Equivalent Linearization for Random Vibration

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Abstract
The concept of equivalence between linear and nonlinear systems undergoing random vibration is investigated, and the advantages and limitations of each of several definitions of equivalence are analyzed. The particular nonlinear system considered is the bilinear hysteretic single-degree-of-freedom oscillator, and the linear systems considered include one- and two-degree-of-freedom oscillators. The general characteristics of the stationary response of both the linear and nonlinear systems to random excitation are summarized. Various definitions of equivalence are then proposed on the basis of matching various response statistics of the two systems. The response statistics considered are rms displacement and velocity levels and power spectral density. Experimental values for the response statistics of the bilinear system are used with analytical results for the linear systems to obtain values for the equivalent linear system parameters under each definition of equivalence. The relationship of the proposed definitions and their results to previous work for similar systems with harmonic excitation and to previously suggested approximate analytical methods for random vibration is presented.

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