• Journal of Advanced Marine Engineering and Technology
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• 제30권1호
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• pp.73-80
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• 2006

In order to compute the radiated sound from a vibrating structure, the Rayleigh's integral equation has to be derived from the Helmholtz equation using Green's function. Generally, the surface velocity in the Rayleigh's integral equation uses the root mean square(rms) velocity. The calculation value is too large, because it's not considered cancelation. On the other hand. using the complex velocity, the sound pressure is calculated too small, because it considers that sound is perfectly canceled out. Therefore, this thesis proposes a correction factor(CF) which considers vibration modes and the method by which to calculate the radiating sound pressure. The theoretical results are compared with the experimental values, and the proposed method can be verified with confluence.

• 한국음향학회지
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• 제27권8호
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• pp.411-417
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• 2008

본 논문에서는 헬름홀쯔 적분 방정식에서 유도된 식을 이용하여 구조물의 표면 압력을 구조진동 성분에 대한 단순한 적분형태로 표현하여 음향방사 및 구조/음향 연성 문제를 수치적으로 푸는 방법에 대하여 다룬다. 이 식은 임의의 형상에 대하여 유도된 식으로 Rayleigh 식과 유사한 형태를 갖는다. 이 식을 이용하면 표면 압력을 구조물의 속도에 대한 단순 적분 형태로 나타낼 수 있기 때문에 경계요소법과 같이 연립방정식에 대한 행렬식을 풀 필요가 없다. 또한 헬름홀쯔 적분 방정식에 기반을 둔 다른 방법 들이 가지는 해의 유일성 문제도 갖지 않는 장점이 있다. 본 논문에서는 구형 셀에 대하여 수치해와 정해를 비교하여 제안한 방법의 타당성을 검증하였다.

• 호남수학학술지
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• 제43권2호
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• pp.183-197
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• 2021

Recently several authors have extended the Beta function by using its integral representation. However, in many cases no expression of these extended functions in terms of classic special functions is known. In the present paper, we introduce a further extension by defining a family of functions G_r,s : ℝ^*₊ → ℂ, with r, s ∈ ℂ and ℜ(r) > 0. For given r, s, we prove that this function satisfies a second-order linear differential equation with rational coefficients. Solving this ODE, we express G_r,s as a combination of confluent hypergeometric functions. From this we deduce a new integral relation satisfied by Tricomi's function. We then investigate additional specific properties of G_r,1 which take the form of new non trivial integral relations involving exponential and error functions. We discuss the connection between G_r,1 and Stokes' first problem (or Rayleigh problem) in fluid mechanics which consists in determining the flow created by the movement of an infinitely long plate. For $r{\in}{\frac{1}{2}}{\mathbb{N}}^*$, we find additional relations between G_r,1 and Hermite polynomials. In view of these results, we believe the family of extended beta functions G_r,s will find further applications in two directions: (i) for improving our knowledge of confluent hypergeometric functions and Tricomi's function, (ii) and for engineering and physics problems.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.1078-1082
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• 2001

An alternative formulation of the Helmholtz integral equation is derived to express the pressure field explicitly in terms of the velocity vector of a radiating surface. This formulation, derived for arbitrary sources, is similar in form to the Rayleigh's formula for planar sources. Because the pressure field is expressed explicitly as a surface integral of the particle velocity, which can be implemented numerically using standard Gaussian quadratures, there is no need to use Boundary element method to solve a set of simultaneous equations for the surface pressure at the discretized nodes. Furthermore the non-uniqueness problem inherent in methods based on Helmholtz integral equation is avoided. Validation of this formulation is demonstrated for some simple geometries.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2012년도 춘계학술대회 논문집
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• pp.763-768
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• 2012

Active window system which can reduce the environmental noises, such as traffic noise and construction noise, from an open window into a room was proposed in the previous works. The key idea of the proposed active window system was that the control sources are approximately collocated with the primary noise source in terms of the acoustic power for global noise reduction throughout the interior room. Moreover, because it is important not to intrude into the living space in the building environment, no error sensors were used and an open-loop control method using control sources at the window frame and the reference sensors outside the room was used for the proposed system. The open-loop control gain was calculated by the interior room model assumed as the semi-infinite space, and the interior sound field was estimated by Rayleigh integral equation under the baffled window model assumption. However, windows with a finite thickness should were considered for the calculation of the open-loop control gain of the active window system since these are representative of most window cases. Therefore, the finite thickness window model based on the Sgard's model was derived and the open-loop control gain using the interior sound field estimated by that model was calculated for active window system. To compare the performance of these two models, a scale-model experiment was performed in an anechoic chamber according to noise source directions. Experimental results showed that the performance for the thickness window model is better than the baffled window model as the angle with respect to the perpendicular direction is larger.

• Advances in Computational Design
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• 제5권4호
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• pp.363-380
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• 2020

In this paper, a cylindrical shell is immersed in a non-viscous fluid using first order shell theory of Sander. These equations are partial differential equations which are solved by approximate technique. Robust and efficient techniques are favored to get precise results. Employment of the Rayleigh-Ritz procedure gives birth to the shell frequency equation. Use of acoustic wave equation is done to incorporate the sound pressure produced in a fluid. Hankel's functions of second kind designate the fluid influence. Mathematically the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. Throughout the computation, simply supported edge condition is used. Expressions for modal displacement functions, the three unknown functions are supposed in such way that the axial, circumferential and time variables are separated by the product method. Comparison is made for empty and fluid-filled cylindrical shell with circumferential wave number, length- and height-radius ratios, it is found that the fluid-filled frequencies are lower than that of without fluid. To generate the fundamental natural frequencies and for better accuracy and effectiveness, the computer software MATLAB is used.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2007년도 추계학술대회논문집
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• pp.812-819
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• 2007

Acoustic Target Strength (TS) is a major parameter of the active sonar equation, which indicates the ratio of the radiated intensity from the source to the re-radiated intensity by a target. This research provides the time pattern of TS in time domain, which is applicable to pulse modulated acoustic pressure field. If the time pattern of TS is predicted by using TS equation in frequency domain, it takes long time and difficult since time function pulsed acoustic wave may be decomposed into their frequency domain components. But TS equation in time domain has a convenience. If the expression for pulsed acoustic field has been obtained, the problem can be solved. Furthermore this paper introduces about mathematical equivalence quantities between EM wave and Acoustic Wave.

• 한국광학회지
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• 제5권3호
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• pp.349-355
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• 1994

Rayleigh의 분해능 한계 $\epsilon_R$보다 작은 선폭 $\epsilon_0$을 분해할 수 있는 광결상계사 이론적으로 취급되었고, 이어서 초분해능을 지니는 광학계가 제시되었다. 먼저 초분해능을 역변환 문제로 취급하여 초분해능 회절상의 진폭 임펄스 함수를 주는 적분방정식을 도입하고 매개변수 $\beta$(양정수)에 따라서 진폭 임펄스 함수의 반치폭이 조사되었다. 이 초분해능 광학계의 구경함수의 진폭 분포가 변조되었고 또 구경에서 나가는 Huygens 파동의 위상도 Holography로 변조되었다. 이들의 변조를 위하여 이용된 광변조 소자가 제시되었다. 초미세 광리소그라피에 유용한 결론을 얻었다.

• 소음진동
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• 제8권2호
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• pp.267-273
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• 1998

This study aims at performing sensitivity analysis of piezoelectric smart structure for minimizing radiated noise from the structure, The structure consists of a flat plate on which disk shaped piezoelectric actuator is mounted, and finite element modeling is used for the structure. The finite element modeling uses a combination of three dimensional piezoelectric, flat shell and transition elements so thus it can take into account the coupling effects of the piezoelectric device precisely and it can also reduce the degrees of freedom of the finite element model. Electric potential on the piezoelectric actuator is taken as a design variable and total radiated power of the structure is chosen as an objective function. The objective function can be represented as Rayleigh's integral equation and is a function of normal displacements of the structure. For the convenience of computation, all degrees of freedom of the finite element equation is condensed out except the normal displacements of the structure. To perform the design sensitivity analysis, the derivative of the objective function with respect to the normal displacements is found, and the derivative of the norma displacements with respect to the design variable is calculated from the finite element equation by using so called the adjoint variable method. The analysis results are compared with those of the finite difference method, and shows a good agreement. This sensitivity analysis is faster and more accurate than the finite difference method. Once the sensitivity analysis program is used for gradient-based optimizations, one could achieve a better convergence rate than non-derivative methods for optimal design of piezoelectric smart structures.

• 비파괴검사학회지
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• 제26권3호
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• pp.181-189
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• 2006

A 2D finite-element numerical simulation has been developed to investigate the generation of ultrasonic waves in a homogeneous isotropic elastic slab under a line-focused laser irradiation. Discussing the physical processes involved in the thermoelastic phenomena, we describe a model for the pulsed laser generation of ultrasound in a metal slab. Addressing an analytic method, on the basis of an integral transform technique, for obtaining the solutions of the elastodynamic equation, we outline a finite element method for a numerical simulation of an ultrasonic wave propagation. We present the numerical results for the displacements and the stresses generated by a line-focused laser pulse on the surface of a stainless steel slab.