scholarly journals The Vibration of Tubular Beam Conveying Fluid with Variable Cross Section

2020 ◽  
Vol 65 (1) ◽  
pp. 56-62
Author(s):  
Mohamed Gaith
Keyword(s):  
Flow Velocity ◽  
Cross Section ◽  
Natural Frequencies ◽  
Variable Cross Section ◽  
System Stability ◽  
Variable Cross ◽  
Cross Sectional ◽  
Critical Flow Velocity ◽  
Constant Flow Rate ◽  
The Impact

The dynamics and stability of flow induced vibration of flow conveying in pipes particularly in case of high velocity flow may lead to severe damage. Predicting the circular natural frequencies and critical fluid velocities is an important tool in design and prevent system failures. In this study transverse dynamic response of simply supported pipe with variable tubular cross sectional area carrying fluid with a constant flow rate is investigated. Euler Bernoulli's beam theory is used to model the pipe. Hamilton's principle will be used to produce the governing equation of motion for the system. The resulting partial differential equation is solved using Galerkin's technique. The impact of the flow velocity and non-uniform variable cross section on the natural frequencies of the system, critical flow velocity and system stability is presented.

Longitudinal oscillation of a rod with a variable cross section

2019 ◽  
Vol 14 (2) ◽  
pp. 138-141
Author(s):  
I.M. Utyashev
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Liouville Problem ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Independent Functions ◽  
The Cross ◽  
The Right

Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of longitudinal vibrations. The paper presents a method that allows numerically finding the natural frequencies of longitudinal vibrations of an elastic rod with a variable cross section. This method is based on representing the cross-sectional area as an exponential function of a polynomial of degree n. Based on this idea, it was possible to formulate the Sturm-Liouville problem with boundary conditions of the third kind. The linearly independent functions of the general solution have the form of a power series in the variables x and λ, as a result of which the order of the characteristic equation depends on the choice of the number of terms in the series. The presented approach differs from the works of other authors both in the formulation and in the solution method. In the work, a rod with a rigidly fixed left end is considered, fixing on the right end can be either free, or elastic or rigid. The first three natural frequencies for various cross-sectional profiles are given. From the analysis of the numerical results it follows that in a rigidly fixed rod with thinning in the middle part, the first natural frequency is noticeably higher than that of a conical rod. It is shown that with an increase in the rigidity of fixation at the right end, the natural frequencies increase for all cross section profiles. The results of the study can be used to solve inverse problems of restoring the cross-sectional profile from a finite set of natural frequencies.

scholarly journals Eco-friendly technology of manufacturing complex products made of composites

2019 ◽  
Vol 140 ◽  
pp. 02004
Author(s):  
Aleksey Ignatov ◽  
Rustam Subkhankulov
Keyword(s):  
Composite Materials ◽  
Cross Section ◽  
Manufacturing Process ◽  
Volume Fraction ◽  
Turbine Blades ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Technological Parameters ◽  
Technological Support ◽  
The Impact

Numerous studies in application of modern composite materials show that their advantages can be successfully implemented in manufacturing «smart» products. This study proposes an improved technological method of manufacturing multilayer environmentally friendly products with a variable cross section, which allows us to expand the possibilities of using modern polymer composite materials (PCM). The technology allows manufacturing products of the most complex geometric shapes, such as wind turbine blades. The aim of the study is the technological support of engineering production in the manufacture of multilayer products of variable cross section made from PCM. Scientific novelty consists in identifying the patterns of implementation and management of the manufacturing process of multilayer products of variable cross-section, and establishing the influence of structural and technological parameters of the manufacturing process on their operational characteristics. The relationship between the pressure of a hot directed air stream and the volume fraction of pores in the hardened material of a multilayer composite product with a variable cross section during layer-by-layer application is investigated. During the study, fundamental and applied principles of mechanical engineering technology, material resistance, adhesion theory, mathematical statistics tools and software were used to process the results of the experiment. Based on the results of laboratory studies, a methodology has been developed for effective prediction of pore content in the manufacturing of composite products. The introduction of the presented technology and the corresponding original methodology into production will reduce the complexity and energy costs of manufacturing composite products, improve their quality and reduce the impact of toxic components from composite materials on workers.

scholarly journals Theoretical and Experimental Research of The Stability of The Eccentrically Loaded Steel Columns with Variable Cross–Section

2018 ◽  
Vol 7 (3.2) ◽  
pp. 458
Author(s):  
Gennady Trusov ◽  
Vladimir Ruban
Keyword(s):  
Cross Section ◽  
Research Work ◽  
Variable Cross Section ◽  
Suggested Method ◽  
National Standards ◽  
Discrete Models ◽  
Practical Calculation ◽  
Variable Cross ◽  
Cross Sectional ◽  
Steel Columns

The article deals with the problem of determining the ultimate load for the eccentrically loaded steel columns with variable-cross section.The purpose of the research work is to offer an evaluation technique and practical calculation of load-bearing ability of the beam-columns with variable cross-section on the basis of numerical research, which will allow to consider the true form of element deflection curve, the effect of cross-section form, physical nonlinearity of the material, and variety of element boundary conditions. The distinctive characteristic of the suggested method is usage of the discrete models for cross-sectional parts, for the true stress-strain curves of the materials, and for the other input data. The method was tested and the results were compared to known theoretical solutions and national standards. To establish the reliability of the developed method, the experimental study of steel columns with variable cross-section was conducted. The suggested method allows to obtain column curves tables of lowering coefficients for these elements, that can be used in practice of civil engineering, and are convenient with national standards and Eurocode. 

The Changes of Internal Forces and the Reliability of Curved Bridge Taking the Cross-Sectional Design of Axial Symmetrical

2014 ◽  
Vol 587-589 ◽  
pp. 1631-1636
Author(s):  
Zheng Jiu Zhao ◽  
Jing Hong Gao
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Radius Of Curvature ◽  
Variable Cross ◽  
Cross Sectional ◽  
Box Girder ◽  
Curved Bridge ◽  
The Cross ◽  
Cross Sectional Design ◽  
Bridge Models

Taking a bridge of 160m long variable cross-section prestressed continuous curved box-girder as the research object and analyzing the cross-sectional design of axis with axial symmetrical or axial non-symmetrical to research the structure forces change of the upper part of bridge in different curvature. In order to test and verify the variable cross-section of prestressed continuous curved box-girder bridge is safe and reliable via cross-sectional design with axial symmetrical instead of axial non-symtrical within a radius of curvature of the interval. Creating the straight bridge and curved bridge models with different radius of curvature in same span by Midas/Civil to compare their structure forces.

Solar Concentrator Structural Optimization: A Variable Beam Cross Section Design

2017 ◽  
Author(s):  
Moucun Yang ◽  
Yuezhao Zhu ◽  
Wei Fu ◽  
Garth Pearce ◽  
Robert A. Taylor
Keyword(s):  
Structural Optimization ◽  
Cross Section ◽  
Cost Savings ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Maximum Displacement ◽  
Cross Sectional ◽  
Optical Efficiency ◽  
Box Structure ◽  
Section Design

The design and construction of solar concentrators heavily affects their cost, heat utilization and optical efficiency. Current trough concentrators support the reflector with an equivalent uniform beam configured from a metal grid sub-structure. Under gravity and wind loads, the support-structure stress distribution varies as a function of position of the structure and the tracking angle. In the conventional design, there is ample surplus stiffness and strength designed into some beams of the structure, which increases the overall weight and cost of the structure. This paper describes an approach towards structural optimization of trough concentrators (with the Eurotrough design taken as an example, that means that the safety factors and structure is similar with Eurotrough design) using a variable cross section beam. The main improvement of this approach comes from keeping the beams rigid and strong near the two ends (at the torque box structure) while allowing the middle of the structure to be relatively weak. Reducing the cross-sectional area of the central beams not only reduces amount of material needed for the structure but also reduces the deflection of the reflector. The simulated results show that the concentrator’s structural weight (including the torque box, endplates and cantilever arms) and the maximum displacement of the reflector are reduced about 15.3% (about 151.2kg per 12-metre long element) and 15.5%, respectively. This represents a meaningful capital and installation cost savings while at the same time improving the optical efficiency.

scholarly journals A well-balanced solver for the Saint Venant equations with variable cross-section

2015 ◽  
Vol 23 (2) ◽  
Author(s):  
Raul Borsche
Keyword(s):  
Numerical Method ◽  
Cross Section ◽  
Variable Cross Section ◽  
Test Cases ◽  
Variable Cross ◽  
Bottom Slope ◽  
Cross Sectional ◽  
Analytical Properties ◽  
Saint Venant Equations ◽  
Numerical Solver

AbstractIn this paper we construct a numerical solver for the Saint Venant equations. Special attention is given to the balancing of the source terms, including the bottom slope and variable cross-sectional profiles. Therefore a special discretization of the pressure law is used, in order to transfer analytical properties to the numerical method. Based on this approximation awell-balanced solver is developed, assuring the C-property and depth positivity. The performance of this method is studied in several test cases focusing on accurate capturing of steady states.

Transmission Loss of Variable Cross Section Apertures

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
J. Li ◽  
L. Zhou ◽  
X. Hua ◽  
D. W. Herrin
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Sound Propagation ◽  
Transmission Loss ◽  
Element Model ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Cross Sectional ◽  
Radiation Impedance ◽  
The Cross

Openings in enclosures or walls are frequently the dominant path for sound propagation. In the current work, a transfer matrix method is used to predict the transmission loss of apertures assuming that the cross-sectional dimensions are small compared with an acoustic wavelength. Results are compared with good agreement to an acoustic finite element approach in which the loading on the source side of the finite element model (FEM) is a diffuse acoustic field applied by determining the cross-spectral force matrix of the excitation. The radiation impedance for both the source and termination is determined using a wavelet algorithm. Both approaches can be applied to leaks of any shape and special consideration is given to apertures with varying cross section. Specifically, cones and abrupt area changes are considered, and it is shown that the transmission loss can be increased by greater than 10 dB at many frequencies.

scholarly journals The lateral vibrations of bars of variable section

1917 ◽  
Vol 93 (654) ◽  
pp. 506-519 ◽  
Keyword(s):  
Cross Section ◽  
Formal Analysis ◽  
Detailed Examination ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Biological Application ◽  
Lateral Vibrations ◽  
Variable Section ◽  
Set Up ◽  
The Impact

The present investigation, though strictly mathematical in character, arose in connection with a suggestion, put forward by Prof. A. Dendy and the present author in another paper communicated to the Society, that the siliceous deposits found on certain sponge spicules occurred at nodes of the spicules, regarded as vibrating rods. These vibrations, being set up and maintained by the impact of currents of water on the spicules, are necessarily of the lateral type. For the detailed examination of such a suggestion, it is necessary to obtain a comprehensive account of the positions of the funda­mental nodes on a free-free bar, as dependent on the law of variation of its cross-section. The present paper contains, in fact, the formal analysis whose results were quoted without proof in the other paper. This analysis is of considerable generality, as will appear, and the particular examples selected for purposes of illustration, together with the manner in which the variable cross-section is dealt with, have been determined by the requirements of the biological application already mentioned. One general problem is in view throughout the work, and it may be stated as follows

Analysis of Singly Symmetric Oval Rings with Variable Cross Section

1970 ◽  
Vol 14 (03) ◽  
pp. 143-152
Author(s):  
J. E. Flaherty ◽  
W. P. Vafakos
Keyword(s):  
Cross Section ◽  
Variable Cross Section ◽  
Experimental Results ◽  
Variable Cross ◽  
Cross Sectional ◽  
Shear Loads ◽  
Good Agreement

An analysis of singly symmetric oval rings with variable cross-sectional properties, subjected to arbitrary radial and shear loads, is presented. The flange stresses in nonuniform reinforcing rings of ring-stiffened oval cylinders are obtained by assuming that such cylinders behave as composite rings. The stresses are shown to be in good agreement with available theoretical and experimental results.

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