The response of simple nonlinear systems to a random disturbance of the earthquake type

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Abstract
Stationary properties of the response of simple nonlinear systems to earthquake type (nonstationary) random disturbances are determined. The method used consists in generating member functions of the input processes, integrating the equations of motion using these as inputs to obtain output member functions, and then, from this ensemble of outputs, determining the statistical properties of interest. The method is flexible in that it is easy to apply to simple as well as complex linear and nonlinear systems; it yields a variety of statistical properties of engineering significance; it provides a method for approaching the design of aseismic structures; and more generally, shock resistant structures on a practical basis. In addition to determining and displaying input and corresponding output member functions, we determine individual as well as average velocity spectra, first passage time probabilities, and extreme value distributions of relative displacements. Comments are also offered on the utility of these results in design.

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