Consider a lightly damped, single-degree-of-freedom system subjected to broadband random base excitation. The system will tend to behave as a bandpass filter. The bandpass filter center frequency will occur at or near the system’s natural frequency. The system response will thus tend to be narrowband random.
The probability distribution for its instantaneous values will tend to follow a Normal distribution, which is the same distribution corresponding to a broadband random signal.
The absolute values of the system’s response peaks, however, will tend to have a Rayleigh distribution.
Further information is given at: RayD.pdf
See also: Peak Response for Random Vibration
* * *
Related Matlab scripts:
Response of an SDOF system to an arbitrary base input: arbit.zip
Count the number of time history peaks above a user-specified sigma level: peaks_sigma.zip
Rayleigh distribution probability calculator: Rayleigh_integrate.m
Generate your own base input time history: blog post & scripts
* * *
Band-limited white noise time history used for the example in the paper: white_d.zip
* * *
– Tom Irvine