• Journal of the Korean Society for Nondestructive Testing
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• v.29 no.5
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• pp.415-420
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• 2009

This paper reports the results of a case study for the evaluation of surface damage by using acoustic nonlinearity of surface wave. In this study, the experimental system was constructed to measure the acoustic nonlinear parameter of surface wave in an Aluminum 6061 T6 specimen of which surface was damaged by the three point bending fatigue test, and magnitudes of nonlinear parameter measured before and after the fatigue test were compared. Especially, since the surface fatigue damage by the three point bending is concentrated at the central position of loading, the change in the nonlinear parameter around this position was monitored. Experimental results showed that the measured nonlinear parameter at the outside of this position after the fatigue test was almost same as the initial value before the fatigue test, since the fatigue damage at this position was little. However, clear increase in the nonlinear parameter was noticed after the fatigue test at the central position of specimen where the surface fatigue damage is expected to be concentrated.

• Journal of the Korean Society for Nondestructive Testing
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• v.36 no.2
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• pp.112-120
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• 2016

The nonlinearity parameter is frequently measured as a sensitive indicator in damaged material characterization or tissue harmonic imaging. Several previous studies have employed the plane wave solution, and ignored the effects of beam diffraction when measuring the non-linearity parameter ${\beta}$. This paper presents a multi-Gaussian beam approach to explicitly derive diffraction corrections for fundamental and second harmonics under quasilinear and paraxial approximation. Their effects on the nonlinearity parameter estimation demonstrate complicated dependence of ${\beta}$ on the transmitter-receiver geometries, frequency, and propagation distance. The diffraction effects on the non-linearity parameter estimation are important even in the nearfield region. Experiments are performed to show that improved ${\beta}$ values can be obtained by considering the diffraction effects.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2007.04a
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• pp.13-16
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• 2007

Nonlinear acoustic damping of a half-wave acoustic resonator in a combustion chamber is investigated numerically. First, in a baseline chamber without any resonators, acoustic behavior is investigated over the wide range of acoustic amplitude from 80 dB to 150 dB. Decay rate increases nonlinearly with acoustic amplitude and nonlinearity becomes appreciable at acoustic amplitude above 125 dB. Next, damping effect of a half-wave resonator is investigated. Nonlinear acoustic excitation does not affect optimum tuning condition of the resonator, which is derived from linear acoustics. A half-wave resonator is effective even for acoustic damping of high-amplitude pressure oscillation, but its function of acoustic damper is relatively weakened compared with the case of linear acoustic excitation.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.6
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• pp.751-756
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• 2010

Ultrasonic nonlinearity is very sensitive to changes in material properties. This paper describes the study of the correlation between heat treatment and ultrasonic nonlinearity by taking nonlinear factors into consideration. A modified formula was proposed for ultrasonic velocity. This formula indicated that the changes occurring in nonlinearity during heat treatments cause changes in the ultrasonic velocity. The experimental results show that the relative nonlinearity parameters calculated from the modified ultrasonic velocities and the ratio of amplitudes of the second harmonic and fundamental wave are in good agreement. The experimental results prove that heat treatment can result in changes in material nonlinearity. Moreover, the relative nonlinearity parameter calculated from the modified velocity formula is has a large value. Since this parameter has high sensitivity to changes in nonlinearity, it can be used to represent the relative nonlinearity change calculated in this study by using the modified formula for ultrasonic velocity.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.173-182
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• 2015

In this paper, the blow-up rate of $L^2$-norm for the semi-linear wave equation with a power nonlinearity is obtained in the bounded domain for any p > 1. We also get the blow-up rate of the derivative under the condition 1 < p < $1+\frac{4}{N-1}$ for $N{\geq}2$ or 1 < p < 5 for N = 1.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.205-216
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• 2022

This paper deals with a nonlinear wave equation with boundary damping and source terms of variable exponent nonlinearities. This work is devoted to prove a global nonexistence of solutions for a nonlinear wave equation with nonnegative initial energy as well as negative initial energy.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.3
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• pp.156-160
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• 1992

The evolution of leading waves generated by a wavemaker in a two-dimensional tank has been studied. The front of wave trains can be described in general by the Schrodinger equation. In particular, when the slope of the carrier waves is steep, and hence nonlinearity becomes important, the cubic Schrodinger equation is proved to be an appropriate mathematical model. Computations are made by using the Crank-Nicolson algorithm and compared with experimental data. It is found that the numerical result predicts the evolution of leading waves fairly well and the evolution is significantly affected by nonlinearity for steep waves when kh＞1.36.

• Journal of the Korean Mathematical Society
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• v.31 no.2
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• pp.255-278
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• 1994

• Structural Engineering and Mechanics
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• v.60 no.2
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• pp.193-209
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• 2016

In this study, wave force tests were carried out for the four types of offshore support structures with scale factor 1:25 and wave forces to the support structure shapes were investigated. As the results of this study, it was found that, as the wave period increased at the normal wave condition, wave force decreased for the most cases. Extreme wave force was affected by the impact wave force. Impact wave force of this study significantly effect on Monopile and slightly on GBS and Hybrid type. Accordingly, Hybrid type indicated even lower wave force at the extreme and irregular wave conditions than the Monopile although Hybrid type indicated higher wave force at the normal wave condition of the regular wave because of the larger wave area of wave body. In respects of the structural design, since critical loading is extreme wave force, it should be contributed to improve structural safety of offshore support structure. However, since the impact wave force has nonlinearity and complication dependent on the support structure shape, wave height, wave period, and etc., more research is needed to access the impact wave force for other support structure shapes and wave conditions.

• Journal of the Korean Society for Nondestructive Testing
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• v.34 no.6
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• pp.419-427
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• 2014

Nonlinear features of ultrasonic waves are more sensitive to the presence of a fatigue crack than their linear counterparts are. For this reason, the use of nonlinear ultrasonic techniques to detect a fatigue crack at its early stage has been widely investigated. Of the different proposed techniques, laser nonlinear wave modulation spectroscopy (LNWMS) is unique because a pulse laser is used to exert a single broadband input and a noncontact measurement can be performed. Broadband excitation causes a nonlinear source to exhibit modulation at multiple spectral peaks owing to interactions among various input frequency components. A feature called maximum sideband peak count difference (MSPCD), which is extracted from the spectral plot, measures the degree of crack-induced material nonlinearity. First, the ratios of spectral peaks whose amplitudes are above a moving threshold to the total number of peaks are computed for spectral signals obtained from the pristine and the current state of a target structure. Then, the difference of these ratios are computed as a function of the moving threshold. Finally, the MSPCD is defined as the maximum difference between these ratios. The basic premise is that the MSPCD will increase as the nonlinearity of the material increases. This technique has been used successfully for localizing fatigue cracks in metallic plates.