Random Vibrations for Multi-Support Excitations
This chapter illustrates the concept of linear, stationary random vibrations as applied to multiply-supported structures. For a system subjected to a zero-mean seismic excitation, as is the case for acceleration time histories (Section 2.2.1), the response will have a zero mean and be described, through a random vibration analysis, by its power spectral density (PSD). The PSD can then be utilized for the evaluation of the root-mean-square (rms) response of the system, which provides information about its maximum response . This is the major advantage of the random vibration approach: A single evaluation that utilizes the stochastic characterization of the excitation sufﬁces for the evaluation of the probabilistic properties of the maximum response of the structure. Its disadvantage, however, as will be brieﬂy illustrated later herein, is that, at this point, it is limited to linear structural problems.