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An equivalent spring for nonlinear springs in series

This work is concerned with nonlinear springs in series with the aim of obtaining the equivalent spring and its characteristics. The case of two linear springs in series is presented first as a basis for the extension to the cases of two purely nonlinear springs in series and two or more equal Duffing springs in series, which both allow the exact determination of the equivalent spring. Then, the most general case of two nonlinear springs with odd-power terms and different coefficients is examined. The condition is derived in terms of their characteristics for which the exact solution for the equivalent spring can be obtained.