A method of equivalent linearization for smooth hysteretic systems under random excitation is proposed. The hysteretic restoring force is modeled by a nonlinear differential equation and the equation of motion is linearized directly in closed form without recourse to Krylov-Bogoliubov technique. Compared with previously proposed similar methods, the formulation of the present method is versatile and considerably simpler. The accuracy of this method is verified against Monte-Carlo simulation for all response levels. It has a great potential in the analysis of multidegree-of-freedom and degrading systems.

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