Determination of the frequency spectrum of certain beams of variable cross section

1967 ◽  
Vol 3 (5) ◽  
pp. 81-82
Author(s):  
B. D. Litovchin
Keyword(s):  
Frequency Spectrum ◽  
Cross Section ◽  
Variable Cross Section ◽  
Variable Cross

Geometrical Model for Permeable Material’s Porous Structure

2019 ◽  
Vol 7 (2) ◽  
pp. 42-54 ◽  
Author(s):  
А. Синцов ◽  
A. Sintsov ◽  
Владимир Девисилов ◽  
Vladimir Devisilov
Keyword(s):  
Porous Material ◽  
Porous Structure ◽  
Cross Section ◽  
Structural Characteristics ◽  
Variable Cross Section ◽  
Geometrical Model ◽  
Variable Cross ◽  
Experimental Stand ◽  
Experimental Technology

In this paper have been presented a new model of the porous structure, as well as an analysis of possibilities of a new method for experimental investigation of porous permeable materials and determination of their structural characteristics. An analysis for the majority of used in analytical calculations geometric models for a porous medium has been presented, and a model for a porous material in the form of porous matrix’s elementary cells has been proposed. Each of the cells contains a capillary channel with a variable cross-section. Volumetric structural characteristics, as well as dependencies of surface structural characteristics over the porous matrix’s thickness, are identical to these parameters, which have been obtained during the experimental study of a porous material. As a result of use of an original experimental technology offered by authors, and of experiment processing the porous matrix’s structure can be completely defined. The problem of creating an experimental setup, allowing determine the porous matrix’s characteristics, has been formulated. One of possible options for the experimental stand has been considered.

scholarly journals DETERMINATION OF DIMENSIONAL PARAMETERS FOR ANNULAR CONCENTRATOR OF ULTRASONIC SYSTEM

2018 ◽  
Vol 17 (1) ◽  
pp. 51-55
Author(s):  
V. P. Lugovoi ◽  
I. V. Lugovoi
Keyword(s):  
Cross Section ◽  
Acoustic Waves ◽  
Visual Analysis ◽  
Variable Cross Section ◽  
Vibrational Amplitude ◽  
External Diameter ◽  
Variable Cross ◽  
Thin Sections ◽  
Dimensional Parameters

Conventional ultrasonic systems contain concentrators of longitudinal type to amplify and transfer vibrations to a tool. Along with them, elastic rings with variable cross section thickness can be used effectively as concentrators for ultrasonic vibrations of acoustic systems. Their practical application requires a scientifically substantiated methodology for determination of geometric parameters. The paper provides substantiation of the method used to determine dimensions of annular concentrators with a variable cross section which can enhance effectiveness of the ultrasound equipment while performing various technological tasks. Visual analysis of acoustic waves radiated by annular concentrators has shown that the most intensive vibrations are produced in the most thin sections. Computer simulation of oscillations in rings with an external diameter of 50 mm and a variable cross section has demonstrated that the largest increase of vibration amplitude is achieved at a certain ratio of ring thicknesses and diameters. An analysis of numerical values for amplication factor of vibrational amplitude Kд has revealed that there is a limit boundary for the ratio of ring wall thicknesses which, in its turn, depends on the ratio of ring outer and inner diameters at certain values of hole axis eccentricity. The ratio of diameters is expressed quantitatively by the coefficient Kд. An analysis of the results concerning numerical calculations of amplitude amplification factor performed for the specified model of the ring having 50 mm diameter have illustrated that this ratio should lie between 1.3 > Kд > 1.15. The obtained results can be used in ultrasonic devices with annular concentrators in order to perform various technological tasks.

A Tabular Collocation Method for Beam Vibration

1961 ◽  
Vol 83 (4) ◽  
pp. 373-376 ◽  
Author(s):  
R. Chicurel ◽  
E. Suppiger
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Integral Equation Method ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Lateral Vibration ◽  
Static Deflection ◽  
Preliminary Step ◽  
Stepped Beam

This paper presents a procedure, based on the integral equation method, for the calculation of the natural frequencies of lateral vibration of beams with variable cross section. The approximate solution is obtained by collocation [1, 2]. A preliminary step in the analysis is the determination of static deflection curves; this is carried out in a convenient tabular form. An example of a stepped beam is given and the results are compared to those obtained by Myklestad’s method [3].

Determination of the Natural Frequencies of the Bending Vibrations of Beams

1947 ◽  
Vol 14 (1) ◽  
pp. A1-A6
Author(s):  
A. I. Bellin
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Moment Equation ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Bending Vibrations ◽  
Elastic Beams ◽  
Lateral Vibrations

Abstract This paper presents a method for determining the natural frequencies of lateral vibrations for elastic beams. The beams may be of variable cross section and may have any number of spans. The five-moment equation is developed and is then applied to beams supported in various ways. The author reduces the necessary calculations to a simple tabular scheme. Several illustrative examples are included to demonstrate the method of computation.

scholarly journals Deformation of a cantilever curved beam with variable cross section

2021 ◽  
Vol 16 (1) ◽  
pp. 23-36
Author(s):  
István Escedi ◽  
Attila Baksa
Keyword(s):  
Cross Section ◽  
Elastic Beam ◽  
Beam Theory ◽  
Variable Cross Section ◽  
The Other ◽  
Curved Beam ◽  
Variable Cross ◽  
Cross Sectional ◽  
Euler Bernoulli Beam

This paper deals with the determination of the displacements and stresses in a curved cantilever beam. The considered curved beam has circular centerline and the thickness of its cross section depends on the circumferential coordinate. The kinematics of Euler-Bernoulli beam theory are used. The curved elastic beam is fixed at one end and on the other end is subjected to concentrated moment and force; three different loading cases are considered. The paper gives analytical solutions for radial and circumferential displacements and cross-sectional rotation and circumferential stresses. The presented examples can be used as benchmark for the other types of solutions as given in this paper.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

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.

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