• 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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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• pp.800-804
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• 2005

In this paper, the radiated sound pressure induced by low velocity impact is obtained by solving the Rayleigh integral equation. For structurally radiated noise, the sound field is directly coupled to the structural motion. Therefore the impact response should be analyzed. It is well known that the presence of the delamination in a composite laminate introduces a local flexibility which changes the dynamic characteristic of the structure. The 2-D simplified delamination model is used to analyze the impact response. And the 3-D non-linear finite element model is developed using gap element to avoid the overlap and penetration between the upper and lower sub-laminates at delamination region. Predicted impact response using 2-D equivalent delamination model are compared with the numerical ones from the 3-D non-linear finite element model.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 춘계학술대회
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• pp.503-507
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• 2004

The radiated sound pressure induced by low-velocity impact is obtained by solving the Rayleigh integral equation. This paper established the sound analysis procedure using impact analysis model. For structurally radiated noise, the sound field is directly coupled to the structural motion. Therefore the impact response should be analyzed. The impact response is computed using the spring-mass model. And the influence of damage on the sound pressure and impacted force history of laminated were investigated. The results show that both radiated sound pressure and impact force history are strongly influenced by damage on laminated.

• Structural Engineering and Mechanics
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• 제55권3호
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• pp.655-674
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• 2015

In this paper, a new and simplified method is presented in which the natural frequencies of the uniform and non-uniform beams are calculated through simple mathematical relationships. The various vibration problems such as: Rayleigh beam under variable axial force, axial vibration of a bar with and without end discrete spring, torsional vibration of a bar with an attached mass moment of inertia, flexural vibration of the beam with laterally distributed elastic springs and also flexural vibration of the beam with effects of viscose damping are investigated. The governing differential equations are first obtained and then; according to a harmonic vibration, are converted into single variable equations in terms of location. Through repetitive integrations, the governing equations are converted into weak form integral equations. The mode shape functions of the vibration are approximated using a power series. Substitution of the power series into the integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of a non-trivial solution for system of equations. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained with those obtained from other published references and results of available finite element software.

• 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.

• 한국광학회지
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• 제7권2호
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• pp.89-95
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• 1996

Gauss pupil를 이용하는 초분해능 광학계가 .lambda.=0.013.mu.m인 연 X-선영역에서 정밀하게 취급되었다. 회절상의 적분에서 허수축방향의 선적분치가 작은 값이 된다는 것을 증명하고 이것을 무시하여 실수축 위의 선적분 만으로서 회절상을 구하였다. 이 광학게에서 회절상이 분해능에 대한 구경의 공간주파수대폭(2.omega. $_{o}$ )의 제약 조건이 없다. .omega..rarw..inf.일 때의 회절상의 중심의 강도의 e$^{-2}$ 배의 강도를 초분해능 광학계가 지니고 있어야 한다는 추가적인 조건에서 부터 .omega.$_{o}$ .geq.1/2.sigma.(.omega.$_{o}$ =12*$10^{5}$ , 1/2.sigma.=5.0*$10^{5}$ )의 조건을 얻고, 이 조건에서부터 .DELTA.x=1/2(FWHM).geq. 0.26.lambda.=0.0034.mu.의 관계식을 얻었다 (단, NA=0.25, Rayleigh resolution limit=2.lambda.). 본 연구에서 .DELTA.x=0.008.mu.m인 초분해능 연X-선 결상계를 제시하였으며 이 분해능은 Rayleigh의 분해한계 2.lambda.=0.026.mu.m보다 작다.

• 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.

• Journal of Communications and Networks
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• 제16권2호
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• pp.162-171
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• 2014

Spectrum sensing is a key technical challenge for cognitive radio (CR). It is well known that multicycle cyclostationarity (MC) detection is a powerful method for spectrum sensing. However, a conventional MC detector is difficult to implement because of its high computational complexity. This paper considers reducing computational complexity by simplifying the test statistic of a conventional MC detector. On the basis of this simplification process, an improved MC detector is proposed. Compared with the conventional detector, the proposed detector has low-computational complexity and high-accuracy sensing performance. Subsequently, the sensing performance is further investigated for the cases of Rayleigh, Nakagami-m, Rician, and Rayleigh fading and lognormal shadowing channels. Furthermore, square-law combining (SLC) is introduced to improve the detection capability in fading and shadowing environments. The corresponding closed-form expressions of average detection probability are derived for each case by the moment generation function (MGF) and contour integral approaches. Finally, illustrative and analytical results show the efficiency and reliability of the proposed detector and the improvement in sensing performance by SLC in multipath fading and lognormal shadowing environments.

• 한국음향학회지
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• 제6권3호
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• pp.5-16
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• 1987

본 논문에서는 충격으로 인한 점탄성층을 가진 경계가 고정된 원형 평판으로부터의 음압복사에 대해 이론적, 실험적으로 연구한다. 층을 가진 평판의 운동을 모우드 해석법과 회전 관성효과와 전단력에 의한 변형을 고려한 Mindlin 의 평판이론으로부터 구한 고유치를 이용하여 구한다. 탄성구와 평판사이의 접촉력은 Hertz 이론으로 구하고 평판의 진동으로부터 복사되는 음압은 Rayleigh integral에 의해 구한다. 또한 층을 가진 평판으로부터 복사되는 음의 파형과 발생되는 음을 감소시키는 방법을 예측한다.

• 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.