Threshold value and applicable range of nonlinear behavior detection method using second derivative of acceleration

摘要

A previously proposed nonlinearity detection method using the second derivative “snap” of the recorded absolute acceleration requires the determination of a threshold value based on the yield strength of the target vibration system, which may not be known. Therefore, this study aims to extend this detection method by determining the mathematical relation between the snap and stiffness change and velocity of the vibration system; the results indicate that the threshold value required to detect nonlinearities can be explicitly expressed by mathematical equations. Although the accuracy of this detection method is affected by the intensity of noise and the time intervals of the acceleration records, the introduced mathematical model can both explain these effects and allow the user to decide a priori whether this method can be used to detect nonlinearities. Furthermore, the proposed mathematical model for nonlinearity detection was verified by dynamic response analysis with varying natural periods, showing that the detectable range estimated by the model agreed with the range where the accuracy of nonlinearity detection by snap increases. The threshold value and the applicable range for nonlinearity detection method using second time derivative are theoretically formulated. The introduced equations are verified through comparison to dynamic response analysis result.