Abstract
The equivalent linearization method is a standard technique for the approximate solution of non-linear random vibration problems. It is known that in some cases the method can yield multiple stable solutions for the mean value and the standard deviation of the system response. The validity and accuracy of this type of solution is investigated here by considering a single degree of freedom system for which the multiple solutions which are obtained may be compared with the exact response statistics. It is found that the multiple solutions correspond to distinguishable “states” which occur in the response of the system. A “state” is defined here as a form of response which persists for some time and whose local temporal statistics differ from the ensemble statistics of the complete response. The accuracy of the equivalent linearization method is found to be variable.
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