• Title/Summary/Keyword: integral equations

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Combined influence of variable distribution models and boundary conditions on the thermodynamic behavior of FG sandwich plates lying on various elastic foundations

  • Djamel Eddine Lafi;Abdelhakim Bouhadra;Belgacem Mamen;Abderahmane Menasria;Mohamed Bourada;Abdelmoumen Anis Bousahla;Fouad Bourada;Abdelouahed Tounsi;Abdeldjebbar Tounsi;Murat Yaylaci
    • Structural Engineering and Mechanics
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    • v.89 no.2
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    • pp.103-119
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    • 2024
  • The present research investigates the thermodynamically bending behavior of FG sandwich plates, laying on the Winkler/Pasternak/Kerr foundation with various boundary conditions, subjected to harmonic thermal load varying through thickness. The supposed FG sandwich plate has three layers with a ceramic core. The constituents' volume fractions of the lower and upper faces vary gradually in the direction of the FG sandwich plate thickness. This variation is performed according to various models: a Power law, Trigonometric, Viola-Tornabene, and the Exponential model, while the core is constantly homogeneous. The displacement field considered in the current work contains integral terms and fewer unknowns than other theories in the literature. The corresponding equations of motion are derived based on Hamilton's principle. The impact of the distribution model, scheme, aspect ratio, side-to-thickness ratio, boundary conditions, and elastic foundations on thermodynamic bending are examined in this study. The deflections obtained for the sandwich plate without elastic foundations have the lowest values for all boundary conditions. In addition, the minimum deflection values are obtained for the exponential volume fraction law model. The sandwich plate's non-dimensional deflection increases as the aspect ratio increases for all distribution models.

Linear Spectral Method for Simulating the Generation of Regular Waves by a Moving Bottom in a 3-dimensional Space (3차원 공간에서 바닥의 움직임에 의한 규칙파의 생성을 모의할 수 있는 선형 스펙트럼법)

  • Jae-Sang Jung;Changhoon Lee
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.36 no.2
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    • pp.70-79
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    • 2024
  • In this study, we introduce a linear spectral method capable of simulating wave generation and transformation caused by a moving bottom in a 3-dimensional space. The governing equations are linear dynamic free-surface boundary conditions and linear kinematic free-surface boundary conditions, which are solved in Fourier space. Solved velocity potential and free-surface displacement should satisfy continuity equation and kinematic bottom boundary condition. For numerical analysis, a 4th order Runge-Kutta method was utilized to analyze the time integral. The results obtained in Fourier space can be converted into velocity potential and free-surface displacement in a real space using inverse Fourier transform. Regular waves generated by various types of moving bottoms were simulated with the linear spectral method. Additionally, obliquely generated regular waves using specified bottom movements were simulated. The results obtained from the spectral method were compared to analytical solutions, showing good agreement between the two.

Optimization of Growth Environments Based on Meteorological and Environmental Sensor Data (기상 및 환경 센서 데이터 기반 생육 환경 최적화 연구)

  • Sook Lye Jeon;Jinheung Lee;Sung Eok Kim;Jeonghwan Park
    • Journal of Sensor Science and Technology
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    • v.33 no.4
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    • pp.230-236
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    • 2024
  • This study aimed to analyze the environmental factors affecting tomato growth by examining the correlation between weather and growth environment sensor data from P Smart Farm located in Gwangseok-myeon, Nonsan-si, Chungcheongnam-do. Key environmental variables such as the temperature, humidity, sunlight hours, solar radiation, and daily light integral (DLI) significantly affect tomato growth. The optimal temperature and DLI conditions play crucial roles in enhancing tomato growth and the photosynthetic efficiency. In this study, we developed a model to correct and predict the time-series variations in internal environmental sensor data using external weather sensor data. A linear regression analysis model was employed to estimate the external temperature variations and internal DLI values of P Smart Farm. Then, regression equations were derived based on these data. The analysis verified that the estimated variations in external temperature and internal DLI are explained effectively by the regression models. In this research, we analyzed and monitored smart-farm growth environment data based on weather sensor data. Thereby, we obtained an optimized model for the temperature and light conditions crucial for tomato growth. Additionally, the study emphasizes the importance of sensor-based data analysis in dynamically adjusting the tomato growth environment according to the variations in weather and growth conditions. The observations of this study indicate that analytical solutions using public weather data can provide data-driven operational experiences and productivity improvements for small- and medium-sized facility farms that cannot afford expensive sensors.

Closed Integral Form Expansion for the Highly Efficient Analysis of Fiber Raman Amplifier (라만증폭기의 효율적인 성능분석을 위한 라만방정식의 적분형 전개와 수치해석 알고리즘)

  • Choi, Lark-Kwon;Park, Jae-Hyoung;Kim, Pil-Han;Park, Jong-Han;Park, Nam-Kyoo
    • Korean Journal of Optics and Photonics
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    • v.16 no.3
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    • pp.182-190
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    • 2005
  • The fiber Raman amplifier(FRA) is a distinctly advantageous technology. Due to its wider, flexible gain bandwidth, and intrinsically lower noise characteristics, FRA has become an indispensable technology of today. Various FRA modeling methods, with different levels of convergence speed and accuracy, have been proposed in order to gain valuable insights for the FRA dynamics and optimum design before real implementation. Still, all these approaches share the common platform of coupled ordinary differential equations(ODE) for the Raman equation set that must be solved along the long length of fiber propagation axis. The ODE platform has classically set the bar for achievable convergence speed, resulting exhaustive calculation efforts. In this work, we propose an alternative, highly efficient framework for FRA analysis. In treating the Raman gain as the perturbation factor in an adiabatic process, we achieved implementation of the algorithm by deriving a recursive relation for the integrals of power inside fiber with the effective length and by constructing a matrix formalism for the solution of the given FRA problem. Finally, by adiabatically turning on the Raman process in the fiber as increasing the order of iterations, the FRA solution can be obtained along the iteration axis for the whole length of fiber rather than along the fiber propagation axis, enabling faster convergence speed, at the equivalent accuracy achievable with the methods based on coupled ODEs. Performance comparison in all co-, counter-, bi-directionally pumped multi-channel FRA shows more than 102 times faster with the convergence speed of the Average power method at the same level of accuracy(relative deviation < 0.03dB).

Analysis of 2-D Potential Problem with L-shape Domain by p-Convergent Boundary Element Method (p-수렴 경계요소법에 의한 L-형 영역을 갖는 2차원 포텐셜 문제 해석)

  • Woo, Kwang-Sung;Jo, Jun-Hyung
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.22 no.1
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    • pp.117-124
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    • 2009
  • The p-convergent boundary element method has been proposed to analyze two-dimensional potential problem on the basis of high order Legendre shape functions that have different property comparing with the shape functions in conventional boundary element method. The location of nodes corresponding to high order shape function are not defined along the boundary, called by nodeless node, similar to the p-convergent finite element method. As the order of shape function increases, the collocation point method is used to solve linear simultaneous equations. The collocation patterns of p-convergent boundary element method consist of non-symmetric hierarchial or symmetric non-hierarchical. As the order of shape function increases, the number of collocation point increases. The singular integral that appears in p-convergent boundary element has been calculated by special numeric quadrature technique and semi-analytical integration technique. The L-shape domain problem including singularity in the vicinity of reentrant comer is analyzed and the numerical results show that the relative error is smaller than $10^{-2}%$ range as compared with other results in literatures. In case of same condition, the symmetric p-collocation point pattern shows high accuracy of solution.

Highly Linear Wideband LNA Design Using Inductive Shunt Feedback (Inductive Shunt 피드백을 이용한 고선형성 광대역 저잡음 증폭기)

  • Jeonng, Nam Hwi;Cho, Choon Sik
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.24 no.11
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    • pp.1055-1063
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    • 2013
  • Low noise amplifiers(LNAs) are an integral component of RF receivers and are frequently required to operate at wide frequency bands for various wireless systems. For wideband operation, important performance metrics such as voltage gain, return loss, noise figures and linearity have been carefully investigated and characterized for the proposed LNA. An inductive shunt feedback configuration is successfully employed in the input stage of the proposed LNA which incorporates cascaded networks with a peaking inductor in the buffer stage. Design equations for obtaining low and high input matching frequencies are easily derived, leading to a relatively simple method for circuit implementation. Careful theoretical analysis explains that poles and zeros are characterized and utilized for realizing the wideband response. Linearity is significantly improved because the inductor between gate and drain decreases the third-order harmonics at the output. Fabricated in $0.18{\mu}m$ CMOS process, the chip area of this LNA is $0.202mm^2$, including pads. Measurement results illustrate that input return loss shows less than -7 dB, voltage gain greater than 8 dB, and a little high noise figure around 7~8 dB over 1.5~13 GHz. In addition, good linearity(IIP3) of 2.5 dBm is achieved at 8 GHz and 14 mA of current is consumed from a 1.8 V supply.

Aerodynamic noise reduction of fan motor unit of cordless vacuum cleaner by optimal designing of splitter blades for impeller (임펠라 스플리터 날개 최적 설계를 통한 무선진공청소기 팬 모터 단품의 공력 소음 저감)

  • Kim, Kunwoo;Ryu, Seo-Yoon;Cheong, Cheolung;Seo, Seongjin;Jang, Cheolmin;Seol, Hanshin
    • The Journal of the Acoustical Society of Korea
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    • v.39 no.6
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    • pp.524-532
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    • 2020
  • In this study, noise radiated from a high-speed fan-motor unit for a cordless vacuum cleaner is reduced by designing splitter blades on the existing impeller. First of all, in order to investigate the flow field through a fan-motor unit, especially impeller, the unsteady incompressible Reynolds-Averaged Navier-Stokes (RANS) equations are numerically solved by using computational fluid dynamic technique. With predicted flow field results as input, the Ffowcs Williams-Hawkings (FW-H) integral equation is solved to predict aerodynamic noise radiated from the impeller. The validity of the numerical methods is confirmed by comparing the predicted sound pressure spectrum with the measured one. Further analysis of the predicted flow field shows that the strong vortex is formed between the impeller blades. As the vortex induces the loss of the flow field and acts as an aerodynamic noise source, supplementary splitter blades are designed to the existing impeller to suppress the identified vortex. The length and position of splitter are selected as design factors and the effect of each design factor on aerodynamic noise is numerically analyzed by using the Taguchi method. From this results, the optimum location and length of splitter for minimum radiated noise is determined. The finally selected design shows lower noise than the existing one.

Probability Distribution of Nonlinear Random Wave Heights Using Maximum Entropy Method (최대 엔트로피 방법을 이용한 비선형 불규칙 파고의 확률분포함수)

  • 안경모
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.10 no.4
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    • pp.204-210
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    • 1998
  • This paper presents the development of the probability density function applicable for wave heights (peak-to-trough excursions) in finite water depth including shallow water depth. The probability distribution applicable to wave heights of a non-Gaussian random process is derived based on the concept of the maximum entropy method. When wave heights are limited by breaking wave heights (or water depth) and only first and second moments of wave heights are given, the probability density function developed is closed form and expressed in terms of wave parameters such as $H_m$(mean wave height), $H_{rms}$(root-mean-square wave height), $H_b$(breaking wave height). When higher than third moment of wave heights are given, it is necessary to solve the system of nonlinear integral equations numerically using Newton-Raphson method to obtain the parameters of probability density function which is maximizing the entropy function. The probability density function thusly derived agrees very well with the histogram of wave heights in finite water depth obtained during storm. The probability density function of wave heights developed using maximum entropy method appears to be useful in estimating extreme values and statistical properties of wave heights for the design of coastal structures.

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A Study on the Design of Ship′s Bow Form using Surface Panel Method (판요소법을 이용한 선수형상 설계에 관한 연구[1])

  • Jae-Hoon Yoo;Hyo-Chul Kim
    • Journal of the Society of Naval Architects of Korea
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    • v.33 no.3
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    • pp.35-47
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    • 1996
  • A surface panel method treating a boundary-value problem of the Dirichlet type is presented to design a three dimensional body with free surface corresponding to a prescribed pressure distribution. An integral equation is derived from Green's theorem, giving a relation between total potential of known strength and the unknown local flux. Upon discretization, a system of linear simultaneous equations is formed including free surface boundary condition and is solved for an assumed geometry. The pseudo local flux, present due to the incorrect positioning of the assumed geometry, plays a role f the geometry corrector, with which the new geometry is computed for the next iteration. Sample designs for submerged spheroids and Wigley hull and carried out to demonstrate the stable convergence, the effectiveness and the robustness of the method. For the calculation of the wave resistance, normal dipoles and Rankine sources are distributed on the body surface and Rankine sources on the free surface. The free surface boundary condition is linearized with respect to the oncoming flow. Four-points upwind finite difference scheme is used to compute the free surface boundary condition. A hyperboloidal panel is adopted to represent the hull surface, which can compensate the defects of the low-order panel method. The design of a 5500TEU container carrier is performed with respect to reduction of the wave resistance. To reduce the wave resistance, calculated pressure on the hull surface is modified to have the lower fluctuation, and is applied as a Dirichlet type dynamic boundary condition on the hull surface. The designed hull form is verified to have the lower wave resistance than the initial one not only by computation but by experiment.

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Optimal design of impeller in fan motor unit of cordless vacuum cleaner for improving flow performance and reducing aerodynamic noise (무선진공청소기 팬 모터 단품의 유량성능 향상과 공력소음 저감을 위한 임펠라 최적설계)

  • Kim, KunWoo;Ryu, Seo-Yoon;Cheong, Cheolung;Seo, Seongjin;Jang, Cheolmin
    • The Journal of the Acoustical Society of Korea
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    • v.39 no.5
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    • pp.379-389
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    • 2020
  • In this study, the flow and noise performances of high-speed fan motor unit for cordless vacuum cleaner is improved by optimizing the impeller which drives the suction air through flow passage of the cordless vacuum cleaner. Firstly, the unsteady incompressible Reynolds averaged Navier-Stokes (RANS) equations are solved to investigate the flow through the fan motor unit using the computational fluid dynamics techniques. Based on flow field results, the Ffowcs-Williams and Hawkings (FW-H) integral equation is used to predict flow noise radiated from the impeller. Predicted results are compared to the measured ones, which confirms the validity of the numerical method used. It is found that the strong vortex is formed around the mid-chord region of the main blades where the blade curvature change rapidly. Given that vortex acts as a loss for flow and a noise source for noise, impeller blade is redesigned to suppress the identified vortex. The response surface method using two factors is employed to determine the optimum inlet and outlet sweep angles for maximum flow rate and minimum noise. Further analysis of finally selected design confirms the improved flow and noise performance.