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

Abstract

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.

Jerk within the Context of Science and Engineering—A Systematic Review

“…Jerk in standards [13][14][15][16][17][18][19] 18. Jerk in structural health monitoring [173][174][175][176]; 19. Jerk in technical pain [177]; 20.…”

“…The higher derivatives are less familiar, and different terminologies have been used by different groups. The term "jounce" is sometimes used to describe the fourth derivative of position, and in some Japanese articles it is referred to as "jerk-dot" [148,173,175].…”

Inverse Dynamics Problems

“…Its capability of detecting the local damage in the structural members is investigated through low-cycle fatigue tests, which prove its significant sensitivity to the abnormal responses due to the development of macroscopic damages. Further fracture tests are carried out to obtain the correlation between the measured jerk-dot and the crack length, which suggests that this sensor could provide an early alert before the crack grows to the fatal stage.Comment by Iyama & Wakui on this paper[175]: "Although they found that the high-frequency components accompanying crack initiation by jerk or jerk-dot can be used for detection, only a qualitative relation was shown. The determination of threshold values for damage detection thus remains difficult."…”