scholarly journals Analysis of boundary conditions in design circuits influence on the shaft line operating state

2020 ◽  
Vol 217 ◽  
pp. 03006
Author(s):  
Alexei Khalyavkin ◽  
Sergey Makeev ◽  
Ali Salamekh ◽  
Aleksandra Ivanovskaya
Keyword(s):  
Boundary Conditions ◽  
Weight Bearing ◽  
Performance Criterion ◽  
Concentrated Load ◽  
Elastic Supports ◽  
Shaft Line ◽  
Design Scheme ◽  
Shaft System ◽  
Action Point ◽  
The One

The work investigates the bearing piece boundary conditions influence on the shaft line operating state, with respect to elastic properties of stern-tube bearings. It is noted that the shaft line is a part of the ship’s power plant and it is a shaft system, located on the same axis. Performance criterion is the deflection of the concentrated load in the design scheme`s action point, modeling the propeller`s weight, bearing parts reactions and the natural frequency of linear lateral oscillations. The design scheme itself is a beam, resting on two elastic supports with a k stiffness factor, with concentrated load acting on the one end and three variants of the boundary conditions: pinched, hinged and sliding supports on another one. The results of calculations are given for different boundary conditions and the stiffness factors of elastic supports. The diagram of natural frequencies of linear lateral oscillations of ship`s shafting line is presented.

scholarly journals Electrically turning periodic structures in cholesteric layer with conical–planar boundary conditions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Oxana Prishchepa ◽  
Mikhail Krakhalev ◽  
Vladimir Rudyak ◽  
Vitaly Sutormin ◽  
Victor Zyryanov
Keyword(s):  
Boundary Conditions ◽  
Periodic Structures ◽  
Cholesteric Liquid Crystal ◽  
Growth Direction ◽  
Smooth Transition ◽  
Defect Structures ◽  
Optical Cell ◽  
Elastic Continuum ◽  
The One ◽  
Experimental Findings

AbstractElectro-optical cell based on the cholesteric liquid crystal is studied with unique combination of the boundary conditions: conical anchoring on the one substrate and planar anchoring on another one. Periodic structures in cholesteric layer and their transformation under applied electric field are considered by polarizing optical microscopy, the experimental findings are supported by the data of the calculations performed using the extended Frank elastic continuum approach. Such structures are the set of alternating over- and under-twisted defect lines whose azimuthal director angles differ by $$180^\circ$$ 180 ∘ . The $$U^+$$ U + and $$U^-$$ U - -defects of periodicity, which are the smooth transition between the defect lines, are observed at the edge of electrode area. The growth direction of defect lines forming a diffraction grating can be controlled by applying a voltage in the range of $$0\le \, V \le 1.3$$ 0 ≤ V ≤ 1.3  V during the process. Resulting orientation and distance between the lines don’t change under voltage. However, at $$V>1.3$$ V > 1.3  V $$U^+$$ U + -defects move along the defect lines away from the electrode edges, and, finally, the grating lines collapse at the cell’s center. These results open a way for the use of such cholesteric material in applications with periodic defect structures where a periodicity, orientation, and configuration of defects should be adjusted.

scholarly journals An Inverse Source Problem for the Generalized Subdiffusion Equation with Nonclassical Boundary Conditions

2021 ◽  
Vol 5 (3) ◽  
pp. 63
Author(s):  
Emilia Bazhlekova
Keyword(s):  
Boundary Conditions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Stability Estimates ◽  
Inverse Source Problem ◽  
Time Data ◽  
Final Time ◽  
Generalized Eigenfunction ◽  
The One ◽  
Initial Boundary Value

An initial-boundary-value problem is considered for the one-dimensional diffusion equation with a general convolutional derivative in time and nonclassical boundary conditions. We are concerned with the inverse source problem of recovery of a space-dependent source term from given final time data. Generalized eigenfunction expansions are used with respect to a biorthogonal pair of bases. Existence, uniqueness and stability estimates in Sobolev spaces are established.

Initial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay

2020 ◽  
Vol 75 (8) ◽  
pp. 713-725 ◽  
Author(s):  
Guenbo Hwang
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Asymptotically Periodic ◽  
The One ◽  
Initial Boundary Value

AbstractInitial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay (LAD) are studied by utilizing a unified method, known as the Fokas method. The method takes advantage of the spectral analysis of both parts of Lax pair and the global algebraic relation coupling all initial and boundary values. We present the explicit analytical solution of the LAD equation posed on the half line and a finite interval with general initial and boundary conditions. In addition, for the case of periodic boundary conditions, we show that the solution of the LAD equation is asymptotically t-periodic for large t if the Dirichlet boundary datum is periodic in t. Furthermore, it can be shown that if the Dirichlet boundary value is asymptotically periodic for large t, then so is the unknown Neumann boundary value, which is uniquely characterized in terms of the given asymptotically periodic Dirichlet boundary datum. The analytical predictions for large t are compared with numerical results showing the excellent agreement.

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

scholarly journals Order parameter profiles in a system with Neumann – Neumann boundary conditions

2018 ◽  
Vol 145 ◽  
pp. 01009 ◽  
Author(s):  
Vassil M. Vassilev ◽  
Daniel M. Dantchev ◽  
Peter A. Djondjorov
Keyword(s):  
Boundary Conditions ◽  
Order Parameter ◽  
Neumann Boundary ◽  
Elliptic Functions ◽  
Thermodynamic System ◽  
Neumann Boundary Conditions ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
The One ◽  
Field Plane

In this article we consider a critical thermodynamic system with the shape of a thin film confined between two parallel planes. It is assumed that the state of the system at a given temperature and external ordering field is described by order-parameter profiles, which minimize the one-dimensional counterpart of the standard ϕ4 Ginzburg–Landau Hamiltonian and meet the so-called Neumann – Neumann boundary conditions. We give analytic representation of the extremals of this variational problem in terms ofWeierstrass elliptic functions. Then, depending on the temperature and ordering field we determine the minimizers and obtain the phase diagram in the temperature-field plane.

Dynamic Instability Analysis and Design Charts of Curved Panels with Linearly Varying Periodic In-Plane Load

2021 ◽  
pp. 2150130
Author(s):  
G. Patel ◽  
A. N. Nayak ◽  
A. K. L. Srivastava
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Dynamic Instability ◽  
Excitation Frequency ◽  
Instability Region ◽  
Concentrated Load ◽  
Simply Supported ◽  
Finite Element Software ◽  
Design Charts ◽  
Curved Panels

The present paper reports an extensive study on dynamic instability characteristics of curved panels under linearly varying in-plane periodic loading employing finite element formulation with a quadratic isoparametric eight nodded element. At first, the influences of three types of linearly varying in-plane periodic edge loads (triangular, trapezoidal and uniform loads), three types of curved panels (cylindrical, spherical and hyperbolic) and six boundary conditions on excitation frequency and instability region are investigated. Further, the effects of varied parameters, such as shallowness parameter, span to thickness ratio, aspect ratio, and Poisson’s ratio, on the dynamic instability characteristics of curved panels with clamped–clamped–clamped–clamped (CCCC) and simply supported-free-simply supported-free (SFSF) boundary conditions under triangular load are studied. It is found that the above parameters influence significantly on the excitation frequency, at which the dynamic instability initiates, and the width of dynamic instability region (DIR). In addition, a comparative study is also made to find the influences of the various in-plane periodic loads, such as uniform, triangular, parabolic, patch and concentrated load, on the dynamic instability behavior of cylindrical, spherical and hyperbolic panels. Finally, typical design charts showing DIRs in non-dimensional forms are also developed to obtain the excitation frequency and instability region of various frequently used isotropic clamped spherical panels of any dimension, any type of linearly varying in-plane load and any isotropic material directly from these charts without the use of any commercially available finite element software or any developed complex model.

scholarly journals Simplified Grinding Temperature Model Study

2019 ◽  
Vol 6 (2) ◽  
pp. a1-a7
Author(s):  
N. V. Lishchenko ◽  
V. P. Larshin ◽  
H. Krachunov
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Heat Source ◽  
Boundary Conditions ◽  
Grinding Temperature ◽  
Temperature Model ◽  
One Dimensional ◽  
Heating And Cooling ◽  
Equation Of Heat Conduction ◽  
The One

A study of a simplified mathematical model for determining the grinding temperature is performed. According to the obtained results, the equations of this model differ slightly from the corresponding more exact solution of the one-dimensional differential equation of heat conduction under the boundary conditions of the second kind. The model under study is represented by a system of two equations that describe the grinding temperature at the heating and cooling stages without the use of forced cooling. The scope of the studied model corresponds to the modern technological operations of grinding on CNC machines for conditions where the numerical value of the Peclet number is more than 4. This, in turn, corresponds to the Jaeger criterion for the so-called fast-moving heat source, for which the operation parameter of the workpiece velocity may be equivalently (in temperature) replaced by the action time of the heat source. This makes it possible to use a simpler solution of the one-dimensional differential equation of heat conduction at the boundary conditions of the second kind (one-dimensional analytical model) instead of a similar solution of the two-dimensional one with a slight deviation of the grinding temperature calculation result. It is established that the proposed simplified mathematical expression for determining the grinding temperature differs from the more accurate one-dimensional analytical solution by no more than 11 % and 15 % at the stages of heating and cooling, respectively. Comparison of the data on the grinding temperature change according to the conventional and developed equations has shown that these equations are close and have two points of coincidence: on the surface and at the depth of approximately threefold decrease in temperature. It is also established that the nature of the ratio between the scales of change of the Peclet number 0.09 and 9 and the grinding temperature depth 1 and 10 is of 100 to 10. Additionally, another unusual mechanism is revealed for both compared equations: a higher temperature at the surface is accompanied by a lower temperature at the depth. Keywords: grinding temperature, heating stage, cooling stage, dimensionless temperature, temperature model.

scholarly journals New Application for the Generalized Incomplete Gamma Function in the Heat Transfer of Nanofluids via Two Transformations

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Abdelhalim Ebaid ◽  
Hibah S. Alhawiti
Keyword(s):  
Heat Transfer ◽  
Exact Solution ◽  
Boundary Conditions ◽  
Gamma Function ◽  
Transfer Equation ◽  
Nonlinear Differential Equations ◽  
Incomplete Gamma Function ◽  
Heat Transfer Equation ◽  
Layer Flow ◽  
The One

The boundary layer flow of nanofluids is usually described by a system of nonlinear differential equations with infinity boundary conditions. These boundary conditions at infinity are transformed into classical boundary conditions via two different transformations. Accordingly, the original heat transfer equation is changed into a new one which is expressed in terms of the new variable. The exact solutions have been obtained in terms of the exponential function for the stream function and in terms of the incomplete Gamma function for the temperature distribution. Furthermore, it is found in this project that a certain transformation reduces the computational work required to obtain the exact solution of the heat transfer equation. Hence, such transformation is recommended for future analysis of similar physical problems. Besides, the other published exact solution was expressed in terms of the WhittakerM function which is more complicated than the generalized incomplete Gamma function of the current analysis. It is important to refer to the fact that the analytical procedure followed in our project is easier and more direct than the one considered in a previous published work.

Comments on “Lamb's problem for fluid-saturated porous media”

1992 ◽  
Vol 82 (5) ◽  
pp. 2263-2273
Author(s):  
M. D. Sharma
Keyword(s):  
Porous Media ◽  
Boundary Conditions ◽  
Solid Phase ◽  
Elastic Solid ◽  
Porous Solid ◽  
Surface Boundary ◽  
Vertical Force ◽  
Saturated Porous Media ◽  
Concentrated Load ◽  
Lamb’S Problem

Abstract Philippacopoulos (1988) discusses axisymmetric wave propagation in a fluid-saturated porous solid half-space. The disturbance is considered to be produced by the concentrated load P0exp(iωt) acting vertically at the surface. Boundary conditions chosen imply that a vertical force acting on the surface of fluid-saturated porous solid exerts no pressure on the interstitial liquid. These boundary conditions do not seem appropriate. In the present study, the boundary conditions have been changed in order to satisfy the concept of porosity. These are also in accordance with those discussed by Deresiewicz and Skalak (1963) for the special case of interface between liquid and liquid-saturated porous media. Analytic expressions have been derived for the displacements at the surface. The limiting case of a dry elastic solid is also deduced. Effects of intergranular energy losses due to solid phase and of dissipation due to flow of pore fluid are exhibited on the displacements at the surface. Contrary to Philippacopoulos (1988), the displacements in saturated poroelastic solids are found to be larger than those in a dry elastic solid with same Lamb's moduli.

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