scholarly journals Ranges of Backwater Curves in Lower Odra

2018 ◽  
Vol 28 (4) ◽  
pp. 25-35
Author(s):  
Robert Mańko
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Cross Section ◽  
River Network ◽  
Hydrological Conditions ◽  
Complicated System ◽  
Odra River ◽  
The Cross

Abstract In the paper, the backwater curve ranges at the mouth of the Odra River with changing boundary conditions were analysed. The aim of the study is to determine which boundary condition, i.e. stage of lower cross-section or flow in upper cross-section, has a greater impact on the formation of the backwater curve at the mouth of the Odra River. Due to the complicated system of the Lower Odra River network (Międzyodrze and Dabie Lake), the analysis takes into consideration a section of the Odra River from a weir in Widuchowa upwards, thereby accepting as an axiom that the cross-section in Widuchowa is within the range of sea impact, regardless of other hydrological conditions.

The Transverse Vibration of a Doubly Tapered Beam

1977 ◽  
Vol 44 (1) ◽  
pp. 123-126 ◽  
Author(s):  
D. O. Banks ◽  
G. J. Kurowski
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Cross Section ◽  
Transverse Vibration ◽  
Eigenvalues And Eigenfunctions ◽  
Free Boundary Conditions ◽  
Tapered Beam ◽  
Transverse Vibrations ◽  
The Cross ◽  
Homogeneous Beam

We analyze the transverse vibrations of a thin homogeneous beam which is symmetric with respect to the x-y and x-z planes. The cross section of the beam at x is assumed to have the form D(x)={(x,y,z)|x∈[0,1],y=xαy1,z=xβz1,(y1,z1)∈D1} where D1 is the cross section at x = 1. Expressions are obtained from which the eigenvalues and eigenfunctions can be easily found for 0 ≤ α < 2 and all combinations of clamped, hinged, guided, and free boundary conditions at both ends of the beam.

Convective Heat Transfer in Elliptical Microchannels Under Slip Flow Regime and H1 Boundary Conditions

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Pamela Vocale ◽  
Gian Luca Morini ◽  
Marco Spiga
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Convective Heat Transfer ◽  
Cross Section ◽  
Convective Heat ◽  
Slip Flow ◽  
The Cross ◽  
Cross Section Geometry

In this work, hydrodynamically and thermally fully developed gas flow through elliptical microchannels is numerically investigated. The Navier–Stokes and energy equations are solved by considering the first-order slip flow boundary conditions and by assuming that the wall heat flux is uniform in the axial direction, and the wall temperature is uniform in the peripheral direction (i.e., H1 boundary conditions). To take into account the microfabrication of the elliptical microchannels, different heated perimeter lengths are analyzed along the microchannel wetted perimeter. The influence of the cross section geometry on the convective heat transfer coefficient is also investigated by considering the most common values of the elliptic aspect ratio, from a practical point of view. The numerical results put in evidence that the Nusselt number is a decreasing function of the Knudsen number for all the considered configurations. On the contrary, the role of the cross section geometry in the convective heat transfer depends on the thermal boundary condition and on the rarefaction degree. With the aim to provide a useful tool for the designer, a correlation that allows evaluating the Nusselt number for any value of aspect ratio and for different working gases is proposed.

The eigenvalues of ∇2u + λu=0 when the boundary conditions are given on semi-infinite domains

1953 ◽  
Vol 49 (4) ◽  
pp. 668-684 ◽  
Author(s):  
D. S. Jones
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Continuous Spectrum ◽  
Discrete Spectrum ◽  
Cross Section ◽  
Radiation Condition ◽  
Finite Width ◽  
Infinite Domains ◽  
Counter Example ◽  
Submerged Cylinder

ABSTRACTThe spectrum of −∇2 (and of −∇2 + b) is investigated when the boundary conditions are given on surfaces which extend to infinity. Simple criteria are obtained for determining whether point-eigenvalues are present in the lower part of the spectrum.Semi-infinite domains which are conical at infinity are found to possess purely continuous spectra when the boundary condition is u = 0 or ∂u/∂v = 0; the radiation condition ensures a unique solution. A counter-example shows that this is not true in general for the boundary condition ∂u/∂v + σu = 0.Semi-infinite domains which are cylindrical at infinity have a continuous spectrum with a discrete spectrum embedded in it. An example is given.The results are applied to the theory of surface waves. It is shown that Ursell's ‘trapping modes’ can occur in a canal of finite width when the bed has a protrusion over a finite longth but is otherwise of uniform depth. Trapping modes can also occur when the canal contains a submerged cylinder (not necessarily small in cross-section).

scholarly journals An accurate and efficient series solution for the longitudinal vibration of elastically restrained rods with arbitrarily variable cross sections

2019 ◽  
Vol 38 (2) ◽  
pp. 403-414 ◽  
Author(s):  
Deshui Xu ◽  
Jingtao Du ◽  
Zhigang Liu
Keyword(s):  
Boundary Condition ◽  
Fourier Series ◽  
Boundary Conditions ◽  
Cross Section ◽  
Longitudinal Vibration ◽  
Variable Cross ◽  
Arbitrary Boundary ◽  
Cross Section Area ◽  
Section Area ◽  
Area Variation

Longitudinal vibration of non-uniform rod has been of great significance in various engineering occasions. The existing works are usually limited to the certain area variation and/or classical boundary condition. Motivated by this limitation, an efficient accurate solution is developed for the longitudinal vibration of a general variable cross-section rod with arbitrary boundary condition. Displacement function is invariantly expressed as the summation of standard Fourier series and supplementary polynomials, with an aim to make the calculation of all derivatives more straightforwardly in the whole solving region [0, L]. Energy principle is employed for system dynamics formulation, with the elastic boundaries considered as potential energy stored in the restraining spring. Arbitrary cross-section area variation is uniformly expanded into Fourier series. Numerical examples are presented for the natural frequency and mode shapes of non-uniform rod of free and clamped boundary conditions and compared with literature data. Results show good agreement with the previous analytical solutions. Influence of cross section area variation on vibration characteristics of non-uniform rods is then studied and discussed. One of the most advantages of the proposed model is that there is no need to reformulate the problem or rewrite the codes when the cross-section area distribution and/or boundary conditions change arbitrarily.

scholarly journals Evaluating the Effect of Asymmetric Cross-section in Free Vibration and Bending Analysis Results of FG Sandwich Beam by Proposing Simple Efficient Element

2021 ◽  
Author(s):  
Majid Yaghoobi ◽  
Mohsen Sedaghatjo ◽  
Reyhaneh Alizadeh ◽  
Mohammad KARKON
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Equilibrium Equation ◽  
Vertical Displacement ◽  
Asymmetric Effect ◽  
Bending Analysis ◽  
Different Boundary Conditions ◽  
The Cross

In this paper, the asymmetric effect of the cross-section on the free vibration and bending analysis of FG sandwich beams are evaluated. For this purpose, a simple, efficient element is formulated. The new element is created based on the Timoshenko beam theory. The third- and second-order polynomials will be used for vertical displacement and rotation fields, respectively. The proposed formulation will be written based on satisfying the equilibrium equation. Satisfying the equilibrium equation of the Timoshenko beam, in addition to increasing element efficiency, will reduce the number of nodal unknowns. Several benchmark tests with different boundary conditions are used for thin and thick beams to prove the efficiency of the proposed element. The responses of the good elements of other researchers have been used for comparison. Numerical tests prove the rapid convergence rate and high accuracy of the proposed element in free vibration and bending analysis of the beams with various cross-section types and different boundary conditions. The pinned-sliding support conditions for the beam are used to evaluate the asymmetric effect of the cross-section. The use of asymmetric cross-sections creates additional axial displacements and intensifies the deflection of the beam under the lateral load. By increasing the asymmetry, the additional axial displacement and vertical displacement increase. These additional deflections for thin beams are more than thick ones. Also, asymmetry results in increasing the natural frequencies of beams. In the free vibration analysis, the effect of asymmetry on thick beams is more than thin ones.

Is the Stress Distribution Uniform in the Cross Section of SMA Bars Subjected to Uniaxial Loading? Is it Related to Rate Dependency?

2011 ◽  
Author(s):  
Reza Mirzaeifar ◽  
Reginald DesRoches ◽  
Arash Yavari
Keyword(s):  
Boundary Condition ◽  
Stress Distribution ◽  
Latent Heat ◽  
Cross Section ◽  
Cross Sections ◽  
Uniaxial Loading ◽  
Rate Dependency ◽  
The Cross ◽  
Definition Of ◽  
Vast Range

In this paper, a coupled thermo-mechanical framework which takes into account the effect of phase transformation latent heat is presented for shape memory alloys. The governing equations are discretized for SMA bars and wires with circular cross sections by considering the non-uniform temperature distribution in the cross section. It is shown that a combination of three various effects (boundary condition, loading rate, and size) governs the intensity of temperature gradient in the cross section of SMA bars subjected to uniaxial loading. Also, it is shown that because of the strong coupling between the thermal and mechanical fields in SMAs, temperature difference in the cross section causes a non-uniform stress distribution in the cross section. The maximum non-uniformity in the stress and temperature distributions are calculated for a vast range of practical sizes, boundary conditions, and loading rates. The relation between the latent heat flux in the cross section and the rate dependency is studied. It is shown that the rate dependency in the response of SMAs cannot be studied independent of size and boundary condition effects. This phenomenon reveals that the definition of quasi-static loading is not absolute; it is affected by a number of parameters, e.g., the ambient condition and size of the structure.

An asymptotic approximation of the maximum runup produced by a Tsunami wave train entering an inclined bay with parabolic cross section

2020 ◽  
Author(s):  
Nazmi Postacioglu ◽  
M. Sinan Özeren ◽  
Ebubekir Çelik
Keyword(s):  
Boundary Condition ◽  
Integral Equation ◽  
Boundary Conditions ◽  
Cross Section ◽  
Incident Wave ◽  
Dirichlet Boundary ◽  
Decay Rates ◽  
Dirichlet Boundary Conditions ◽  
Open Boundary ◽  
Open Sea

&lt;p&gt;Investigation of the behavior of various types of Tsunami wave trains entering bays is of practical importance for coastal hazard assessments. The linear shallow water equations admit two types of solutions inside an inclined bay with parabolic cross section: Energy transmitting modes and decaying modes. In low frequency limit there is only one mode susceptible of transmitting energy to the inland tip of the bay. The decay rates of decaying modes are controlled by the boundary conditions at the sides of the bay. Therefore a complicated eigenvalue problem needs to be solved in order to compute these decay rates. To determine the amplitude of the energy transmitting mode one should solve an integral equation, involving not just the energy transmitting mode but also decaying modes, the scattered field into the open sea, the incident wave and the reflected wave in the open sea. However, in the long wave limit, all these complications can be avoided if one applies the Dirichlet boundary conditions at the open boundary. That is to take the displacement of the free surface at the open boundary being equal to the twice of the disturbance associated with the incident wave in the open sea, just like a wall boundary condition. The runup produced by the solution obtained from this Dirichlet boundary condition, can be easily calculated using a series of images. In this model no energy is allowed to escape from the bay therefore the error arising from the simplification of the boundary conditions at the open boundary grows with time. Nevertheless the maximum runup occurs before this error becomes significant. If the characteristic wavelength of the incident wave train is equal to 5 times the width of the bay then this simple solution overestimates the first maximum of the runup only by %15 compared to the &amp;#8220;exact&amp;#8221; solution derived from the integral equation. This overestimation is partly due to the fact that Dirichlet boundary conditions violates the continuity of depth integrated velocities. The solution associated with Dirichlet boundary condition is perturbed in order to match fluxes inside and outside of the bay. This perturbation does not use the decaying modes inside the bay. The height of the first maximum of the runup coming from the perturbation theory is in excellent agreement with that obtained using the integral equation. This perturbation theory can also be applied to narrow bays with arbitrary cross section as long as their depth does not not change in the longitudinal direction.&lt;/p&gt;

The Impact of Boundary Conditions on the Response of NiMnGa Samples in Actuation and Power Harvesting Applications

2013 ◽  
Author(s):  
Isaac Nelson ◽  
Constantin Ciocanel ◽  
Doug LaMaster ◽  
Heidi Feigenbaum
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Cross Section ◽  
Effective Length ◽  
Power Harvesting ◽  
Simply Supported ◽  
Voltage Output ◽  
The Cross ◽  
The Difference ◽  
The Impact

Magnetic shape memory alloys (MSMAs) are materials that can display up to 10% recoverable strain in response to the application of a magnetic field or compressive mechanical stress. The magnetomechanical response of the material makes MSMAs suitable for applications such as actuation, sensing, and power harvesting. While the magnetomechanical response of the material has been extensively investigated to date, there is no report in the literature on the effect of the boundary conditions (BCs) on its response. The response of MSMAs is primarily driven by the reorientation of internal martensite variants, in conjunction with rotation of magnetization vectors, and domain wall motion. During the reorientation process a change in material’s magnetization occurs. For sensing and power harvesting applications, a pick-up coil may be used to convert this change in magnetization into an electric potential/voltage. To date, it has been confirmed experimentally that, according to Faraday’s law of induction, the magnitude of the output voltage depends on the number of turns of the pick-up coil, the amplitude of the reorientation strain, the magnitude and direction of the biased magnetic field, and the frequency at which the reorientation occurs. However, to our knowledge, no study has been carried out to investigate the effect of the BCs on the voltage output. This paper examines the effect of the BCs on the material’s magnetomechanical response, as well as on the corresponding voltage output. Three BCs are considered in the performed experiments: i) simply supported, ii) clamped, and iii) mixed (i.e. one end clamped and one end guided). The difference observed in the magnetomechanical response of the material, between the tested BCs, is attributed to the local effects caused by the grips (particularly the clamped and mixed conditions) and by the rotation of the specimen within the grips (in the simply supported condition). The latter is facilitated by the difference between the cross section of the specimen and the cross section of the cavity receiving the sample and by the larger effective length of the specimen in this case.

A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

1973 ◽  
Vol 31 ◽  
pp. 698-699
Author(s):  
V. Mizuhira ◽  
Y. Futaesaku
Keyword(s):  
Cross Section ◽  
Tannic Acid ◽  
Elastic Fiber ◽  
The Other ◽  
New Approach ◽  
Tissue Block ◽  
Active Reaction ◽  
The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

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