scholarly journals ANALYTICAL CALCULATIONS OF THE VIBRATIONS OF VERTICAL STRUCTURES CONSIDERING THEIR DEAD WEIGHT

2021 ◽  
Vol 12 (22) ◽  
pp. 29-40
Author(s):  
Yurii Krutii ◽  
◽  
Victor Vandynskyi ◽  
Petr Konstantinov ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Mechanical Characteristics ◽  
Free Vibrations ◽  
Approximate Methods ◽  
Dead Weight ◽  
Distributed Load ◽  
Analytical Formulas ◽  
Rod Structures ◽  
Physical And Mechanical Characteristics

This paper presents the results of studies on the analytical dependence between the value of a longitudinal distributed load and the frequency of free vibrations in a uniform rod. Based on the exact solution of the corresponding differential equation, a method for calculating vibrations in rod structures, while considering their dead weight, is implemented. The method algorithm is shown using the example of a rod with both ends clamped. This article contains graphs and analytical formulas for displaying dependencies. A table is provided that contains all the necessary coefficients to perform similar calculations for other boundary conditions. These results allow the physical and mechanical characteristics of a system to be used to determine the natural frequency of rod structures without using approximate methods.

scholarly journals Analytic formulas for the natural frequencies of hinged structures with taking into account the dead weight

2018 ◽  
Vol 230 ◽  
pp. 02016 ◽  
Author(s):  
Yurii Krutii ◽  
Mykola Suriyaninov ◽  
Victor Vandynskyi
Keyword(s):  
Exact Solution ◽  
Solid Mechanics ◽  
Physical Phenomenon ◽  
Analytical Form ◽  
Variable Coefficients ◽  
Vibration Frequencies ◽  
Bending Vibrations ◽  
Approximate Methods ◽  
Dead Weight ◽  
The Dead

Free bending vibrations of hinged vertical uniform rod with taking into account the dead weight are investigated. The research is based on the exact solution of the partial differential vibration equation with variable coefficients. This approach allows to get more reliable picture of rod’s vibration because only the exact solution carries information of a qualitative nature and forms the most complete picture of the physical phenomenon under consideration. The frequencies equation of problem was written in dimensionless form and the way of its root finding is shown. It has been shown that the problem of determination the nature frequencies of structures is reduced to finding corresponding dimensionless vibration coefficients from equation. The formulas for the first three vibration frequencies of structures were obtained in analytical form. An analytic relationship between the frequencies with and without taking into account the dead weight of the structures was established. The nature of the dependence of frequencies on the value of the longitudinal load was revealed. The presence of conclusive analytical formulas for determining the vibration frequencies of hinged vertical structures with taking into account the dead weight is a real alternative for using the approximate methods for solving this class of problems of solid mechanics.

Analytic Formulas for the Cantilever Structures' Natural Frequencies with Taking into Account the Dead Weight

2019 ◽  
Vol 968 ◽  
pp. 450-459
Author(s):  
Yurii Krutii ◽  
Mykola Surianinov ◽  
Victor Vandynskyi
Keyword(s):  
Exact Solution ◽  
Natural Frequencies ◽  
Analytical Form ◽  
Variable Coefficients ◽  
Bending Vibrations ◽  
Dead Weight ◽  
Vibration Equation ◽  
The Dead ◽  
Rod Structures ◽  
Free Bending

The article has deal with investigations of free bending vibrations of uniform cantilever structures with taking into account the dead weight. The investigation uses the exact solution of the partial differential vibration equation with variable coefficients. The formulas for the natural frequencies of a rod structures are obtained in analytical form. An analytic relationship between the frequencies with and without taking into account the dead weight of the structures is established. The nature of the dependence of frequencies on the value of the longitudinal load is revealed. An example is considered, in which the values of the first three nature frequencies obtained by the author's method are given.

Difference Schemes for Nonlinear BVPS on the Semiaxis

2007 ◽  
Vol 7 (1) ◽  
pp. 25-47 ◽  
Author(s):  
I.P. Gavrilyuk ◽  
M. Hermann ◽  
M.V. Kutniv ◽  
V.L. Makarov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Boundary Value Problem ◽  
Difference Scheme ◽  
Adaptive Algorithm ◽  
Order Differential Equation ◽  
Constructive Method ◽  
Numerical Examples ◽  
Exact Difference ◽  
The Given

Abstract The scalar boundary value problem (BVP) for a nonlinear second order differential equation on the semiaxis is considered. Under some natural assumptions it is shown that on an arbitrary finite grid there exists a unique three-point exact difference scheme (EDS), i.e., a difference scheme whose solution coincides with the projection of the exact solution of the given differential equation onto the underlying grid. A constructive method is proposed to derive from the EDS a so-called truncated difference scheme (n-TDS) of rank n, where n is a freely selectable natural number. The n-TDS is the basis for a new adaptive algorithm which has all the advantages known from the modern IVP-solvers. Numerical examples are given which illustrate the theorems presented in the paper and demonstrate the reliability of the new algorithm.

BENCH DESIGN AND STUDY OF PHYSICAL AND MECHANICAL CHARACTERISTICS OF A TEAT CUP LINER WITH ANTIBACTERIAL FILLER

2020 ◽  
pp. 22-26
Author(s):  
YURY G. IVANOV ◽  
◽  
YELENA V. MASHOSHINA ◽  
LYUDMILA N. VERLIKOVA ◽  
DARIA G. GELETIY ◽  
...  
Keyword(s):  
Mechanical Characteristics ◽  
Physical And Mechanical Characteristics

Discharge-pulse Geotechnical Electro Discharge Technology of Bases Strengthening

2020 ◽  
Vol 787 (12) ◽  
pp. 63-65
Author(s):  
N.S. Sokolov
Keyword(s):  
Bearing Capacity ◽  
Mechanical Characteristics ◽  
Discharge Pulse ◽  
Zero Values ◽  
Traditional Technologies ◽  
Negative Friction ◽  
Geotechnical Problems ◽  
Physical And Mechanical Characteristics

The problem of increasing the bearing capacity of the base is an relevant problem in modern geotechnical construction. When significant loads are transmitted to the base, the use of traditional technologies is not always justified. Often there is an urgent need to use non-standard ways to strengthen the bases. In many cases, the geotechnical situation is aggravated by the presence of weak underlying layers with unstable physical and mechanical characteristics in engineering-geological sections. When strengthening such bases with the help of traditional piles, the latter can get negative friction, which significantly reduces their bearing capacity on the ground, sometimes reaching zero values. This may lead to additional precipitations of the objects being constructed and constructed in the zone of geotechnical influence. The use of ERT piles in most cases successfully solves many complex geotechnical problems.

Solution of heat and mass transfer problems with non-linear coefficients

2019 ◽  
Vol 5 (4) ◽  
pp. 10-20
Author(s):  
Boris G. Aksenov ◽  
Yuri E. Karyakin ◽  
Svetlana V. Karyakina
Keyword(s):  
Mass Transfer ◽  
Exact Solution ◽  
Numerical Methods ◽  
Heat And Mass Transfer ◽  
Unknown Function ◽  
Comparison Theorems ◽  
Upper And Lower Bounds ◽  
Maximum Deviation ◽  
Approximate Methods ◽  
Nonmonotonic Dependence

Equations, which have nonlinear nonmonotonic dependence of one of the coefficients on an unknown function, can describe processes of heat and mass transfer. As a rule, existing approximate methods do not provide solutions with acceptable accuracy. Numerical methods do not involve obtaining an analytical expression for the unknown function and require studying the convergence of the algorithm used. The value of absolute error is uncertain. The authors propose an approximate method for solving such problems based on Westphal comparison theorems. The comparison theorems allow finding upper and lower bounds of the unknown exact solution. A special procedure developed for the stepwise improvement of these bounds provide solutions with a given accuracy. There are only a few problems for equations with nonlinear nonmonotonic coefficients for which the exact solution has been obtained. One of such problems, presented in this article, shows the efficiency of the proposed method. The results prove that the proposed method for obtaining bounds of the solution of a nonlinear nonmonotonic equation of parabolic type can be considered as a new method of the approximate analytical solution having guaranteed accuracy. In addition, the proposed here method allows calculating the maximum deviation from the unknown exact solution of the results of other approximate and numerical methods.

Promising hybrid fabrics based on carbon and aramid fibers as a reinforcing filler for polymer composites

2019 ◽  
pp. 86-95 ◽  
Author(s):  
G. F. Zhelezina ◽  
V. G. Bova ◽  
S. I. Voinov ◽  
A. Ch. Kan
Keyword(s):  
Composite Material ◽  
Polymer Composites ◽  
Carbon Fibers ◽  
Mechanical Characteristics ◽  
High Strength ◽  
High Modulus ◽  
Hybrid Composite Material ◽  
Hybrid Fabric ◽  
Reinforcing Filler ◽  
Physical And Mechanical Characteristics

The paper considers possibilities of using a hybrid fabric made of high-modulus carbon yarn brand ZhGV and high-strength aramid yarns brand Rusar-NT for polymer composites reinforcement. The results of studies of the physical and mechanical characteristics of hybrid composite material and values of the implementation of the strength and elasticity carbon fibers and aramid module for composite material are presented. 

On Approximate Large Deviations for 1D Diffusion

2003 ◽  
Vol 10 (2) ◽  
pp. 381-399
Author(s):  
A. Yu. Veretennikov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Large Deviations ◽  
Stochastic Differential Equation ◽  
Approximation Scheme ◽  
Sufficient Conditions ◽  
Rate Function ◽  
Euler Approximation ◽  
One Dimensional

Abstract We establish sufficient conditions under which the rate function for the Euler approximation scheme for a solution of a one-dimensional stochastic differential equation on the torus is close to that for an exact solution of this equation.

The Composite Reinforcement of LLC «SK»

2015 ◽  
Vol 752-753 ◽  
pp. 749-757
Author(s):  
Svetlana Kiski ◽  
Zhanna Teplova ◽  
Alexey Sokolov
Keyword(s):  
Construction Industry ◽  
Russian Federation ◽  
Mechanical Characteristics ◽  
Analysis And Synthesis ◽  
The Russian Federation ◽  
Under Construction ◽  
Available Information ◽  
Main Producer ◽  
Physical And Mechanical Characteristics ◽  
Composite Reinforcements

The review of the main physical and mechanical characteristics of steel and nonmetallic composite reinforcements is presented in the article. Also there are complex studying, analysis and synthesis of available information. Much attention is paid to recommendations for designing building constructions of different functions with nonmetallic composite reinforcements. Scopes of nonmetallic composite reinforcements in the construction industry in Russia and abroad are considered.Information about main producer and the official distributor of composite reinforcements is provided in the article. This company is the official distributor in the Northwest of the Russian Federation. Their production is successfully used on many objects under construction in Russia. Materials of the article are based on the real photographic materials provided by personal archive of the company.

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