Random vibration analysis let us to find out the response of structures to random vibration loads.
Typical applications of random vibration analysis are evaluation of the stress level of important devices mounted on vehicles (cars, trucks, railway vehicles etc.). The source of random vibrations are from the engine, road etc.
Loads such as the acceleration due to the road roughness are not deterministic, i.e. the time history of the load does not repeat every time the car runs over the same section of road. It is not practical to define a definite time history of the load. The road load input are therefore characterised statistically. Random loads are non-periodic and contain a multitude of frequencies. The frequency content of the time history (spectrum) is captured along with the statistics and used as the load in the random vibration analysis. This spectrum is called Power Spectral Density or PSD.
In a random vibration analysis, because the input loads are statistical, the output responses such as displacements, stresses etc. should also be considered to be of statistical nature.
Other applications of random vibration analysis include electronic packaging components on aeroplanes subject to engine vibration, turbulence and acoustic pressures; tall buildings under wind load and offshore structures under ocean wave loading.
A response spectrum analysis is similar to a random vibration analysis but its input is defined instead of random. This analysis evaluates the maximum response based upon the input response spectrum.
Response spectrum analyses are used to evaluate the structural response under a shock load. This analysis is commonly used for evaluating buildings or plants under seismic loads.
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