TABLE OF CONTENTS We have seen from the preceding section that the auto-power spectrum and the cross-power spectrum are the Fourier transforms, respectively, of the ACF and CCF. It can also be shown that the frequency response function, h( ?), is the Fourier transform of the impulse response h( t). This means that, in theory, there are always two ways to calculate the response of a structure to a random input, or inputs, or to calculate the characteristics of a structure when the input and response are given:
In the time domain, using correlation functions to describe the input and response, and the impulse response to represent the structure, or:
In the frequency domain, using power spectra to describe the input and output, and the frequency response function to represent the structure.
In practice, the first method is much more difficult to use than the second, and most practical work is carried out using power spectra and FRFs.
When a system, assumed linear, is excited by several random forces, which may be correlated, the auto-power and cross-power spectral density functions provide a convenient method for finding its response, provided all the individual frequency response functions between excitation points and response points are known.
The following example describes the calculation of the response at a single point on a structure, when the loading can be represented by two concentrated, random, forces at...
