scholarly journals Influence of longitudinal force and internal pressure on the frequency of free vibrations of an underground oil pipeline

2020 ◽  
Vol 217 ◽  
pp. 01010
Author(s):  
Andrey Dmitriev ◽  
Vladimir Sokolov ◽  
Aleksey Bereznyov
Keyword(s):  
Cross Section ◽  
Large Diameter ◽  
Normal Component ◽  
Longitudinal Force ◽  
Free Vibrations ◽  
Oil Pipeline ◽  
Rod Theory ◽  
The Cross ◽  
Pipeline Wall ◽  
Inertia Forces

This paper is based on the equation obtained earlier by V.G. Sokolov to find the frequencies of natural vibrations of straight sections of large-diameter pipelines. In this work, to take into account the effect of hydrostatic pressure on the pipeline wall from oil flowing at different speeds, the solution obtained by M.A. Ilgamov and A.S. Volmyr is used. At the same time, the effect of a stationary fluid flow on the pipeline wall is taken into account in the equation written in forces for the last term of the normal component of inertia forces. The resulting modified equation allows determining the frequency characteristics of the pipeline both according to the rod theory (without taking into account the deformation of the cross section) and according to the theory of shells (taking into account the deformation of the cross section).

scholarly journals GENERAL CASE OF REINFORCED CONCRETE ROD ELEMENTS CALCULATION USING THE DIAGRAM METHOD

2021 ◽  
Vol 93 (1) ◽  
pp. 26-37
Author(s):  
O.V. RADAYKIN ◽  
◽  
L.S. SABITOV ◽  
L.SH. AKHTYAMOVA ◽  
T.P. ARAKCHEEV ◽  
...  
Keyword(s):  
Reinforced Concrete ◽  
Cross Section ◽  
Longitudinal Force ◽  
Internal Force ◽  
The Other ◽  
Bending Moments ◽  
Diagram Method ◽  
The Cross ◽  
Three Components

In SP 63.13330 the general calculation case for the diagram method is oblique off-center compression, which takes into account only three components of internal force factors in the cross section: the longitudinal force-Nz – and two bending moments relative to the corresponding axes – Mx and My. The other three components-the QX and Qy transfer forces and the MZ torque – are left out of consideration. In addition, for this case, the search in the available literature, including the founders of the diagram method, for the output of calculation formulas was not successful – in all sources they are given in ready-made form without evidence. This article is intended to try to fill in these gaps. For this purpose, based on the expressions for rod displacements that are generally accepted in mechanics, in particular on the Mora integral of displacements, the resolving expressions of the diagram method are obtained in the most general form.

METHODS AND RESULTS OF MICROMETER STUDIES OF HYDRAULIC SYSTEM SEALING UNITS OF AGRICULTURAL MACHINERY

2020 ◽  
Vol 4 (141) ◽  
pp. 12-19
Author(s):  
MIKHAIL BEREZIN ◽  
Keyword(s):  
Cross Section ◽  
Hydraulic Drive ◽  
Research Purpose ◽  
Working Fluid ◽  
Initial Contact ◽  
Thickness Gauge ◽  
Agricultural Machinery ◽  
Oil Pipeline ◽  
Compression Deformation ◽  
The Cross

End-type sealing units based on round-section rubber rings are the most common types of seals for volumetric hydraulic drive units of various agricultural machinery. Its service life depends on the correspondence of the geometric dimensions of the elements that make them up, as well as on the combination of limit deviations of the specified elements. (Research purpose) The research purpose is in studying deviations and identifying statistical distribution of the cross-section diameters of new rings and the depth of grooves under them in order to determine the number of connections that meet the requirements of the standard. (Materials and methods) Author examined the sealing joints of the oil pipeline and the valve cover of the hydraulic distributor of the MTZ 80/82 tractor and new rubber rings that are part of repair kits intended for repair. Micrometric studies were performed using the GM-50 micrometer depth gauge and the TN 1060T thickness gauge. (Results and discussion) About 90 percent of the examined compounds do not meet the requirements of the standard, which explains to a large extent the low level of their reliability. At the same time, a significantly higher level of inconsistencies is in the metal parts of these connections. The vast majority of nonconforming joints have a combination of ring and groove sizes, which provides increased initial compression deformation of the ring in the groove. (Conclusions) Inconsistencies in the dimensions of the groove and the cross-section of the ring, which lead to an increase in the initial compression deformation of the seal, and thus the initial contact stresses, cause a certain increase in the theoretical life of the connection. To predict the connection reliability more accurate, it is necessary to study the influence on leaks not only of the geometric dimensions of the mating elements, but also other factors: surface roughness, as well as the actual operating temperature of the node and the aggressiveness of the hydraulic working fluid.

scholarly journals Analytical-numerical method for calculating the stability of rod elements of lightweight steel structures

2020 ◽  
Vol 17 (4) ◽  
pp. 39-46
Author(s):  
G. I. Belyy ◽  
Keyword(s):  
Numerical Method ◽  
Cross Section ◽  
Steel Structures ◽  
Longitudinal Force ◽  
Initial Section ◽  
Limiting State ◽  
Lightweight Steel ◽  
Combined Action ◽  
The Cross ◽  
The Stability

The article proposes an analytical-numerical method for calculating the rod elements of lightweight steel structures for general stability, in which the reduced section is replaced with the unreduced one with compensating loading with a fictitious longitudinal force. The dependence of this force with uniaxial or biaxial eccentricities on the acting longitudinal force is established when they are combined acting on fictitious stresses in the center of the weakening gravity of the rod most stressed section. Therewith, the effect of displacements corresponding to the stability tasks (bending, bending-torsional or spatial ones) is taken into consideration. The analytical part of the stability problems` solution is constructed for the known parameters of the real abatement of the cross section, which is determined numerically under the combined action of all efforts using the EN 1993-1-3-2004 in combination with the "Cross-section" algorithm. To reduce the volume of calculations, there is proposed a reverse course of solving the stability problem in dimensionless parameters. The section reduction and the actual forces are numerically determined according to the limiting state of the rod in the most loaded initial section at given force parameters (relative eccentricities of the longitudinal force, taking into account displacements). Then, depending on the flexibility of the rod, the corresponding loading of the rod on its supports is specified by the reverse analytical solution.

scholarly journals DETERMINATION OF THE OPTIMAL CURVATURE OF ELASTIC DEFORMED CABLES IN THE MIDDLE OF THE SPAN IN A HANGING COATING BY USING THE MATHCAD COMPUTER SYSTEM

2021 ◽  
pp. 64-72
Author(s):  
O.E. Yanin ◽  
◽  
S.M. Novikova ◽  
Keyword(s):  
Objective Function ◽  
Computer System ◽  
Cross Section ◽  
Target Function ◽  
Minimum Cost ◽  
Longitudinal Force ◽  
Cross Sectional ◽  
Linear Load ◽  
The Cross ◽  
Sectional Parameters

Abstract. The paper presents the theoretical results of improving and refining the general methodology for selecting the cross section of a flexible elastic thread for cable-stayed using the capabilities of computer programs. A technique is proposed for finding the optimal curvature of the cable in the middle of the span by compiling the target function of the cable cost and coverage and determining its minimum. The hanging coating of the building is considered, consisting of parallel-located flexible cables. Coating elements are laid on them. It is assumed that the load is evenly distributed over the curved surface of the coating. With this application of load, the sag curve is adopted as a chain line. In the calculation, two states of the thread are considered. In the first state, it is loaded with a linear load uniformly distributed along its length from its own weight. In the second state, the thread is loaded with the total calculated linear load evenly distributed along its length. To select the cross section of the thread, the maximum longitudinal force arising in it in the second state is determined, which depends on the curvature in the middle of the span. This curvature is determined on the basis that the difference between the lengths of the thread in the first and second states is equal to the elastic elongation according to Hooke's law. Using ordinary algebraic methods, solving the problem is quite complicated. Therefore, it was proposed to solve it using the MathCAD computer system. With the found value of the curvature in the middle of the span, the required cross-sectional area of the thread is calculated. After that, the appropriate rope is selected according to the assortment. To optimize the cable-stayed coating, the optimal curvature in the middle of the span is determined in the first state, at which the total cost of cable-stayed and coating will be minimal. For this purpose, the objective function of the cost of the cable and the coverage that lies on this cable has been compiled. To determine the optimal curvature, it is proposed to accept a series of values of this curvature with some step in a certain range. For each curvature, the value of the objective function is calculated. Using the MathCAD computer system, it is proposed to build the graph of the objective function and find the value of the optimal curvature at which this function has a minimum. After that, it is proposed to find the corresponding optimal sagging arrow. The proposed method allows us to determine the optimal parameters of the hanging coating with parallel cables on the basis of the minimum cost, as well as to calculate the necessary cross-sectional parameters of the flexible cable from the strength condition.

scholarly journals A study of the length parameter and the longitudinal compressive forces in the determination of frequencies of free vibrations of thin-walled underground pipelines of large diameter

2019 ◽  
Vol 6 (3) ◽  
Author(s):  
Andrey Dmitriev ◽  
Vladimir Sokolov ◽  
Aleksey Bereznev
Keyword(s):  
Cross Section ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Large Diameter ◽  
Pressure Coefficient ◽  
Critical Force ◽  
The Core ◽  
Underground Pipelines ◽  
Thin Walled ◽  
The Cross

Earlier work on the study of frequency characteristics of thin-walled underground pipeline to obtain an equation for finding the natural frequencies of the straight sections of the pipeline, taking into account the parameter of the longitudinal force, the magnitude of internal pressure, coefficient of elastic resistance of the soil, the option of thin tubing and added mass of the soil. In this article, using the obtained equation, we study the influence of the length of the section of the pipeline laid in the soil with different physical-mechanical characteristics, and the effect of the parameter of the longitudinal compressive forces at the frequency of free oscillations of thin-walled straight pipeline under the action of various internal working pressure for pipes of different diameters with different wall thicknesses. On the basis of the design data defined in the derived formulae, is determined by the criterion of application of shell theory or the core theory for finding the natural frequencies of thin-walled underground pipelines of large diameter, depending on the length of the element. Simultaneously, the obtained expression allows to determine the critical force at which buckling occurs in the core of the theory («beam buckling»), as well as the formula to determine the critical force, from which buckling occurs by shell theory (flattening of the cross section). Based on these data, it is concluded that flattening the cross section of the pipeline will occur when the force is at times less than required for the formation of «arch release», and consequently to ensure the reliability of underground thin-walled large diameter pipeline should be the first thing to check for resistance on the shell theory.

A Higher-Order Theory for Open and Closed Curved Rods and Tubes Using a Novel Curvilinear Cylindrical Coordinate System

2018 ◽  
Vol 85 (9) ◽  
Author(s):  
A. Arbind ◽  
A. R. Srinivasa ◽  
J. N. Reddy
Keyword(s):  
Coordinate System ◽  
Cross Section ◽  
3D Structure ◽  
Order Theory ◽  
Rod Theory ◽  
Exterior Calculus ◽  
Cylindrical Coordinate ◽  
The Cross ◽  
General Material ◽  
Higher Order Theory

In this study, the governing equation of motion for a general arbitrary higher-order theory of rods and tubes is presented for a general material response. The impetus for the study, in contrast to the classical Cosserat rod theories, comes from the need to study bulging and other deformation of tubes (such as arterial walls). While Cosserat rods are useful for rods whose centerline motion is of primary focus, here we consider cases where the lateral boundaries also undergo significant deformation. To tackle these problems, a generalized curvilinear cylindrical coordinate (CCC) system is introduced in the reference configuration of the rod. Furthermore, we show that this results in a new generalized frame that contains the well-known orthonormal moving frames of Frenet and Bishop (a hybrid frame) as special cases. Such a coordinate system can continuously map the geometry of any general curved three-dimensional (3D) structure with a reference curve (including general closed curves) having continuous tangent, and hence, the present formulation can be used for analyzing any general rod or pipe-like 3D structures with variable cross section (e.g., artery or vein). A key feature of the approach presented herein is that we utilize a non-coordinate “Cartan moving frame” or orthonormal basis vectors, to obtain the kinematic quantities, like displacement gradient, using the tools of exterior calculus. This dramatically simplifies the calculations. By the way of this paper, we also seek to highlight the elegance of the exterior calculus as a means for obtaining the various kinematic relations in terms of orthonormal bases and to advocate for its wider use in the applied mechanics community. Finally, the displacement field of the cross section of the structure is approximated by general basis functions in the polar coordinates in the normal plane which enables this rod theory to analyze the response to any general loading condition applied to the curved structure. The governing equation is obtained using the virtual work principle for a general material response, and presented in terms of generalized displacement variables and generalized moments over the cross section of the 3D structure. This results in a system of ordinary differential equations for quantities that are integrated across the cross section (as is to be expected for any rod theory).

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.

Energy Distribution in Electron Beams

1972 ◽  
Vol 30 ◽  
pp. 568-569
Author(s):  
Tamotsu Ohno
Keyword(s):  
Electron Beam ◽  
Energy Distribution ◽  
Cross Section ◽  
Integral Curve ◽  
Electron Beams ◽  
Electron Gun ◽  
Angular Divergence ◽  
Apparent Increase ◽  
Integral Width ◽  
The Cross

The energy distribution in an electron; beam from an electron gun provided with a biased Wehnelt cylinder was measured by a retarding potential analyser. All the measurements were carried out with a beam of small angular divergence (<3xl0-4 rad) to eliminate the apparent increase of energy width as pointed out by Ichinokawa.The cross section of the beam from a gun with a tungsten hairpin cathode varies as shown in Fig.1a with the bias voltage Vg. The central part of the beam was analysed. An example of the integral curve as well as the energy spectrum is shown in Fig.2. The integral width of the spectrum ΔEi varies with Vg as shown in Fig.1b The width ΔEi is smaller than the Maxwellian width near the cut-off. As |Vg| is decreased, ΔEi increases beyond the Maxwellian width, reaches a maximum and then decreases. Note that the cross section of the beam enlarges with decreasing |Vg|.

Research in the cross-section of community psychology and global climate change: A call for action

2009 ◽  
Author(s):  
Marci Culley ◽  
Holly Angelique ◽  
Courte Voorhees ◽  
Brian John Bishop ◽  
Peta Louise Dzidic ◽  
...  
Keyword(s):  
Climate Change ◽  
Cross Section ◽  
Global Climate Change ◽  
Community Psychology ◽  
Global Climate ◽  
The Cross

Experimental Studies Of Multilayer Glass Structures On Compression, Compression With Bending And Simple Bending

2019 ◽  
pp. 22-30
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Applied Load ◽  
Experimental Studies ◽  
Strength Properties ◽  
Research Topic ◽  
Normative Values ◽  
Laminated Glass ◽  
The Cross ◽  
Experimental Values

The work of multilayer glass structures for central and eccentric compression and bending are considered. The substantiation of the chosen research topic is made. The description and features of laminated glass for the structures investigated, their characteristics are presented. The analysis of the results obtained when testing for compression, compression with bending, simple bending of models of columns, beams, samples of laminated glass was made. Overview of the types and nature of destruction of the models are presented, diagrams of material operation are constructed, average values of the resistance of the cross-sections of samples are obtained, the table of destructive loads is generated. The need for development of a set of rules and guidelines for the design of glass structures, including laminated glass, for bearing elements, as well as standards for testing, rules for assessing the strength, stiffness, crack resistance and methods for determining the strength of control samples is emphasized. It is established that the strength properties of glass depend on the type of applied load and vary widely, and significantly lower than the corresponding normative values of the strength of heat-strengthened glass. The effect of the connecting polymeric material and manufacturing technology of laminated glass on the strength of the structure is also shown. The experimental values of the elastic modulus are different in different directions of the cross section and in the direction perpendicular to the glass layers are two times less than along the glass layers.

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