In
mechanical engineering
Mechanical engineering is the study of physical machines and mechanism (engineering), mechanisms that may involve force and movement. It is an engineering branch that combines engineering physics and engineering mathematics, mathematics principl ...
, random vibration is motion which is non-deterministic, meaning that the exact behavior at a future point in time cannot be predicted, but general trends and statistical properties can be known. 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
In mathematics, ergodicity expresses the idea that a point of a moving system, either a dynamical system or a stochastic process, will eventually visit all parts of the space that the system moves in, in a uniform and random sense. This implies th ...
and
stationary process
In mathematics and statistics, a stationary process (also called a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose statistical properties, such as mean and variance, do not change over time. M ...
.
A measurement of the
acceleration spectral density
In signal processing, the power spectrum S_(f) of a continuous time signal x(t) describes the distribution of power into frequency components f composing that signal. According to Fourier analysis, any physical signal can be decomposed into ...
(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
In signal processing, the power spectrum S_(f) of a continuous time signal x(t) describes the distribution of power into frequency components f composing that signal. According to Fourier analysis, any physical signal can be decomposed into ...
(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
[Crandall, S.H., Mark, W.D.,1963, Random Vibration in Mechanical Systems, New York: Academic Press.] is uniformly considered as the father of random vibration analysis.
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 specifies environmental tests to determine whether equipment is suitably desig ...
, RTCA
DO-160, 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 thermod ...
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 analysisNASA lecture series on random vibration
Mechanical vibrations