ELASTIC-PLASTIC OSCILLATORS UNDER RANDOM-EXCITATION

Simulation studies reveal that the elastic-plastic oscillator cannot be successfully treated by any linearization procedure. In order to compute the main response quantities, such as the yielding increment, the permanent set, the dissipated energy and the crossing rates, a so-called two-state approach is suggested. With the separation between the elastic and plastic parts of the response kept as originally proposed by Karnopp and Scharton, one linear equation is obtained for each state. The fundamental step then is to set up a conditional probability density for the plastic state variable under Gaussian stationary or non-stationary white noise excitation. The yielding duration is found to be half-normal distributed. Numerical results demonstrate the approach and the range of parameters where it can be successfully applied. © 1979.