic approaches. Mathematically, random vibration is characterized as an
ergodic and
stationary process
In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time. Con ...
.
A measurement of the
acceleration spectral density (ASD) is the usual way to specify random vibration. The root mean square acceleration (G
rms) is the square root of the area under the ASD curve in the frequency domain. The G
rms value is typically used to express the overall energy of a particular random vibration event and is a statistical value used in mechanical engineering for structural design and analysis purposes.
While the term
power spectral density
The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, ...
(PSD) is commonly used to specify a random vibration event, ASD is more appropriate when acceleration is being measured and used in structural analysis and testing.
Crandall is uniformly considered as the father of random vibrations (see also books by Bolotin,
Elishakoff et al.). The dramatic effect of often neglected cross-correlations is elucidated in the monograph by
Elishakoff.
[Elishakoff, I.,2020, Dramatic Effect of Cross-Correlations in Random Vibrations of Discrete Systems, Beams, Plates, and Shells, Springer, Nature, Switzerland, ]
Random vibration testing
Test specifications can be established from real environment measurements using an ASD envelope or a fatigue damage equivalence criterion (
Extreme response spectrum and
Fatigue damage spectrum). Random vibration testing is one of the more common types of vibration testing services performed by vibration test labs. Some of the more common random vibration test standards are
MIL-STD-810
MIL-STD-810, U S Department of Defense Test Method Standard, Environmental Engineering Considerations and Laboratory Tests, is a United States Military Standard that emphasizes tailoring an equipment's environmental design and test limits to the ...
, RTCA
DO-160
DO-160, Environmental Conditions and Test Procedures for Airborne Equipment is a standard for the environmental testing of avionics hardware. It is published by the Radio Technical Commission for Aeronautics (RTCA) and supersedes DO-138.
Outline ...
, and IEC 60068-2-64.
See also
*
Random noise
In electronics, noise is an unwanted disturbance in an electrical signal.
Noise generated by electronic devices varies greatly as it is produced by several different effects.
In particular, noise is inherent in physics, and central to the ...
References
{{Reflist
* Random Vibrations, Spectral & Wavelet Analysis, D.E. Newland
*''Mechanical Vibration and Shock Analysis. Volume 3: Random Vibration'', Second Edition, ISTE - Wiley, 2009.
External links
NASA Goddard website about random vibration analysis
Mechanical vibrations