Abstract
Cumulative second harmonic of ultrasonic guided waves is considered to have great application potential in evaluating internal stress of structures. One difficulty with the application is the diversity and complexity of modal response to the stress change in waveguide. At present, there is a lack of relevant theoretical studies and experimental results to guide the applications. In this article, a method is proposed to characterize the amplitude change of cumulative second harmonic mode in a plate under stress through calculating the amplitude coefficient, which can be acquired based on mode shape analysis. The steel plate is taken as an example to demonstrate the analysis method. Experimental studies are presented with results consistent with the theoretical predictions. The results of this study indicate that the amplitudes of different cumulative second harmonic modes may increase or decrease monotonically with the change of stress. Therefore, when the phenomenon of modes mixing occurs in the waveguide, it is necessary to analyze and predict the amplitude of selected cumulative second harmonic mode with the change of stress in advance; otherwise, wrong results may be obtained. The method and conclusions proposed in this paper can also be applicable to waveguide of arbitrary cross-section and have universality.
Highlights
When the ultrasonic waves propagate in the solid medium, because of the anharmonicity of the crystal structure and the existence of the internal micro defects, the ultrasonic waves will have “distortion” in the process of propagation, showing a strong nonlinear effect
The results demonstrate that the change trends of amplitudes of different second harmonic modes with stress are not the same, which are monotonic increasing or decreasing
The simulation and experimental results confirm validity of the method and show that when the nonlinear ultrasonic guided waves are applied to detect the stress in plate, the amplitudes of second harmonic modes produced by the different excitation and receiving modes have different trends with the change of stress, which are monotonically decreasing or increasing
Summary
When the ultrasonic waves propagate in the solid medium, because of the anharmonicity of the crystal structure and the existence of the internal micro defects (micro cracks, stress concentration, etc.), the ultrasonic waves will have “distortion” in the process of propagation, showing a strong nonlinear effect. In the current studies of applying nonlinear ultrasonic guided waves to detect structural stress, second harmonic mode is selected from the mode pairs meet the conditions, and the corresponding relative nonlinear parameter is calculated. Due to the multi-modal characteristics of ultrasonic guided waves, the mode pair which satisfy the conditions is not unique, and there may be possibly more cumulative second harmonic modes. The changes of the amplitudes of different second harmonic modes with stress are not necessarily the same, and that will lead to the different trends of the relative nonlinear parameters. The variation of second harmonic modal amplitude with stress should be considered and predicted in advance, when the nonlinear ultrasonic guided waves are selected for stress detection in plate
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