Stationary Random Vibration of Hysteretic Systems

A more rigorous derivation of the modified power balance method is given for general yielding systems. It is demonstrated that the physical meaning of the equivalent linearization criteria derived by the mean-square minimization (Krylov-Bogoliubov) method are the equivalency of the dissipative and potential energies of the linear and nonlinear systems. Thus, linearization by power balance can be the same as by mean-square minimization. Simple gradient-stiffness approximations for the amplitude-dependent average frequency of hysteresis cycles and the overall average frequency of random response are presented for systems of Masing's type. In addition to the previously studied bilinear hysteretic system, the method is applied to compute rms response levels of trilinear hysteretic and Ramberg-Osgood type systems.