• 제목/요약/키워드: Integral equations

검색결과 749건 처리시간 0.027초

Separation Performance of Zigzag Air Classifier

  • Hirajima, Tsuyoshi;Nishida, Takuji;Toshima, Ryutaro;Kataoka, Kenji;Tsunekawa, Masami;Asakura, Kuniomi
    • 대한전자공학회:학술대회논문집
    • /
    • 대한전자공학회 2001년도 The 6th International Symposium of East Asian Resources Recycling Technology
    • /
    • pp.759-764
    • /
    • 2001
  • The separation performance of zigzag air classifier with angle of 90 degrees was studied using narrow size fractions of thin square samples and granular samples. The simulation results of air velocity inside the classifier indicated that the zigzag geometry induces a new pattern consisting of an upward flow and a circulation flow, Experimental results showed that overflow product recovery was described as an integral calculus of normal distribution as a function of dimensionless air velocity ( $V_{A}$ $V_{A50}$), where $V_{A}$ is superficial air velocity and $V_{A50}$ is the $V_{A}$ at the fifty percent recovery. The $V_{A}$ values were predicted using the equations derived from dynamics for a particle dropping in air. A monitoring system that utilizes changes in acoustic signals emitted during the process of air classification was developed to separate PET with desired recovery or grade. The technical feasibility of the on-line monitoring of the PET recovery and grade was demonstrated by measuring relative energy of the signals.signals.als.

  • PDF

현수교케이블의 응력부식에 관한 신뢰성해석 (Reliability Analysis for Stress Corrosion Cracking of Suspension Bridge Wires)

  • Taejun;Andrzej S. Nowak
    • 한국전산구조공학회:학술대회논문집
    • /
    • 한국전산구조공학회 2003년도 봄 학술발표회 논문집
    • /
    • pp.537-544
    • /
    • 2003
  • This paper deals with stress corrosion cracking behavior of high strength steel exposed to marine environments. The objective is to determine the time to failure as a function of hydrogen concentration and tensile stress in the wires. A crack growth curve is modeled using finite element method (FEM) program. The coupled hydrogen diffusion-stress analyses of SCC were programmed separately. The first part is calculating stress and stress intensity /sup 1)/factor of a cylindrical shell, prestressing tendon or suspension bridge wires, from the initiation of cracks to rupture. Virtual crack extension method, contour integral method, and crack tip elements are used for the calculation of stresses in front of the crack tip. Comparisons of the result show a good agreement with the analytical equations and wire tests. The second part of the study deals with the programming of hydrogen diffusion, affected by hydrostatic stress, calculated at the location of boundary of plastic area around the crack tip. The results of paper can be used in the design and management of prestressed structures, cable stayed and suspension bridges. Time dependent correlated parallel reliabilities of a cable, composed of 36 wires, were evaluated by the consideration of the deterioration of stress corrosion cracking.

  • PDF

A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates

  • Benbakhti, Abdeldjalil;Bouiadjra, Mohamed Bachir;Retiel, Noureddine;Tounsi, Abdelouahed
    • Steel and Composite Structures
    • /
    • 제22권5호
    • /
    • pp.975-999
    • /
    • 2016
  • This work investigates a thermomechanical bending analysis of functionally graded sandwich plates by proposing a novel quasi-3D type higher order shear deformation theory (HSDT). The mathematical model introduces only 5 variables as the first order shear deformation theory (FSDT). Unlike the conventional HSDT, the present one presents a novel displacement field which includes undetermined integral variables. The mechanical properties of functionally graded layers of the plate are supposed to change in the thickness direction according to a power law distribution. The core layer is still homogeneous and made of an isotropic ceramic material. The governing equations for the thermomechanical bending investigation are obtained through the principle of virtual work and solved via Navier-type method. Interesting results are determined and compared with quasi-3D and 2D HSDTs. The influences of functionally graded material (FGM) layer thickness, power law index, layer thickness ratio, thickness ratio and aspect ratio on the deflections and stresses of functionally graded sandwich plates are discussed.

Free vibration and buckling analysis of orthotropic plates using a new two variable refined plate theory

  • Issad, Mohammed Naim;Fekrar, Abdelkader;Bakora, Ahmed;Bessaim, Aicha;Tounsi, Abdelouahed
    • Geomechanics and Engineering
    • /
    • 제15권1호
    • /
    • pp.711-719
    • /
    • 2018
  • The present work presents a free vibration and buckling analysis of orthotropic plates by proposing a novel two variable refined plate theory. Contrary to the conventional higher order shear deformation theories (HSDT) and the first shear deformation theory (FSDT), the proposed theory utilizes a novel displacement field which incorporates undetermined integral terms and involves only two unknowns. The governing equations are obtained from the dynamic version of principle of virtual works. The analytical solution of a simply supported orthotropic plate has been determined by using the Navier method. Numerical investigations are performed by employing the proposed model and the obtained results are compared with the existing HSDTs.

Vibration analysis of thick orthotropic plates using quasi 3D sinusoidal shear deformation theory

  • Sadoun, Mohamed;Houari, Mohammed Sid Ahmed;Bakora, Ahmed;Tounsi, Abdelouahed;Mahmoud, S.R.;Alwabli, Afaf S.
    • Geomechanics and Engineering
    • /
    • 제16권2호
    • /
    • pp.141-150
    • /
    • 2018
  • In this current work a quasi 3D "trigonometric shear deformation theory" is proposed and discussed for the dynamic of thick orthotropic plates. Contrary to the classical "higher order shear deformation theories" (HSDT) and the "first shear deformation theory" (FSDT), the constructed theory utilizes a new displacement field which includes "undetermined integral terms" and presents only three "variables". In this model the axial displacement utilizes sinusoidal mathematical function in terms of z coordinate to introduce the shear strain impact. The cosine mathematical function in terms of z coordinate is employed in vertical displacement to introduce the impact of transverse "normal deformation". The motion equations of the model are found via the concept of virtual work. Numerical results found for frequency of "flexural mode", mode of shear and mode of thickness stretch impact of dynamic of simply supported "orthotropic" structures are compared and verified with those of other HSDTs and method of elasticity wherever considered.

Effect of Pasternak foundation: Structural modal identification for vibration of FG shell

  • Hussain, Muzamal;Selmi, Abdellatif
    • Advances in concrete construction
    • /
    • 제9권6호
    • /
    • pp.569-576
    • /
    • 2020
  • Employment of the wave propagation approach with the combination of Pasternak foundation equation gives birth to the shell frequency equation. Mathematically, the integral form of the Lagrange energy functional is converted into a set of three partial differential equations. A cylindrical shell is placed on the elastic foundation of Pasternak. For isotropic materials, the physical properties are same everywhere, whereas the laminated and functionally graded materials, they vary from point to point. Here the shell material has been taken as functionally graded material. The influence of the elastic foundation, wave number, length and height-to-radius ratios is investigated with different boundary conditions. The frequencies of length-to-radius and height-to-radius ratio are counter part of each other. The frequency first increases and gain maximum value in the midway of the shell length and then lowers down for the variations of wave number. It is found that due to inducting the elastic foundation of Pasternak, the frequencies increases. It is also exhibited that the effect of frequencies is investigated by varying the surfaces with stainless steel and nickel as a constituent material. MATLAB software is utilized for the vibration of functionally graded cylindrical shell with elastic foundation of Pasternak and the results are verified with the open literature.

조석(潮汐)의 영향을 받는 수역(水域)에서 연직상향부력(鉛直上向浮力)? -정지수역(靜止水域)- (Vertical Buoyant Jet in Tidal Water-Stagnant Environment)

  • 윤태훈;차영기;김창완
    • 대한토목학회논문집
    • /
    • 제6권2호
    • /
    • pp.93-101
    • /
    • 1986
  • 정지수역(靜止水域)에서 연직상향(鉛直上向)으로 방류(放流)되는 평면부력(平面浮力)?의 거동을 연속방정식(連續方程式), 운동량수송식(運動量輸送式) 및 추적물(追跡物) 수송식(輸送式)에 의하여 수치적(數値的)으로 해석한다. 이 해석은 유함수(流凾數)와 과수송식(過輸送式)을 도입하고 Prandtl 난류모형(亂流模型)을 이용하였다. 방류밀도(放流密度) Froude 수(數)가 4~32인인 부력(浮力)?의 발달된 흐름영역(領域)에서 구한 ?중심선의 속도(速度)와 온도변화(溫度變化), ?주변수역(周邊水域)의 온도분포(溫度分布)와 흐름양상은 기존자료와 잘 맞음을 확인할 수 있다. 적분형해석(積分型解析)에 필요한 퍼짐율과 확산비(擴散比)가 방류밀도(放流密度) Froude 수(數)와 방류구(放流口)로부터의 거리의 함수로 유도된다.

  • PDF

On the modeling of dynamic behavior of composite plates using a simple nth-HSDT

  • Djedid, I. Klouche;Draiche, Kada;Guenaneche, B.;Bousahla, Abdelmoumen Anis;Tounsi, Abdelouahed;Bedia, E.A. Adda
    • Wind and Structures
    • /
    • 제29권6호
    • /
    • pp.371-387
    • /
    • 2019
  • In the present paper, a simple refined nth-higher-order shear deformation theory is applied for the free vibration analysis of laminated composite plates. The proposed displacement field is based on a novel kinematic in which include the undetermined integral terms and contains only four unknowns, as against five or more in case of other higher-order theories. The present theory accounts for adequate distribution of the transverse shear strains through the plate thickness and satisfies the shear stress-free boundary conditions on the top and bottom surfaces of the plate, therefore, it does not require problem dependent shear correction factor. The governing equations of motion are derived from Hamilton's principle and solved via Navier-type to obtain closed form solutions. The numerical results of non-dimensional natural frequencies obtained by using the present theory are presented and compared with those of other theories available in the literature to verify the validity of present solutions. It can be concluded that the present refined theory is accurate and efficient in predicting the natural frequencies of isotropic, orthotropic and laminated composite plates.

평면 배열형 사각형 음향 트랜스듀서의 상호 방사 임피던스 연구 (An Investigation of Mutual Radiation Impedance in a Plane Array Acoustic Transducer)

  • 이종길;서인창
    • 한국음향학회지
    • /
    • 제14권6호
    • /
    • pp.21-26
    • /
    • 1995
  • 본 연구에서는 사각형 음향 진동체가 무한 배플에 고정되어 있을때 진동체 상호간의 방사 임피던스의 양을 예측하기 위하여 적분식을 유도하고 이를 수치해석 하였다. 상호 방사 임피던스를 방사 저항 및 방사 리액턴스로 분리하여 계산하고 이를 ka및 kd의 함수로 출력 하였다. 방사 저항은 ka값의 증가에 따라 요동을 하면서 감소 하였다. 방사 리액턴스는 ka값의 증가에 따라 감소 하였다. 또한 상호 방사 임피던스는 ka의 값이 클수록 방사 임피던스의 양은 요동을 하면서 감소 하였다. 그러나 ka가6, 13및 19의 근처에서는 오히려 상호 임피던스의 영향이 거의 없음을 볼 수 있었고 진동체 상호간의 거리가 멀어질수록 임피던스의 영향이 현저히 감소함을 보았다. 또한ka의 값이 클수록 진동체 상호간의 배치에서 45도의 경우에 상호 간섭이 오히려 감소하였다.

  • PDF

초음파 유량계를 통하는 기체유동의 CFD 해석 (A CFD Analysis of Gas Flow through an Ultrasonic Meter)

  • 김재형;김희동;이호준;황상윤
    • 대한기계학회:학술대회논문집
    • /
    • 대한기계학회 2003년도 추계학술대회
    • /
    • pp.998-1003
    • /
    • 2003
  • Ultrasonic flow metering(UFM) technology is being received much attention from a variety of industrial fields to exactly measure the flow rate. The UFM has much advantage over other conventional flow meter systems, since it has no moving parts, and offers good accuracy and reliability without giving any disturbances to measure the flow rate, thereby not causing pressure losses in the flow fields. In the present study, 3-dimensional, unsteady, compressible Navier-Stokes equations are solved by a finite volume scheme, based upon the second order upwind scheme for spatial derivatives and the multi-stage Runge-Kutta integral method for time derivatives. In order to simulate multi-path ultrasonic flow meter, an excited pressure signal is applied to three different locations upstream, and the pressure signals are received at three different locations downstream. The mean flow velocities are calculated by the time difference between upstream and downstream propagating pressure signals. The obtained results show that the present CFD method simulates successfully ultrasonic meter gas flow and the mean velocity measured along the chord near the wall is considerably influenced by the boundary layers.

  • PDF