• Title/Summary/Keyword: harmonic function

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Vibration of multilayered functionally graded deep beams under thermal load

  • Bashiri, Abdullateef H.;Akbas, Seref D.;Abdelrahman, Alaa A.;Assie, Amr;Eltaher, Mohamed A.;Mohamed, Elshahat F.
    • Geomechanics and Engineering
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    • v.24 no.6
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    • pp.545-557
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    • 2021
  • Since the functionally graded materials (FGMs) are used extensively as thermal barriers in many of applications. Therefore, the current article focuses on studying and presenting dynamic responses of multilayer functionally graded (FG) deep beams placed in a thermal environment that is not addressed elsewhere. The material properties of each layer are proposed to be temperature-dependent and vary continuously through the height direction based on the Power-Law function. The deep layered beam is exposed to harmonic sinusoidal load and temperature rising. In the modelling of the multilayered FG deep beam, the two-dimensional (2D) plane stress continuum model is used. Equations of motion of deep composite beam with the associated boundary conditions are presented. In the frame of finite element method (FEM), the 2D twelve-node plane element is exploited to discretize the space domain through the length-thickness plane of the beam. In the solution of the dynamic problem, Newmark average acceleration method is used to solve the time domain incrementally. The developed procedure is verified and compared, and an excellent agreement is observed. In numerical examples, effects of graduation parameter, geometrical dimension and stacking sequence of layers on the time response of deep multilayer FG beams are investigated with temperature effects.

On the wave propagations of football game ball after contacting with the player foot

  • Lei Sun;Cancan Wei;Fei Liu;Lijun Wang;Bo Ren
    • Geomechanics and Engineering
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    • v.33 no.6
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    • pp.529-542
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    • 2023
  • Wave propagation with high transverse deflection could affect the stability of the ball in its trajectory. For low stiffness balls similar to soccer and volleyball balls, the waves are more noticeable in comparison to other balls like ping-pong ball. On the other hand, the soccer balls are under heavy impact loads from shoots and contacting different objects in the field. The maximum recorded speed of a soccer ball after kicking is the 211 km/hr and the average maximum speed is around 112 km/hr. Therefore, in such speeds the aerodynamic forces become important which are directly related to geometrical shape of the ball. In this regard, the wave propagation in soccer ball is examined in the current study using large deformation shear deformable formulations. Classical relations of stress-strain components are taken into consideration along with minimum total energy principle. The final derived relations were solved by using harmonic differential quadrature method. The results are generally presented ion term of phase velocity as function of different influencing parameters of the materials, geometry and mass of the ball.

Hygrothermal sound radiation analysis of layered composite plate using HFEM-IBEM micromechanical model and experimental validation

  • Binita Dash;Trupti R Mahapatra;Punyapriya Mishra;Debadutta Mishra
    • Structural Engineering and Mechanics
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    • v.89 no.3
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    • pp.265-281
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    • 2024
  • The sound radiation responses of multi-layer composite plates subjected to harmonic mechanical excitation in hygrothermal environment is numerically investigated. A homogenized micromechanical finite element (FE) based on the higher-order mid-plane kinematics replicating quadratic function as well as the through the thickness stretching effect together with the indirect boundary element (IBE) scheme has been first time employed. The isoparametric Lagrangian element (ten degrees of freedom per node) is used for discretization to attain the hygro-thermo-elastic natural frequencies and the modes of the plate via Hamilton's principle. The effective material properties under combined hygrothermal loading are considered via a micromechanical model. An IBE method is then implemented to attain structure-surrounding coupling and the Helmholtz wave equation is solved to compute the sound radiation responses. The effectiveness of the model is tested by converging it with the similar analytical/numerical results as well as the experimentally acquired data. The present scheme is further hold out for solving diverse numerical illustrations. The results revealed the relevance of the current higher-order FE-IBE micromechanical model in realistic estimation of hygro-thermo-acoustic responses. The geometrical parameters, volume fraction of fiber, layup, and support conditions alongside the hygrothermal load is found to have significant influence on the vibroacoustic characteristics.

Inhomogeneous Helmholtz equation for Water Waves on Variable Depth (비균질 Helmholtz 방정식을 이용한 변동 수심에서의 파랑변형)

  • Kim, Hyo-Seob;Jang, Chang-Hwan
    • Journal of the Korean Society for Marine Environment & Energy
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    • v.13 no.3
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    • pp.174-180
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    • 2010
  • The inhomogeneous Helmholtz equation is introduced for variable water depth and potential function and separation of variables are introduced for the derivation. Only harmonic wave motions are considered. The governing equation composed of the potential function for irrotational flow is directly applied to the still water level, and the inhomogeneous Helmholtz equation for variable water depth is obtained. By introducing the wave amplitude and wave phase gradient the governing equation with complex potential function is transformed into two equations of real variables. The transformed equations are the first and second-order ordinary differential equations, respectively, and can be solved in a forward marching manner when proper boundary values are supplied, i.e. the wave amplitude, the wave amplitude gradient, and the wave phase gradient at a side boundary. Simple spatially-centered finite difference numerical schemes are adopted to solve the present set of equations. The equation set is applied to two test cases, Booij’ inclined plane slope profile, and Bragg’ wavy bed profile. The present equations set is satisfactorily verified against other theories including the full linear equation, Massel's modified mild-slope equation, and Berkhoff's mild-slope equation etc.

The Developed Study for SMPS to Protect the Noise and Inrush Current at LED Lighting Source (LED 광원에서 잡음 및 돌입전류 방지를 위한 스위칭모드 전원공급 장치 (SMPS) 개발 연구)

  • Chung, Chansoo;Hong, Gyujang;We, Sungbok;Yu, Geonsu;Kim, Mijin
    • KEPCO Journal on Electric Power and Energy
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    • v.2 no.4
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    • pp.577-582
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    • 2016
  • This Study focused on the development of SMPS (Switching Mode Power Supply) to supply the constant votage and current nevertheless LED fluorescent Light generated the electric noise (with Harmonics) and Inrush current at instant time of turn-on and off. Recently, according to the Green policy in government, the LED fluorescent Lighter showed the rapidly increasing tend as indoor and outdoor Lighter. But, because of costs, LED fluorescent Light not considered and neglected the following items; power factor, efficiency, Harmonics and Inrush current. So, we are developed the SMPS about 3 key issues as follows: 1st, power factor and efficiency is 85%. 2nd, the switching noisy by harmonic is minimized. 3rd, the Inrush current at turn on and off time is reduced the minimum 0.3 A after $100{\mu}sec$ on turnon time. The proposed SMPS adjusted by LNK 409 driver (included the high frequency modulation function). Although, the developed SMPS maintained the about 85% of power factor and efficiency. but, the SMPS must be generated low heat by the variation of minute load current at switching timing. To improve the above weak point, the developed SMPS have the feedback monitoring circuit between input side and output side to maintain the power factor and efficiency. Also, we are studied the time-constant of control circuit to output the constant voltage and current nevertheless the load disturbance of LED lighting. The LED fluorescent Light of 46W is checked the above items.

A Study on Maximum Responses of Rotational Shells Subjected to Uneven Settlements by Stochastic Method (부등침하를 받는 회전 쉘의 최대응답 추정에 관한 연구)

  • 정명채
    • Computational Structural Engineering
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    • v.10 no.3
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    • pp.175-184
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    • 1997
  • The objective of this paper is to study arelationship between maximum response and its standard deviation of rotational shells that are subjected to uneven settlements. For this, the ratio, .eta, of the maximum response to standard deviation and it's approximate, .eta./sub apr/, are investigated by stochastic methods. Also, an equation for .eta./sub apr/, that is a function of predominant harmonic number is suggested. The settlements are represented by the Fourier series. Each term in the series contains two coefficients; the amplitude and the phase angle. It is assumed that phase angles are random variables and amplitudes are deterministic. To investigate the characteristics of .eta. and .eta./sub apr/, 100 phase angles for two types of artificial amplitudes spectra are used in the analysis. .eta. and .eta./sub apr/, are almost constant regardless of amplitude type, position of a shell or type of responses; they fall into from 2.0 to 2.5. .eta./sub apr/ is always close to .eta., but tends to be somewhat greater. It may be concluded that a maximum responses of rotational shells subjected to uneven settlements are .eta./sub apr/ (about 2.5) times of its standard deviation. It is considered that this result is used when we design rotational shell structures subjected to differential settlements.

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Variation Pattern Analysis on the Air and Surface Water Temperatures of the Yellow Sea Monitoring Buoy (황해중부부이에서 관측된 기온 및 표층수온의 변화양상 분석)

  • Cho, Hong-Yeon;Jeong, Jin-Yong;Shim, Jae-Seol;Kim, Seon-Jeong
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.22 no.5
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    • pp.316-325
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    • 2010
  • Harmonic analyses are carried out in order to obtain the major frequency components of the air temperature (AT) and surface water temperature (SWT) data monitored in the Middle Area of the Yellow Sea (Yellow Sea monitoring buoy). The analysis shows the annual and semi-annual components are predominant and the higher frequency components are relatively weak with contribution to the short fluctuations, i.e. below $0.2{\sim}0.5^{\circ}C$, in the AT and SWT. The standard deviation of the AT residual is 2.4 times larger than that of the SWT residual and the occurrence frequency distributions of the AT and SWT residual components are both closely fitted to a normal-distribution function. The variation pattern on the AT-SWT plane forms the clear continuous hysteresis loop in anti-clockwise direction which is composed of the AT-SWT rising period, AT-SWT falling period, and the constant SWT period in winter season.

Prototype Development of Marine Information based Supporting System for Oil Spill Response (해양정보기반 방제지원시스템 프로토타입 구축에 관한 연구)

  • Kim, Hye-Jin;Lee, Moonjin
    • Journal of the Korean Association of Geographic Information Studies
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    • v.11 no.4
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    • pp.182-192
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    • 2008
  • In oder to develop a decision supporting system for oil spill response, the prototype of pollution response support system which has integrated oil spill prediction system and pollution risk prediction system has developed for Incheon-Daesan area. Spill prediction system calculates oil spill aspects based on real-time wind data and real-time water flow and the residual volume of spilt oil and spread pattern are calculated considering the characteristic of spilt oil. In this study, real-time data is created from results of real-time meteorological forecasting model(National Institute of Environmental Research) using ftp, real-time tidal currents datasets are built using CHARRY(Current by Harmonic Response to the Reference Yardstick) model and real-time wind-driven currents are calculated applying the correlation function between wind and wind-driven currents. In order to model the feature which is spilt oil spreading according to real-time water flow is weathered, the decrease ratio by oil kinds was used. These real-time data and real-time prediction information have been integrated with ESI(Environmental Sensitivity Index) and response resources and then these are provided using GIS as a whole system to make the response strategy.

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Output Characteristics of a Pulsed Ti:sapphire Laser Oscillator Pumped Longitudinally by Second Harmonic Wave of Nd:YAG Laser and a Ti:sapphire Laser Amplifier Operated along the Single Path of the Oscillator Beam (Nd:YAG 레이저의 제 2조화파로 종여기하는 펄스형 Ti:sapphire 레이저 발진기와 이를 이용한 단일경로 형태의 Ti:sapphire 증폭기의 출력특성)

  • Kim, Kyung-Nam;Jo, Jae-Heung;Lim, Gwon;Cha, Byung-Heon
    • Korean Journal of Optics and Photonics
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    • v.18 no.1
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    • pp.66-73
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    • 2007
  • The various output characteristics of a pulsed Ti:sapphire laser oscillator with a plane-parallel resonator, pumped longitudinally by the second harmonic wave of a Nd:YAG laser, and the output of a Ti:sapphire laser amplifier operated along the single path of the oscillator beam were investigated and analyzed. In the case of the oscillator, we measured the spectrum, the pulse buildup time, the temporal duration time of the pulse, and the output energy according to the variation of the pumping energy, resonator length, and the reflectance of the output coupler. And, in the case of the amplifier, we investigated and analyzed the output energy of the amplifier as a function of the time difference between the two pump beams of the oscillator and the amplifier, the pumping energy of the oscillator, and the pumping energy of the amplifier When pump energies of both the oscillator and the amplifier were 18 mJ/pulse, we could find that the output energy of the amplifier increased linearly and gradually up to the time difference of 35 ns. Finally, we determined that the slope efficiencies of the oscillator and the amplifier were 23.5 % and 11.6 %, respectively.

Geomagnetic Field Distribution in the Korean Peninsula by Spherical Harmonic Analysis (구면조화해석(球面調和解析)에 의(依)한 한반도내(韓半島內)의 지구자기장(地球磁氣場)의 분포(分布)에 관(關)한 연구(硏究))

  • Min, Kyung Duck;Lee, Sunhee
    • Economic and Environmental Geology
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    • v.12 no.2
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    • pp.95-104
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    • 1979
  • The position of any point on the earth's surface can be. represented in the spherical coordinates by surface spherical harmonics. Since geomagnetic field is a function of position on the earth, it can be also expressed by spherical harmonic analysis as spherical harmonics of trigonometric series of $a_m({\theta})$ cos $m{\phi}$ and $b_m({\theta})$ sin $m{\phi}$. Coefficients of surface spherical harmonics, $a_m({\theta})$ and $b_m({\theta})$, can be drawn from the components of the geomagnetic field, declination and inclination, and vice versa. In this paper, components of geomagnetic field, declination and inclination in the Korean peninsula are obtained by spherical harmonic analysis using the Gauss coefficients calculated from the world-wide magnetic charts of 1960. These components correspond to the values of normal geomagnetic field having no disturbances of subsurface mass, structure, and so on. The vertical and total components offer the zero level for the interpretation of geomagnetic data obtained by magnetic measurement in the Korean peninsula. Using this zero level, magnetic anomaly map is obtained from the data of airborne magnetic. prospecting carried out during 1958 to 1960. The conclusions of this study are as follows; (1) The intensity of horizontal component of normal geomagnetic field in Korean peninsula ranges from $2{\times}10^4$ gammas to $2.45{\times}10^4$ gammas. It decreases about 500 with the increment of $1^{\circ}$ in latitude. Along the same. latitude, it increases 250 gammas with the increment of $1^{\circ}$ in longitude. (2) Intensity of vertical component ranges from $3.85{\times}10^4$ gammas to $5.15{\times}10^4$ gammas. It increases. about 1000 gammas with the increment of $1^{\circ}$ in latitude. Along the same latitude, it decreases. 150~240 gammas with the increment of $1^{\circ}$ in longitude. Decreasing rate is considerably larger in higher latitude than in lower latitude. (3) Total intensity ranges from $4.55{\times}10^4$ gammas to $5.15{\times}10^4$ gammas. It increases 600~700 gammas with the increament of $1^{\circ}$ in latitude. Along the same latitude, it decreases 10~90 gammas. with the increment of $1^{\circ}$ in longitude. Decreasing rate is considerably larger in higher latitude as the case of vertical component. (4) The declination ranges from $-3.8^{\circ}$ to $-11.5^{\circ}$. It increases $0.6^{\circ}$ with the increment of $1^{\circ}$ in latitude. Along the same latutude, it increases $0.6^{\circ}$ with the increment of l O in longitude. Unlike the cases of vertical and total component, the rate of change is considerably larger in lower latitude than in higher latitude. (5) The inclination ranges from $57.8^{\circ}$ to $66.8^{\circ}$. It increases about $1^{\circ}$ with 'the increment of $1^{\circ}$ in latitude Along the same latitude, it dereases $0.4^{\circ}$ with the increment of $1^{\circ}$ in longitude. (6) The Boundaries of 5 anomaly zones classified on the basis of the trend and shape of anomaly curves correspond to the geologic boundaries. (7) The trend of anomaly curves in each anomaly zone is closely related to the geologic structure developed in the corresponding zone. That is, it relates to the fault in the 3rd zone, the intrusion. of granite in the 1st and 5th zones, and mountains in the 2nd and 4th zones.

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