• Title/Summary/Keyword: linear differential equation

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Studies on the Diagnosis of Subclinical Mastitis in Cows by the Measurement of the Electrical Conductivity: 1. Comparison of Various Methods of Handling Conductivity Data with the Use of California Mastitis Test and Direct Somatic Cell Count (전기전도도(電氣傳導度) 측정(測定)에 의한 유우(乳牛) 준임상형(準臨床型) 유방염(乳房炎)의 진단(診斷)에 관한 연구(硏究) 1. 전기전도도법(電氣傳導度法)과 간접검진법(間接檢診法)(CMT 및 총체세포수(總體細胞數))과의 비교(比較))

  • Kang, Byong-kyu
    • Korean Journal of Veterinary Research
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    • v.24 no.1
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    • pp.91-98
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    • 1984
  • A total of 466 foremilk from dairy farms in Chonnam district was examined for the subclinical mastitis over a period of one year, using a method of the electrical conductivities(EC); absolute conductivity(AC) and differential conductivity(DC) and quarter difference value(QD), in relation to the California mastitis test(CMT) and the direct somatic cell count(DSCC). The compatibility and efficiency rating between the EC values and the other screening tests was conducted. Obtained results are summarized as follows. 1. A linear relationship was found between the EC values and the CMT scores and direct somatic cell counts and it was found that electrical conductivity measurements were comparable with other screening tests for diagnosing animals with mastitis. 2. Compatibilities between the EC and CMT were 70.4% in AC, 74.6% in DC and 70.7% in QD, and that of the EC and DSCC were 53.0% in AC, 63.1% in DC and 53.2% in QD. On the other hand, relative efficiency ratings of Postle's equation between EC and CMT were 37.3% in AC, 26.5% in DC and 13.6% in QD, and that of the EC and DSCC were 33.1% in AC, 20.2% in DC and 11.9% in QD. 3. In the foremilk samples collected from damaged quarters determined by EC, the false positive rate wart higher than the false negative rate, and consequently tests of EC produced lower compatibility or efficiency rating scores. These tendencies suggested that any factors other than the mastitic condition influencing the EC values might be existed.

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Geomatrically Non-linear Analysis Method by Curvature Based Flexibility Matrix (유연도 매트릭스를 사용한 기하학적 비선형 해석방법)

  • Kim, Jin Sup;Kwon, Min Ho
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.15 no.2
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    • pp.125-135
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    • 2011
  • The latest study for formulation of finite element method and computation techniques has progressed widely. The classical method in the formulation of frame elements for geometrically nonlinear analysis derives the geometric stiffness directly from the governing differential equation for bending with axial force. From the computational viewpoint of this paper, the most common approach is the finite element method. Commonly, the formulation of frame elements for geometrically nonlinear structures is based on appropriate interpolation functions for the transverse and axial displacements of the member. The formulation of flexibility-based elements, on the other hand, is based on interpolation functions for the internal forces. In this paper, a new method is used to suppose that interpolation functions for the displacements from the curvatures is Lagrangian interpolation. This paper derives flexibility matrix from that displacement functions and is considered the application of it. Using the flexibility matrix, this paper apply the program considered geometrically nonlinear analysis to common problems.

The Phase Space Analysis of 3D Vector Fields (3차원 벡터 필드의 위상 공간 분석)

  • Jung, Il-Hong;Kim, Yong Soo
    • Journal of Digital Contents Society
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    • v.16 no.6
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    • pp.909-916
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    • 2015
  • This paper presents a method to display the 3D vector fields by analyzing phase space. This method is based on the connections between ordinary differential equations and the topology of vector fields. The phase space analysis should be geometric interpolation of an autonomous system of equation in the form of the phase space. Every solution of it system of equations corresponds not to a curve in a space, but the motion of a point along the curve. This analysis is the basis of this paper. This new method is required to decompose the hexahedral cell into five or six tetrahedral cells for 3D vector fields. The critical points can be easily found by solving a simple linear system for each tetrahedron. The tangent curves can be integrated by finding the intersection points of an integral curve traced out by the general solution of each tetrahedron and plane containing a face of the tetrahedron.

An analytic solution for the stirling engines with saw-toothed piston motions in adiabatic cylinders (단열실린더내에서 톱날파형 피스톤운동을 하는 스터링기관에 대한 해석적인 해)

  • 유호선
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.12 no.5
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    • pp.1197-1205
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    • 1988
  • An analytical method to predict qualitative performance characteristics of the Stirling Engines in the preliminary design stages is investigated. Both the expansion and the compression cylinder are treated as adiabatic and piston motions are approximated as saw-toothed waves. Basic equations which were originally proposed by Finkelstein consist of mass conservation and energy balances for each adiabatic cylinder. The approximation on piston motions and physical conditions make it possible to divide an engine cycle into four fundamental processes. In each process, first, pressure can be expressed as a function of the crank angle by solving a nonlinear first order ordinary differential equation and other thermodynamic variables are determined in turn. Application of the cyclic steady condition to the whole processes can complete a cycle. Also, further analysis results in analytic expressions for cyclic work and heat transfer in terms of the engine parameters and thermodynamic variables at boundary points. The results are expected useful as a quick reference for the engine performances. Finally, the present method can be applied to the other adiabatic analyses on the Stirling Engines with piece wise linear piston motions, if mass variations are predictable.

Bending of axially functionally graded carbon nanotubes reinforced composite nanobeams

  • Ahmed Drai;Ahmed Amine Daikh;Mohamed Oujedi Belarbi;Mohammed Sid Ahmed Houari;Benoumer Aour;Amin Hamdi;Mohamed A. Eltaher
    • Advances in nano research
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    • v.14 no.3
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    • pp.211-224
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    • 2023
  • This work presents a modified analytical model for the bending behavior of axially functionally graded (AFG) carbon nanotubes reinforced composite (CNTRC) nanobeams. New higher order shear deformation beam theory is exploited to satisfy parabolic variation of shear through thickness direction and zero shears at the bottom and top surfaces.A Modified continuum nonlocal strain gradient theoryis employed to include the microstructure and the geometrical nano-size length scales. The extended rule of the mixture and the molecular dynamics simulations are exploited to evaluate the equivalent mechanical properties of FG-CNTRC beams. Carbon nanotubes reinforcements are distributed axially through the beam length direction with a new power graded function with two parameters. The equilibrium equations are derived with associated nonclassical boundary conditions, and Navier's procedure are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear, or sinusoidal mechanical loadings. Numerical results are carried out to investigate the impact of inhomogeneity parameters, geometrical parameters, loadings type, nonlocal and length scale parameters on deflections and stresses of the AFG CNTRC nanobeams. The proposed model can be used in the design and analysis of MEMS and NEMS systems fabricated from carbon nanotubes reinforced composite nanobeam.

Static bending response of axially randomly oriented functionally graded carbon nanotubes reinforced composite nanobeams

  • Ahmed Amine Daikh;Ahmed Drai;Mohamed Ouejdi Belarbi;Mohammed Sid Ahmed Houari;Benoumer Aour;Mohamed A. Eltaher;Norhan A. Mohamed
    • Advances in nano research
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    • v.16 no.3
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    • pp.289-301
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    • 2024
  • In this work, an analytical model employing a new higher-order shear deformation beam theory is utilized to investigate the bending behavior of axially randomly oriented functionally graded carbon nanotubes reinforced composite nanobeams. A modified continuum nonlocal strain gradient theory is employed to incorporate both microstructural effects and geometric nano-scale length scales. The extended rule of mixture, along with molecular dynamics simulations, is used to assess the equivalent mechanical properties of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beams. Carbon nanotube reinforcements are randomly distributed axially along the length of the beam. The equilibrium equations, accompanied by nonclassical boundary conditions, are formulated, and Navier's procedure is used to solve the resulting differential equation, yielding the response of the nanobeam under various mechanical loadings, including uniform, linear, and sinusoidal loads. Numerical analysis is conducted to examine the influence of inhomogeneity parameters, geometric parameters, types of loading, as well as nonlocal and length scale parameters on the deflections and stresses of axially functionally graded carbon nanotubes reinforced composite (AFG CNTRC) nanobeams. The results indicate that, in contrast to the nonlocal parameter, the beam stiffness is increased by both the CNTs volume fraction and the length-scale parameter. The presented model is applicable for designing and analyzing microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) constructed from carbon nanotubes reinforced composite nanobeams.

Hydrodynamic Simulation of Midwater Trawl System Behavior (중층 트롤 어구 시스템 운동의 유체역학적 시뮬레이션)

  • 차봉진;이춘우;이주희;김현영
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.38 no.2
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    • pp.164-171
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    • 2002
  • In this study, a mass-spring model is used to dynamically describe and calculate the shape and movement of a mid-water trawl system. This mathematical model theorizes that the factors constituting the system are the material points and the external forces such as hydrodynamic load, gravity, and buoyancy act on these material points. In addition, it surmises that these material points are connected to each other by springs, the springs do not have any mass, and the internal force acts on these springs. The non-linear differential equations are implicitly integrated with time for guaranteeing a stable solution. The dynamic simulation by the mass-spring model shows the status of the gear such as fishing gear depth, distance between doors, shape of the gear, and tension of each line. It depends on the parameters such as towing force, warp length, force of a sinker, buoyancy of a float, type of door and netting materials. The validity of the model is verified by comparing simulation motions of a trawl system obtained from computed values to those from an actual experiment.

Dynamic Behavior Modelling of Augmented Objects with Haptic Interaction (햅틱 상호작용에 의한 증강 객체의 동적 움직임 모델링)

  • Lee, Seonho;Chun, Junchul
    • Journal of Internet Computing and Services
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    • v.15 no.1
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    • pp.171-178
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    • 2014
  • This paper presents dynamic modelling of a virtual object in augmented reality environments when external forces are applied to the object in real-time fashion. In order to simulate a natural behavior of the object we employ the theory of Newtonian physics to construct motion equation of the object according to the varying external forces applied to the AR object. In dynamic modelling process, the physical interaction is taken placed between the augmented object and the physical object such as a haptic input device and the external forces are transferred to the object. The intrinsic properties of the augmented object are either rigid or elastically deformable (non-rigid) model. In case of the rigid object, the dynamic motion of the object is simulated when the augmented object is collided with by the haptic stick by considering linear momentum or angular momentum. In the case of the non-rigid object, the physics-based simulation approach is adopted since the elastically deformable models respond in a natural way to the external or internal forces and constraints. Depending on the characteristics of force caused by a user through a haptic interface and model's intrinsic properties, the virtual elastic object in AR is deformed naturally. In the simulation, we exploit standard mass-spring damper differential equation so called Newton's second law of motion to model deformable objects. From the experiments, we can successfully visualize the behavior of a virtual objects in AR based on the theorem of physics when the haptic device interact with the rigid or non-rigid virtual object.

Forced vibrations of an elastic rectangular plate supported by a unilateral two-parameter foundation via the Chebyshev polynomials expansion

  • Zekai Celep;Zeki Ozcan
    • Structural Engineering and Mechanics
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    • v.90 no.6
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    • pp.551-568
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    • 2024
  • The present study deals with static and dynamic behaviors including forced vibrations of an elastic rectangular nano plate on the two-parameter foundation. Firstly, the rectangular plate is assumed to be subjected to uniformly distributed and eccentrically applied concentrated loads. The governing equations of the problem are derived by considering the dynamic response of the plate, employing a series of the Chebyshev polynomials for the displacement function and applying the Galerkin method. Then, effects of the non-essential boundary conditions of the plate, i.e., the boundary conditions related to the shearing forces, the bending moments and the corner forces, are included in the governing equation of motion to compensate for the non-satisfied boundary conditions and increase the accuracy of the Galerkin method. The approximate numerical solution is accomplished using an iterative process due to the non-linearity of the unilateral property of the two-parameter foundation. The plate under static concentrated load is investigated in detail numerically by considering a wide range of parameters of the plate and the foundation stiffnesses. Numerical treatment of the problem in the time domain is carried out by assuming a stepwise variation of the concentrated load and the linear acceleration procedure is employed in the solution of the system of governing differential equations derived from the equation of motion. Time variations of the contact region and those of the displacements of the plate are presented in the figures for various numbers of the two-parameter of the foundation, as well as the classical and nano parameters of the plate particularly focusing on the non-linearity of the problem due to the plate lift-off from the unilateral foundation. The effects of classical and nonlocal parameters and loading are investigated in detail. Definition of the separation between the plate and the two-parameter foundation is presented and applied to the given problem. The effect of the lift-off on the static and dynamic behavior of the rectangular plate is studied in detail by considering various loading conditions. The numerical study shows that the effect of nonlocal parameters on the behavior of the plate becomes significant, when nonlinearity becomes more profound, due to the lift-off of the plate. It is seen that the size effects are significant in static and dynamic analysis of nano-scaled rectangular plates and need to be included in the mechanical analyses. Furthermore, the corner displacement of the plate is affected more significantly from the lift-off, whereas it is less marked in the time variation of the middle displacement of the plate. Several numerical examples are presented to examine the sensibility of various parameters associated with nonlocal parameters of the plate and foundation. Both stiffening and softening nonlocal parameters behavior of the plate are identified in the numerical solutions which show that increasing the foundation stiffness decreases the extent of the contact region, whereas the stiffness of the shear layer increases the contact region and reduces the foundation settlement considerably.

Sol-Gel Synthesis, Crystal Structure, Magnetic and Optical Properties in ZnCo2O3 Oxide

  • Das, Bidhu Bhusan;Barman, Bittesh
    • Journal of the Korean Chemical Society
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    • v.63 no.6
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    • pp.453-458
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    • 2019
  • Synthesis of ZnCo2O3 oxide is performed by sol-gel method via nitrate-citrate route. Powder X-ray diffraction (XRD) study shows monoclinic unit cell having lattice parameters: a = 5.721(1) Å, b = 8.073(2) Å, c = 5.670(1) Å, β = 93.221(8)°, space group P2/m and Z = 4. Average crystallite sizes determined by Scherrer equation are the range ~14-32 nm, whereas SEM micrographs show nano-micro meter size particles formed in ZnCo2O3. Endothermic peak at ~798 K in the Differential scanning calorimetric (DSC) trace without weight loss could be due to structural transformation and the endothermic peak ~1143 K with weight loss is due to reversible loss of O2 in air atmosphere. Energy Dispersive X-ray (EDX) analysis profile shows the presence of elements Zn, Co and O which indicates the purity of the sample. Magnetic measurements in the range of +12 kOe to -12 kOe at 10 K, 77 K, 120 K and at 300 K by PPMS-II Physical Property Measurement System (PPMS) shows hysteresis loops having very low values of the coercivity and retentivity which indicates the weakly ferromagnetic nature of the oxide. Observed X-band EPR isotropic lineshapes at 300 K and 77 K show positive g-shift at giso ~2.230 and giso ~2.217, respectively which is in agreement with the presence of paramagnetic site Co2+(3d7) in the oxide. DC conductivity value of 2.875 ×10-8 S/cm indicates very weakly semiconducting nature of ZnCo2O3 at 300 K. DRS absorption bands ~357 nm, ~572 nm, ~619 nm and ~654 nm are due to the d-d transitions 4T1g(4F)→2Eg(2G), 4T1g(4F)→4T1g(4P), 4T1g(4F)→4A2g(4F), 4T1g(4F)→4T2g(4F), respectively in octahedral ligand field around Co2+ ions. Direct band gap energy, Eg~ 1.5 eV in the oxide is obtained by extrapolating the linear part of the Tauc plot to the energy axis indicates fairly strong semiconducting nature of ZnCo2O3.