| Summary: | This research presents the evaluation method of contact-type failure level based on nonlinear wave modulation. It is difficult to detect contact-type failures using a linear ultrasonic inspection. The detection method based on nonlinear wave modulation has been proposed to detect the contact-type failure. Nonlinear wave modulation is the phenomenon, which is explained by contact acoustic nonlinearity (CAN) of ultrasonic caused by low-frequency vibration. The SDOF model for nonlinear wave modulation consists of modal mass, modal damping and modal stiffness which coefficient fluctuates caused by CAN of ultrasonic vibration. This model is described by time-varying linear model when the frequency ratio of the frequency of low-frequency vibration to frequency of ultrasonic vibration is sufficiently small. When the fluctuation frequency of coefficient of modal stiffness caused by low-frequency vibration is sufficiently smaller than the frequency of ultrasonic vibration, the instantaneous natural frequency of ultrasonic vibration fluctuates in synchronization with fluctuation of time-varying coefficient of modal stiffness. Therefore, the fluctuation of natural frequency can be used as a novel index for evaluation of failure level independent of viscous damping. In this paper, the estimation method of fluctuation of the natural frequency is proposed and verified using time response analysis. Firstly, the linear time-varying model of nonlinear wave modulation is introduced. The mechanism of fluctuation of natural frequency is explained by introduced model. Secondly, the estimation method of fluctuation of natural frequency based on the linear time-varying model is proposed. The phase fluctuation occurs as the result of the fluctuation of natural frequency. Finally, it is confirmed that the fluctuation of natural frequency can be estimated from time-invariant transfer function and phase modulation. The fluctuation range of natural frequency is the failure index.
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