This paper introduces a simplified random vibrations analysis method of linear secondary systems with nonlinear supports. The method separates, as much as possible, the nonlinear analysis of the supports from the linear analysis of the remainder of the secondary system. Equivalent linearization is used to generate response-dependent linear properties of the supports directly from hysteresis loops. These properties are then combined with the properties of the secondary system, and a response analysis is performed using mode combination. The analysis procedure is simpler than standard random vibration methods, and for narrow-band responses, it accurately models nonlinear behavior. In addition, the procedure uses equivalent modal quantities, such as natural frequencies and damping ratios, which provide insight into the effects of the nonlinear supports on the secondary system.

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