scholarly journals Stochastics of pipeline vibrations under dynamic interna

2020 ◽  
pp. 49-55
Author(s):  
Анатолий Власович Чигарев ◽  
Юрий Власович Чигарев
Keyword(s):  
Standard Deviation ◽  
Diffusion Equation ◽  
Internal Pressure ◽  
Duffing Equation ◽  
Horizontal Axis ◽  
System Of Equations ◽  
Bending Vibrations ◽  
Angular Deflection ◽  
Initial Movement

Рассматриваются колебания заполненного жидкостью трубопровода относительно горизонтальной оси, опирающегося на две опоры - одна из которых неподвижна, другая может смещаться в горизонтальном направлении. Начальное движение трубы характеризуется её изгибным отклонением в вертикальной плоскости, угловым во вращательном движении вокруг горизонтальной оси и гидравлическим ударом, при действии которого внутреннее давление на стенки трубы приобретает вид δ -толчков. Исходная система уравнений колебаний трубопровода приводится к уравнению Дуффинга. В переменных «действие-угол» получена граница стохастичности, которая отделяет детерминированную область решения от стохастической. Получено диффузионное уравнение типа Фоккера-Планка-Колмогорова, решение которого определяет функцию плотности вероятности, с помощью которой можно находить случайные параметры колебаний трубы для оценки её движения. Vibrations of a liquid-filled pipeline relative to the horizontal axis are considered. The pipe is supported by two supports - a movable and a fixed one. The initial movement of the pipe is characterized by is bending, angular deflection and hydraulic shok, after which the internal pressure on the pipe walls takes the form of δ -shoks. The system of equations for pipeline vibrations is reduced to the Duffing equation. A stochasticity boundary is obtained that divides the deterministic domain of the solution from the stochastic one. The Fokker-Plank-Kolmogorov diffusion equation is obtained, which makes it possible to determine the standard deviation of the bending vibrations of the pipe.

scholarly journals Singularly perturbed telegraph equations with applications in the random walk theory

1998 ◽  
Vol 11 (1) ◽  
pp. 9-28 ◽  
Author(s):  
Jacek Banasiak ◽  
Janusz R. Mika
Keyword(s):  
Random Walk ◽  
Diffusion Equation ◽  
Random Walks ◽  
Asymptotic Method ◽  
Singularly Perturbed ◽  
Asymptotic Limit ◽  
System Of Equations ◽  
Telegraph Equations ◽  
Random Walk Theory ◽  
The Relationship

In the paper we analyze singularly perturbed telegraph systems applying the newly developed compressed asymptotic method and show that the diffusion equation is an asymptotic limit of singularly perturbed telegraph system of equations. The results are applied to the random walk theory for which the relationship between correlated and uncorrelated random walks is explained in asymptotic terms.

scholarly journals An efficient convergent method for the delay reaction-diffusion equations

2021 ◽  
Author(s):  
Marzieh Heidari ◽  
Mehdi Ghovatmand ◽  
Mohammad Hadi Noori Skandari
Keyword(s):  
Diffusion Equation ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
System Of Equations ◽  
Equivalent System ◽  
Numerical Examples ◽  
Delay Function ◽  
Mild Conditions ◽  
Convergent Method

In this manuscript, we consider the delay reaction-diffusion equation and implement an efficient spectral collocation method to approximate the solution of this equation. We first replace the delay function in the delay reaction-diffusion equation and achieve an equivalent system of equations. We then utilize the Legendre-Gauss-Lobatto and two-dimensional interpolating polynomial to approximate the solution of obtained system. Moreover, we prove the convergent of method under some mild conditions. Finally, the capability and efficiency of the method is illustrated by providing several numerical examples and comparing them with others

scholarly journals A mathematical model for the accumulation of fatigue in bars subjected to lateral vibrations

2019 ◽  
Vol 112 ◽  
pp. 03002
Author(s):  
Petru Cardei ◽  
Raluca Sfiru ◽  
Vergil Muraru
Keyword(s):  
Mathematical Model ◽  
Ultimate Strain ◽  
Dynamic Loads ◽  
System Of Equations ◽  
Lateral Bending ◽  
Bending Vibrations ◽  
Linear Elastic ◽  
Lateral Vibrations ◽  
Proposed Model ◽  
Great Complexity

The article presents a mathematical model for the phenomenon of fatigue accumulation in the slender bar subjected to lateral bending. The model is based on the Euler-Bernoulli type bar, a bi-linear elastic-plastic model and, for simulation of fatigue, a system of equations describing the decrease resistance parameters of the material: the ultimate strain and stress. In the article is exposes the bar response to two types of dynamic loads, as well as a fatigue test simulating process using the proposed model, which results in the Wöhler diagram of the material for the bending vibrations. The conclusions outline the outlook of the model as well as its shortcomings. The author expounds the advantages of the model, but the reader is also challenged to reflect on the opportunity of using mathematical models of great complexity.

Generalized Susceptibility of Mixed Dislocation in Ferroelastics near Structural Phase Transition

2021 ◽  
Vol 887 ◽  
pp. 610-615
Author(s):  
V.V. Dezhin
Keyword(s):  
Phase Transition ◽  
Fourier Transform ◽  
Structural Phase Transition ◽  
Linear Response ◽  
Complete System ◽  
Structural Phase ◽  
Dislocation Line ◽  
System Of Equations ◽  
Bending Vibrations ◽  
Mixed Dislocation

Bending vibrations of a mixed dislocation in ferroelastics near structural phase transition were considered. It was assumed that the dislocation line performs small bending vibrations near equilibrium position. Complete system of equations describing the vibrations of a mixed dislocation near the structural phase transition is written. Based on these set of equations describing the vibrations of a crystal with a dislocation near the structural phase transition, written equations for dynamics of the mixed dislocation in linear approximation of dislocation displacement. Fourier transform of these equations is satisfied. Expression for Peach-Kohler force acting on the dislocation is obtained, and linear response function (generalized susceptibility) of the mixed dislocation in ferroelastics is found.

Nucleic Acid Molecules Prepared by Monolayer Techniques

1972 ◽  
Vol 30 ◽  
pp. 178-179
Author(s):  
Dimitrij Lang
Keyword(s):  
Electron Microscopy ◽  
Standard Deviation ◽  
Nucleic Acid ◽  
Cytochrome C ◽  
Nucleic Acids ◽  
Contour Length ◽  
Sample Standard Deviation ◽  
Molecular Weights ◽  
Length Measurements ◽  
Protein Monolayer

The success of the protein monolayer technique for electron microscopy of individual DNA molecules is based on the prevention of aggregation and orientation of the molecules during drying on specimen grids. DNA adsorbs first to a surface-denatured, insoluble cytochrome c monolayer which is then transferred to grids, without major distortion, by touching. Fig. 1 shows three basic procedures which, modified or not, permit the study of various important properties of nucleic acids, either in concert with other methods or exclusively:1) Molecular weights relative to DNA standards as well as number distributions of molecular weights can be obtained from contour length measurements with a sample standard deviation between 1 and 4%.

Reliability of the Minimum Masking Level as Outcome Variable in Tinnitus Clinical Research

2020 ◽  
Vol 29 (3) ◽  
pp. 429-435
Author(s):  
Patricia C. Mancini ◽  
Richard S. Tyler ◽  
Hyung Jin Jun ◽  
Tang-Chuan Wang ◽  
Helena Ji ◽  
...  
Keyword(s):  
Standard Deviation ◽  
High Frequency ◽  
Pearson Correlation ◽  
Correlation Coefficients ◽  
Outcome Variable ◽  
Reliable Estimate ◽  
Moderate Correlation ◽  
Trained Subjects ◽  
The Relationship ◽  
Minimum Intensity

Purpose The minimum masking level (MML) is the minimum intensity of a stimulus required to just totally mask the tinnitus. Treatments aimed at reducing the tinnitus itself should attempt to measure the magnitude of the tinnitus. The objective of this study was to evaluate the reliability of the MML. Method Sample consisted of 59 tinnitus patients who reported stable tinnitus. We obtained MML measures on two visits, separated by about 2–3 weeks. We used two noise types: speech-shaped noise and high-frequency emphasis noise. We also investigated the relationship between the MML and tinnitus loudness estimates and the Tinnitus Handicap Questionnaire (THQ). Results There were differences across the different noise types. The within-session standard deviation averaged across subjects varied between 1.3 and 1.8 dB. Across the two sessions, the Pearson correlation coefficients, range was r = .84. There was a weak relationship between the dB SL MML and loudness, and between the MML and the THQ. A moderate correlation ( r = .44) was found between the THQ and loudness estimates. Conclusions We conclude that the dB SL MML can be a reliable estimate of tinnitus magnitude, with expected standard deviations in trained subjects of about 1.5 dB. It appears that the dB SL MML and loudness estimates are not closely related.

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