TABLE OF CONTENTS Many practical problems involving the response of a system to random excitation can be solved by considering a single random input function. As will be seen, the process is then relatively straightforward, requiring only two ingredients: (1) the power spectrum of the input and (2) the frequency response function (FRF) of the system. We have discussed the power spectrum, and its derivation; now we must review the FRF.
The FRF, usually denoted by H( ?) or H( f), depending on whether it is expressed in terms of rad/s or Hz, respectively, is simply the ratio of the steady-state response of a system to an applied sinusoidal input, which can be a force, an imposed displacement, or almost any other quantity. The FRF is usually expressed in complex form, but can also be expressed in magnitude and phase form. When calculating an FRF, the sinusoidal input is considered to have started at -oo, and any transient response to have died away. The response is therefore also sinusoidal, but generally different in magnitude and phase from the input.
The FRFs of several forms of single-DOF system were introduced in Section 4.1.3. As has been seen, FRFs of single-DOF systems are easily calculated, or an FRF can, of course, be measured, by applying a sinusoidal input, and measuring the response.
The FRFs of multi-DOF systems are usually calculated by the normal mode summation method,...
