Random vibration
Encyclopedia
In mechanical engineering
, 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. In mathematical terms, random vibration is characterized as an ergodic and stationary process
.
A measurement of the acceleration spectral density (ASD) is the usual way to specify random vibration. The root mean square acceleration (Grms) is the square root of the area under the ASD curve in the frequency domain. The Grms 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 (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.
Test specification can be established from real environment measurements using an ASD envelope or a fatigue damage equivalence criterion (Extreme response spectrum
and Fatigue damage spectrum
).
Mechanical engineering
Mechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. It is the branch of engineering that involves the production and usage of heat and mechanical power for the...
, 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. In mathematical terms, random vibration is characterized as an ergodic and stationary process
Stationary process
In the mathematical sciences, a stationary process is a stochastic process whose joint probability distribution does not change when shifted in time or space...
.
A measurement of the acceleration spectral density (ASD) is the usual way to specify random vibration. The root mean square acceleration (Grms) is the square root of the area under the ASD curve in the frequency domain. The Grms 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 (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.
Test specification can be established from real environment measurements using an ASD envelope or a fatigue damage equivalence criterion (Extreme response spectrum
Extreme response spectrum
The Extreme Response Spectrum is defined as a curve giving the value of the highest peak of the response of a linear Single Degree of Freedom System to vibration, according to its natural frequency, for a given damping ratio...
and Fatigue damage spectrum
Fatigue damage spectrum
The Fatigue Damage Spectrum of a vibration is obtained by tracing the fatigue damage experienced by a linear Single Degree of Freedom System according to its natural frequency, for given damping ratio and for a given value of parameter b .Regardless of the...
).
External links
- NASA Goddard website about random vibration analysis
- NASA Mars Orbiter website
- Random Vibrations, Spectral & Wavelet Analysis , D.E. Newland
- Lalanne, C., Mechanical Vibration and Shock Analysis. Volume 3: Random Vibration, Second Edition, ISTE - Wiley, 2009.