scholarly journals On the correspondence of theoretical models of longitudinal vibrations of a rod with experimental data

2021 ◽  
Vol 8 (2) ◽  
pp. 270-281
Author(s):  
Alexander L. Popov ◽  
◽  
Sergei A. Sadovsky ◽  
Keyword(s):  
Experimental Data ◽  
Wave Equation ◽  
Theoretical Model ◽  
Natural Frequencies ◽  
Lateral Displacement ◽  
Experimental Spectrum ◽  
Theoretical Models ◽  
Transverse Displacement ◽  
Longitudinal Vibrations ◽  
Longitudinal Waves

A number of theoretical models are known for describing longitudinal vibrations of a rod. The simplest and most common is based on the wave equation. Next comes a model that takes into account lateral displacement (Rayleigh correction). The Bishop model is considered to be more perfect, taking into account both transverse displacement and shear deformation. It would seem that the more perfect the theoretical model, the better it should be consistent with experimental data. Nevertheless, when comparing with a really defined experimental spectrum of longitudinal vibrations of a rod on a large base of natural frequencies, it turns out that this is not quite so. Moreover, in the relative loss is the most complex Bishop model. Comparisons were made for a smooth long cylindrical rod. The questions of refinement with the help of experimentally found frequencies of the velocity of longitudinal waves and the Poisson’s ratio of the rod material are also touched.

Retrieval of Bio-Geophysical Parameters from Remotely Sensing Data by Using Bayesian Methodology

2007 ◽  
pp. 222-252
Author(s):  
C. Notarnicola
Keyword(s):  
Experimental Data ◽  
Theoretical Model ◽  
Theoretical Models ◽  
Data Sets ◽  
Model Errors ◽  
Sources Of Information ◽  
Remotely Sensed Data ◽  
Bayesian Methodology ◽  
Information Models ◽  
Bayesian Methodologies

This chapter introduces the use of Bayesian methodology for inversion purposes: the extraction of bio-geophysical parameters from remotely sensed data. Multisources information, such as different polarizations, frequencies, and sensors are fundamental to the development of operationally useful inversion systems. In this context, Bayesian methodologies offer a convenient tool of combining two or more disparate sources of information, models, and data. The chapter describes the development of a general model starting from a theoretical model, including the sensor noise and the model errors, by using a Bayesian approach. Furthermore, the developed procedure is applied to some experimental data sets. The author hopes that considering theoretical models and experimental data in many different configurations can give an idea of the versatility and robustness of the Bayesian framework.

scholarly journals On Experimental Data of the TCR of TFRs and Their Relation to Theoretical Models of Conduction Mechanism

1985 ◽  
Vol 11 (4) ◽  
pp. 255-259 ◽  
Author(s):  
I. Storbeck ◽  
M. Wolf
Keyword(s):  
Experimental Data ◽  
Grain Size ◽  
Theoretical Model ◽  
Temperature Dependence ◽  
Electrical Conduction ◽  
Conduction Mechanism ◽  
Volume Fraction ◽  
Theoretical Models ◽  
Strain Dependence ◽  
Conducting Component

Any theory of electrical conduction in TFRs encounters mainly two problems: (i) explanation of the dependence of R□on properties of conducting component (volume fraction, grain size, resistivity), (ii) explanation of the temperature dependence of R□taking into account (i). In order to achieve this one has to fit some microscopic parameters to experimental R□-and TCR-values, and to check if they are reasonable or not. The aim of the following discussion is to show, that such a fitting by means of experimental TCR-values is not correct. This is due to the fact that TCR-behaviour, as is well known, is determined also by the dependence of resistivity on strain. But any theoretical model neglects strains, also those who are induced by thermal strains. By means of published experiments concerning the strain dependence of resistance, the magnitude is estimated by which the TCR-values have to be corrected for the described fit.

TEMPERATURE DEPENDENCE BEHAVIOR OF ELECTRICAL RESISTIVITY IN NOBLE METALS AT LOW TEMPERATURES

2014 ◽  
Vol 5 (3) ◽  
pp. 982-992 ◽  
Author(s):  
M AL-Jalali
Keyword(s):  
Experimental Data ◽  
Electrical Resistivity ◽  
Temperature Dependence ◽  
Concentration Dependence ◽  
Low Temperatures ◽  
Noble Metals ◽  
Phonon Scattering ◽  
Theoretical Models ◽  
Residual Resistivity ◽  
Electron Phonon Scattering

Resistivity temperature – dependence and residual resistivity concentration-dependence in pure noble metals(Cu, Ag, Au) have been studied at low temperatures. Dominations of electron – dislocation and impurity, electron-electron, and electron-phonon scattering were analyzed, contribution of these mechanisms to resistivity were discussed, taking into consideration existing theoretical models and available experimental data, where some new results and ideas were investigated.

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.

Simple theoretical models of elimination reactions on polar catalysts; Dehydration reactivity of secondary alcohols on acidic and basic catalysts

1985 ◽  
Vol 50 (4) ◽  
pp. 920-929 ◽  
Author(s):  
Jiří Sedláček
Keyword(s):  
Experimental Data ◽  
Quantum Chemical ◽  
Theoretical Models ◽  
Aliphatic Alcohols ◽  
Secondary Alcohols ◽  
Carbonium Ion ◽  
Dehydration Reactions ◽  
Aromatic Alcohols ◽  
Basic Catalysts ◽  
Simple Models

CNDO/2 calculations for simple models of adsorption and dehydration reactions of secondary aliphatic and aromatic alcohols on polar catalysts are presented. The models involve selected stages of elimination mechanisms of various types (E1, E2 and E1cB elimination). Calculated quantum chemical quantities were correlated with reported experimental data. It is shown that reactivities for the series of substituted phenylethanols correlate very well with the ease of carbonium ion formation. In the case of aliphatic alcohols, calculated quantities correlate generally with the reactivities on SiO2 and are in anticorrelation with the reactivities on Al2O3.NaOH.

Modeling and Experimental Validation of the Effective Bulk Modulus of a Mixture of Hydraulic Oil and Air

2014 ◽  
Vol 136 (5) ◽  
Author(s):  
Hossein Gholizadeh ◽  
Doug Bitner ◽  
Richard Burton ◽  
Greg Schoenau
Keyword(s):  
Experimental Data ◽  
Bulk Modulus ◽  
Theoretical Models ◽  
Operating Conditions ◽  
Air Bubbles ◽  
Pressure Sensitivity ◽  
Hydraulic Oil ◽  
Effective Bulk Modulus ◽  
Experimental Apparatus ◽  
Major Factors

It is well known that the presence of entrained air bubbles in hydraulic oil can significantly reduce the effective bulk modulus of hydraulic oil. The effective bulk modulus of a mixture of oil and air as pressure changes is considerably different than when the oil and air are not mixed. Theoretical models have been proposed in the literature to simulate the pressure sensitivity of the effective bulk modulus of this mixture. However, limited amounts of experimental data are available to prove the validity of the models under various operating conditions. The major factors that affect pressure sensitivity of the effective bulk modulus of the mixture are the amount of air bubbles, their size and the distribution, and rate of compression of the mixture. An experimental apparatus was designed to investigate the effect of these variables on the effective bulk modulus of the mixture. The experimental results were compared with existing theoretical models, and it was found that the theoretical models only matched the experimental data under specific conditions. The purpose of this paper is to specify the conditions in which the current theoretical models can be used to represent the real behavior of the pressure sensitivity of the effective bulk modulus of the mixture. Additionally, a new theoretical model is proposed for situations where the current models fail to truly represent the experimental data.

Investigation on penetration model of shaped charge jet in water

2016 ◽  
Vol 30 (02) ◽  
pp. 1550268 ◽  
Author(s):  
Jinwei Shi ◽  
Xingbai Luo ◽  
Jinming Li ◽  
Jianwei Jiang
Keyword(s):  
Numerical Simulation ◽  
Theoretical Model ◽  
Model Simulation ◽  
Theoretical Models ◽  
Theoretical Research ◽  
Water Medium ◽  
Simulation Results ◽  
Jet Penetration ◽  
The Impact ◽  
Penetration Velocity

To analyze the process of jet penetration in water medium quantitatively, the properties of jet penetration spaced target with water interlayer were studied through test and numerical simulation. Two theoretical models of jet penetration in water were proposed. The theoretical model 1 was established considering the impact of the shock wave, combined with the shock equation Rankine–Hugoniot and the virtual origin calculation method. The theoretical model 2 was obtained by fitting theoretical analysis and numerical simulation results. The effectiveness and universality of the two theoretical models were compared through the numerical simulation results. Both the models can reflect the relationship between the penetration velocity and the penetration distance in water well, and both the deviation and stability of theoretical model 1 are better than 2, the lower penetration velocity, and the larger deviation of the theoretical model 2. Therefore, the theoretical model 1 can reflect the properties of jet penetration in water effectively, and provide the reference of model simulation and theoretical research.

Effect of compact inclusion on the natural frequencies of vibrations of a pipe string in a well

2021 ◽  
pp. 73-77
Author(s):  
A.M. Svalov ◽  
Keyword(s):  
Asymptotic Expansion ◽  
Small Parameter ◽  
Natural Frequencies ◽  
Oscillation Period ◽  
Drill String ◽  
Analytical Relation ◽  
Longitudinal Vibrations ◽  
Bottom Hole ◽  
Tubing String ◽  
Analytical Relations

The influence of small-size inclusion of pipes in a well column on the natural frequency of its longitudinal vibrations is investigated. Using the asymptotic expansion in a small parameter, an analytical relation is obtained that describes the change in the period of the column oscillations in the form of some additional small term to the period of the homogeneous column oscillations. Numerical calculations show that the obtained analytical relations almost accurately describe the oscillation period of a column with a massive compact inclusion, while its difference from the oscillation period of a homogeneous column is within ~20%. The results obtained can be useful for preventing resonant phenomena in the drill string when drilling wells, as well as for optimal use of the longitudinal vibrations of the tubing string to influence the bottom-hole zones of producing wells.

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