scholarly journals Cálculo numérico de la matriz de flexibilidades de vigas de sección variable, con elementos finitos

2020 ◽  
pp. 22-31
Author(s):  
Jaime Retama Velasco ◽  
Ricardo Heras Cruz
Keyword(s):  
Finite Elements ◽  
Numerical Method ◽  
Cross Section ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Complementary Energy ◽  
First Order ◽  
Tapered Beam ◽  
Variable Section ◽  
The Cross

In this work, the flexibility properties of variable cross section beams are derived, through the application of the second theorem of Castigliano; considering the complementary energy by bending and share forces. To perform the integration of the flexibility coefficients, a numerical method, which considers the discretization of the beam domain with first order rectangular finite elements, in conjunction with the Gauss rule, is proposed. At the end of the work, the proposed method is applied to a tapered beam that has been discretized with a maximum of five finite elements. It is shown that the method is general, and that it can be applied to beams of variable section in which the cross section can be complex. The results shown that no more than 3 finite elements are needed to discretize the domain of beams in which, the ratio height-length is of the order of ten.

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 Dynamic Analysis of Single-Layered Graphene Nano-Ribbons (SLGNRs) with Variable Cross-Section Resting on Elastic Foundation

2019 ◽  
Vol 6 (1) ◽  
pp. 132-145 ◽  
Author(s):  
Subrat Kumar Jena ◽  
S. Chakraverty
Keyword(s):  
Elastic Foundation ◽  
Cross Section ◽  
Differential Quadrature Method ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Winkler Elastic Foundation ◽  
The Cross ◽  
Euler Bernoulli Beam

AbstractThis article deals with free vibration of the variable cross-section (non-uniform) single-layered graphene nano-ribbons (SLGNRs) resting on Winkler elastic foundation using the Differential Quadrature Method (DQM). Here characteristic width of the cross-section is varied exponentially along the length of the nano-ribbon while the thickness of the cross section is kept constant. Euler–Bernoulli beam theory in conjunction with Eringen nonlocal elasticity theory is considered in this study. The numerical as well as graphical results are reported by using MATLAB codes developed by authors. Convergence of present method is explored and our results are compared with known results available in literature showing excellent agreement. Further, effects various parameters on frequency parameters are studied comprehensively.

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.

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

On the Accuracy of the Bernoulli-Euler Theory for Beams of Variable Section

1963 ◽  
Vol 30 (3) ◽  
pp. 373-378 ◽  
Author(s):  
Bruno A. Boley
Keyword(s):  
Exact Solution ◽  
Cross Section ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Variable Depth ◽  
Pure Bending ◽  
Variable Section ◽  
Thin Beams ◽  
The Relationship ◽  
Derivatives Of

The stresses and deflections of thin rectangular beams of arbitrary variable depth, in pure bending, according to the theory of plane stress, are considered. They are obtained in the form of series; the first term of each series is identical with the strength-of-materials solution and the others represent the necessary correction to that theory. This form of the solution is chosen because of its convenience in the study of the relationship between the Bernoulli-Euler and the exact solution. The former is found to be quite accurate for thin beams and, when certain conditions are satisfied by the ordinates (and their spanwise derivatives) of the upper and lower edges of the beam. The Bernoulli-Euler theory is ambiguous in prescribing the position of the axis of a beam of variable cross section; admissible choices for the axis are presented.

scholarly journals Work of a railway sleeper as a structure with variable cross-section - the issue of an equivalent cross-section

2018 ◽  
Vol 2018 (6) ◽  
pp. 1-12
Author(s):  
Włodzimierz Czyczuła ◽  
Dorota Błaszkiewicz ◽  
Małgorzata Urbanek
Keyword(s):  
Numerical Model ◽  
Cross Section ◽  
Real Variable ◽  
Variable Cross Section ◽  
Moment Of Inertia ◽  
Variable Cross ◽  
Bending Stress ◽  
Variable Section ◽  
Vertical Displacements ◽  
Railway Sleeper

Abstract: The article presents an analysis of the work of a sleeper as a construction with variable section, and of the method of determining an equivalent section, constant throughout the length, the utilisation of which would have similar shapes of deflection and bending stress lines in relation to the real, variable cross section. Using an analytical and a numerical model, vertical displacements and stresses for two types of sleepers – PS-94 and PS-08 – were determined. The comparison of the methods allows for calculating an equivalent moment of inertia for analytical calculations, specifically the dynamic ones.

scholarly journals Częstość drgań własnych słupa o zmiennym przekroju poprzecznym

2019 ◽  
Vol 18 (3) ◽  
pp. 103-111
Author(s):  
Vazgen Bagdasaryan
Keyword(s):  
Cross Section ◽  
Elastic Material ◽  
Natural Frequencies ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Continuous Change ◽  
The Cross

In the paper natural frequencies of a pole with a variable cross-section were obtained. The pole was made of a homogeneous, elastic material. Solutions were obtained by approximation of the continuous change of the cross-section by changing by steps. The results are compared with the results obtained with Rayleigh’s method.

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