• 대한수학회지
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• 제58권3호
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• pp.633-642
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• 2021

In this paper we consider the following strongly damped wave equation with variable-exponent nonlinearity u_tt(x, t) - ∆u(x, t) - ∆u_t(x, t) = |u(x, t)|^p(x)-2u(x, t), where the exponent p(·) of nonlinearity is a given measurable function. We establish finite time blow-up results for the solutions with non-positive initial energy and for certain solutions with positive initial energy. We extend the previous results for strongly damped wave equations with constant exponent nonlinearity to the equations with variable-exponent nonlinearity.

• 비파괴검사학회지
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• 제36권1호
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• pp.53-59
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• 2016

초음파 비선형 진단을 이용한 기법의 경우 재료의 단순 결함 검출뿐만 아니라 부식, 소성변형과 같은 미세손상을 평가할 때 주로 이용된다. 1차 조화파(primary wave)와 2차 조화파(second harmonic wave)의 진폭의 비를 이용하여 비선형성을 나타내며, 이러한 비선형성의 비교 결과를 진단에 사용한다. 실험 특성상 비선형성은 재료의 비선형성뿐만 아니라 장비의 비선형성 또한 포함하게 된다. 장비 비선형성은 사용자가 측정하고자 하는 값이 아니므로 오차로 작용하여 분석을 방해한다. 본 연구에서는 오차로 작용하는 장비의 비선형성을 감소시켜 보다 정확한 진단을 위해 체적파 혼합기법을 사용하였다. 체적파 혼합기법의 가장 큰 특징은 기존의 초음파 비선형 진단보다 장비의 비선형성을 줄일 수 있다는 점이다. 본 연구에서는 체적파 혼합기법을 이론 및 실험적으로 검증하였으며, 기존의 초음파 비선형 진단기법의 결과와 체적파 혼합기법의 결과를 비교하여 장단점 및 적용 가능성 분석에 초점을 두었다.

• 비파괴검사학회지
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• 제32권4호
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• pp.388-392
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• 2012

본 연구에서는 표면파의 음향비선형 특성 측정을 위해 선 배열 레이저 빔을 이용하여 협대역의 표면파를 발생시키고 레이저 TWM(Two-Wave Mixing) 방식으로 수신하는 완전 비접촉 측정 방법이 도입되었다. 이 기술은 알루미늄 합금의 소성변형과 음향비선형 특성과의 상관성을 조사하는데 적용되었다. 그 결과, 재료의 소성변형에 따라 음향 비선형성이 비례적으로 증가하는 것으로 나타났으며, 이는 접촉식 PZT 탐촉자 수신 방법으로 측정한 결과와 동일한 경향이다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 추계학술대회논문초록집
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• pp.389.2-389
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• 2002

Nonlinear aeroelastic characteristics of a missile control surface are investigated in this study. The wing model has freeplay structural nonlinearity at its pitch axis. Nonlinear aerodynamic flows with unsteady shock waves are also considered in high-speed flow region. To effectively consider a freeplay structural nonlinearity, the fictitious mass method (FMM) is applied to structural vibration analysis based on finite element method (FEM). (omitted)

• 비파괴검사학회지
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• 제30권2호
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• pp.139-145
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• 2010

본 연구에서는 레이저를 이용한 협대역 표면파의 음향 비선형 계측을 통하여 굽힘피로손상된 알루미늄 합금의 피로열화를 평가하였다. 선배열 레이저를 이용할 경우 발생하는 본질적인 고조파 성분을 이론적으로 분석하고 굽힘피로손상된 알루미늄 6061 합금의 표면으로부터 음향 비선형 파라미터를 성공적으로 측정하였다. 피로사이클의 증가에 따라서 음향 비선형 파라미터는 증가하였고 손상 정도와 매우 밀접한 관계를 보였다. 결과적으로 본 연구에서 다룬 레이저 여기된 표면파의 비선형평가기법은 피로손상된 표면열화 평가에 매우 유용할 것으로 판단된다.

• 한국해안해양공학회:학술대회논문집
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• 한국해안해양공학회 1998년도 정기학술강연회 발표논문 초록집 Annual Meeting of Korean Society of Coastal and Ocean Engineers
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• pp.5-11
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• 1998

Wave nonlinearity and dispersivity have mutually counteracting effects on the wave evolution process; i.e., the former makes the wave profile steeper, while the latter milder. Therefore to describe evolution of nonlinear water waves under general condition such as nonlinear random waves over arbitrary depths, both the wave nonlinearity and dispersivity must be properly taken into account in the wave modeling. (omitted)

• 한국해양공학회지
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• 제24권1호
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• pp.1-9
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• 2010

A series of experiments employing particle image velocimetry (PIV) technique was conducted to produce benchmark wave kinematics data for regular waves having four different wave slopes in 2-D wave tank. Water velocities and accelerations near the free surface of regular waves were computed from image pair obtained by PIV systems. With the measured wave velocity field, the wave accelerations were computed using a centered finite difference scheme. Both local and convective components of the total accelerations are obtained from experimental data. With increasing the wave slope, the horizontal velocity and the vertical accelerations near the wave crest obtained by PIV technique became larger than theoretical results, which are well-known phenomena of the wave nonlinearity. It is noted that the relative magnitude of convective acceleration to the local acceleration became larger with increasing wave slope.

• Journal of Ship and Ocean Technology
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• 제9권4호
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• pp.11-22
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• 2005

This paper addresses details of wave load nonlinearity effect on stress RAO and damage ratio using component stochastic fatigue analysis. Traditional spectral fatigue analysis for ship structure is based on linear theory; however, there are a number of nonlinearity sources. Especially loading nonlinearity, such as hydrodynamic pressure applying to ship side and gravity changes due to roll and pitch motion, is thought to critically violate the linearity assumption of spectral fatigue analysis, which involves stress RAO as linear parameter. The main focus is placed on how to idealize complicated characteristics of loading nonlinearity and how to implement the nonlinear bias to linear spectral fatigue analysis.

• 비파괴검사학회지
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• 제33권3호
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• pp.257-263
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• 2013

Acoustic nonlinearity of surface waves is an effective method to evaluate the micro damage on the surface of materials. In this method, the $A_1$ (magnitude of the fundamental wave) and $A_2$ (magnitude of the second-order harmonic wave) are measured for evaluation of acoustic nonlinearity. However, if there is another source of second-order harmonic wave other than the material itself, the linear relationship between $A_1{^2}$ and $A_2$ will not be guaranteed. Therefore, the second-order harmonic generation by another source should be fully suppressed. In this paper, we investigated the initial second-order harmonic generation in narrowband surface waves by multi-line laser beams. The spatial profile of laser beam was considered in the cases of Gaussian and square-like. The temporal profile was assumed to be Gaussian. In case of Gaussian spatial profile, the generation of the initial second-order harmonic wave was inevitable. However, when the spatial profile was square-like, the generation of the initial second-order harmonic wave was able to be fully suppressed at specific duty ratio. These results mean that the multi-line laser beams of square-like profile with a proper duty ratio are useful to evaluate the acoustic nonlinearity of the generated surface waves.

• 한국수학사학회지
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• 제15권2호
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• pp.141-160
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• 2002

We investigate the history of the research of the existence of periodic solutions of a nonlinear wave equation with jumping nonlinearity, suggested by Mckenna and Lazer (cf. [15]). We also investigate the recent research of it; a relation between multiplicity of solutions and source terms of the equation when the nonlinearity -($bu^+$-$au^-$) crosses eigenvalues and the source term f is generated by eigenfuntions.