scholarly journals MATHEMATICAL MODEL OF INTERACTION OF FREE ROLLING FLAT DISK WITH SOIL

2018 ◽  
Vol 13 (1) ◽  
pp. 96-101
Author(s):  
Александр Акимов ◽  
Aleksandr Akimov ◽  
Юрий Константинов ◽  
Yuriy Konstantinov ◽  
Владимир Мазяров ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Unit Length ◽  
Mean Value ◽  
Kinematic Parameter ◽  
Engineering Practice ◽  
Elementary Functions ◽  
Translational Movement ◽  
Flat Disk ◽  
External Forces ◽  
Plane Disk

When constructing a mathematical model for the interaction of a free-rotating plane disk with soil, it is necessary to take into account that the magnitude of its kinematic parameter, equal to the ratio of its circumferential velocity to the speed of translational movement of the disk, is not a given quantity, but a definite quantity. With uniform rotation of the disk and its translational movement at a constant speed, the kinematic parameter is determined from the equilibrium equation of external forces, applied to the disk. The generalized mathematical model of disk-soil interaction, proposed earlier, was taken into account, but in view of relative complexity it was not widely used. The aim of the study is to construct a simpler, but adequate mathematical model for the interaction of a free-spinning disc with soil. The model is constructed under the assumptions of the constancy of the translational velocity of the disk, the permanence of its penetration and the possibility of replacing the pressure on the disc’s lateral surfaces with its mean value and replacing the force per unit length of the blade with its mean value. Since the distribution of the elementary forces of soil reactions is ultimately determined by the distribution of the absolute velocities of the points of the disk in contact with the soil, the resultant reactions of the soil and their total moment are functions of the kinematic parameter of the disk and its relative burial. These functions are given by integrals, that are not expressed in terms of elementary functions by a finite number of operations. However, the proximity of the kinematic parameter of the free-spinning disk to unity makes it possible, with the help of an estimate of these integrals, to obtain approximate expressions in terms of elementary functions for the resultant reactions of the soil and their total angular momentum. It is shown that the accuracy of the approximations obtained is sufficient for engineering practice.

scholarly journals Modeling the seam strength of denim garments by using fuzzy expert system

2021 ◽  
Vol 16 ◽  
pp. 155892502198897
Author(s):  
Joy Sarkar ◽  
Md Abdullah Al Faruque ◽  
Moni Sankar Mondal
Keyword(s):  
Fuzzy Logic ◽  
Expert System ◽  
Linear Density ◽  
Unit Length ◽  
Coefficient Of Determination ◽  
Sewing Thread ◽  
External Forces ◽  
Fuzzy Logic Expert System ◽  
The Relationship ◽  
Sufficient Strength

The main purpose of this study is to predict and develop a model for forecasting the Seam Strength (SS) of denim garments with respect to the thread linear density (tex) and Stitches Per Inch (SPI) by using a Fuzzy Logic Expert System (FLES). The seam strength is an important factor for the serviceability of any garments. As seams bound the fabric pieces together in a garment, the seams must have sufficient strength to execute this property even in the unexpected severe conditions where the garments are subjected to loads or any additional internal or external forces. Sewing thread linear density and number of stitches in a unit length of the seam are the two of the most important factors that affect the seam strength of any garments. But the relationship among these two specific variables and the seam strength is complex and non-linear. As a result, a fuzzy logic based model has been developed to demonstrate the relationship among these parameters and the developed model has been validated by the experimental trial. The coefficient of determination ( R2) was found to be 0.98. The mean relative error also lies withing acceptable limit. The results have suggested a very good performance of the model in the case of the prediction of the seam strength of the denim garments.

scholarly journals SETI, Evolution and Human History Merged into a Mathematical Model

2013 ◽  
Vol 12 (3) ◽  
pp. 218-245 ◽  
Author(s):  
Claudio Maccone
Keyword(s):  
Mathematical Model ◽  
Exponential Growth ◽  
Numerical Estimate ◽  
Mean Value ◽  
Darwinian Evolution ◽  
Human History ◽  
The Galaxy ◽  
Positive Time ◽  
A Cell ◽  
Geometric Locus

AbstractIn this paper we propose a new mathematical model capable of merging Darwinian Evolution, Human History and SETI into a single mathematical scheme:(1) Darwinian Evolution over the last 3.5 billion years is defined as one particular realization of a certain stochastic process called Geometric Brownian Motion (GBM). This GBM yields the fluctuations in time of the number of species living on Earth. Its mean value curve is an increasing exponential curve, i.e. the exponential growth of Evolution.(2) In 2008 this author provided the statistical generalization of the Drake equation yielding the number N of communicating ET civilizations in the Galaxy. N was shown to follow the lognormal probability distribution.(3) We call “b-lognormals” those lognormals starting at any positive time b (“birth”) larger than zero. Then the exponential growth curve becomes the geometric locus of the peaks of a one-parameter family of b-lognormals: this is our way to re-define Cladistics.(4) b-lognormals may be also be interpreted as the lifespan of any living being (a cell, or an animal, a plant, a human, or even the historic lifetime of any civilization). Applying this new mathematical apparatus to Human History, leads to the discovery of the exponential progress between Ancient Greece and the current USA as the envelope of all b-lognormals of Western Civilizations over a period of 2500 years.(5) We then invoke Shannon's Information Theory. The b-lognormals' entropy turns out to be the index of “development level” reached by each historic civilization. We thus get a numerical estimate of the entropy difference between any two civilizations, like the Aztec-Spaniard difference in 1519.(6) In conclusion, we have derived a mathematical scheme capable of estimating how much more advanced than Humans an Alien Civilization will be when the SETI scientists will detect the first hints about ETs.

scholarly journals ON PREVENTIVE MAINTENANCE POLICY FOR WAVE DISSIPATING BLOCKS COVERING CAISSON BREAKWATER

2018 ◽  
pp. 72
Author(s):  
Takao Ota ◽  
Hiroyuki Kawamura ◽  
Yoshiharu Matsumi ◽  
Junji Koyanagi ◽  
Takashi Satow
Keyword(s):  
Mathematical Model ◽  
Preventive Maintenance ◽  
Maintenance Cost ◽  
Maintenance Policy ◽  
Reliability Engineering ◽  
Coastal Structures ◽  
Service Period ◽  
Caisson Breakwater ◽  
External Forces ◽  
Preventive Maintenance Policy

The infrastructures are required to keep a certain level of performance during the duration of service. Because the performance of the infrastructures including harbor and coastal structures deteriorates due to aging and damage that is caused by the action of external forces, it is necessary to perform appropriate maintenance. Satow et al. (2009) proposed a mathematical model for the preventive maintenance of wave dissipating blocks based on the method of the reliability engineering. They also derived the expected maintenance cost over the in service period and the optimal preventive maintenance policy. In this study, the optimal threshold for preventive maintenance to minimize the expected maintenance cost is determined for the wave dissipating blocks covering caisson breakwater by using the above model.

scholarly journals Belt conveyor failure simulation at the design stage with transverse displacements of the belt

2020 ◽  
Vol 168 ◽  
pp. 00056
Author(s):  
Vitalii Monastyrskyi ◽  
Serhii Monastyrskyi ◽  
Denis Nomerovskyi ◽  
Borys Mostovyi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Fourier Transform ◽  
Adaptive Control ◽  
Design Stage ◽  
Belt Conveyor ◽  
Failure Simulation ◽  
The Fourier Transform ◽  
External Forces ◽  
The Mathematical Model

To find possible conveyor failures at the design stage means to determine a transverse belt displacement and compare the obtained data with the permissible ones. The dynamic problem of the belt movement on the conveyor has been defined. Resistance and external forces, limits of the belt displacement have been determined. The transverse belt displacement can be described by partial differential equations. To solve the problem, the Fourier transform has been used. Change patterns in the transverse belt conveyor displacement dependent on conveyor’s parameters, type of load, and skewing of the idlers along the conveyor have been obtained. The results agree with experimental data. The method of adaptive control of the transverse belt displacement has been described. The essence of this method is to adapt the model of the moving belt in the conveying trough to changed conditions and to reveal the uncertainty of the control with the known parameters of the mathematical model.

First Principle-Based Control Oriented Model of a Gasoline Engine

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Ahmed Yar ◽  
A. I. Bhatti ◽  
Qadeer Ahmed
Keyword(s):  
Mathematical Model ◽  
Gasoline Engine ◽  
Mean Value ◽  
First Principle ◽  
Unified Framework ◽  
Engine Model ◽  
Proposed Model ◽  
Suitable Form ◽  
Speed Fluctuations ◽  
The Mathematical Model

A first principle based-control oriented gasoline engine model is proposed that is based on the mathematical model of the actual piston and crankshaft mechanism. Unlike conventional mean value engine models (MVEMs), which involve approximating the torque production mechanism with a volumetric pump, the proposed model obviates this rather over-simplistic assumption. The alleviation of this assumption leads to the additional features in the model such as crankshaft speed fluctuations and tension in bodies forming the mechanism. The torque production dynamics are derived through Lagrangian mechanics. The derived equations are reduced to a suitable form that can be easily used in the control-oriented model. As a result, the abstraction level is greatly reduced between the engine system and the mathematical model. The proposed model is validated successfully against a commercially available 1.3 L gasoline engine. Being a transparent and more capable model, the proposed model can offer better insight into the engine dynamics, improved control design and diagnosis solutions, and that too, in a unified framework.

A Viscoelastic Model of the Neonatal Respiratory System to Assess the Efficacy of CPAP Devices

2008 ◽  
Author(s):  
Prasika I. Reddy ◽  
Ahmed M. Al-Jumaily ◽  
Geoff T. Bold
Keyword(s):  
Mathematical Model ◽  
Airway Pressure ◽  
Distress Syndrome ◽  
Positive Airway Pressure ◽  
Viscoelastic Model ◽  
Engineering Practice ◽  
Neonatal Lung ◽  
Cpap Devices ◽  
Airway Model

The objectives of this research were to; develop a validated mathematical model of the premature neonatal lung. A description of the multi-compartmental, branched airway model of the neonatal lung is presented and shown to compare well with existing in-vivo data from the literature. The model described will be used in engineering practice to assess the design of conventional and emerging forms of continuous positive airway pressure (CPAP) devices in treating respiratory distress syndrome (RDS) in premature neonates.

scholarly journals Commissioning tests of the first hydro-generator of the Bajo de Mina HPP (Panama)

2020 ◽  
Vol 175 ◽  
pp. 05044
Author(s):  
Andrey Zuikov
Keyword(s):  
Mathematical Model ◽  
Free Surface ◽  
Empirical Data ◽  
Thrust Bearing ◽  
Third Party ◽  
Engineering Practice ◽  
Vertical Distributions ◽  
Oil Flow ◽  
The Mathematical Model

A mathematical model has been developed for calculating the distribution of azimuthal velocities and the shape of the free surface of oil in the compartments of an oil bath of a hydro-generator. The mathematical model of oil flow is verified by comparing the calculated radial-vertical distributions of normalized azimuthal velocities obtained on its basis with the free surface of the oil with the empirical data of third-party authors. The verification showed a good fit between the calculated and experimental distributions, which allows recommending the developed mathematical model for use in engineering practice. Calculations were carried out for the modes of the oil movement in the thrust bearing and the guide bearing of the hydro-generator of the Bajo de Mina HPP. Recommendations are made for the elimination of emergency modes associated with oil overflow through the fencing of the thrust bearing oil bath, which separate oil bath from the shaft of hydro-generator.

scholarly journals Numerical Modeling on Hydraulic Fracturing in Coal-Rock Mass for Enhancing Gas Drainage

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Zhigang Yuan ◽  
Yaohua Shao
Keyword(s):  
Mathematical Model ◽  
Rock Mass ◽  
Hydraulic Fracturing ◽  
Gas Flow ◽  
Numerical Solutions ◽  
Fracture Initiation ◽  
Engineering Practice ◽  
Gas Drainage ◽  
Fracturing Process ◽  
Coal Rock

The mechanism of how hydraulic fracturing influences gas drainage in coal-rock mass is still not clear due to its complex mechanism. In this work, statistical distributions are firstly introduced to describe heterogeneity of coal-rock mass; a novel simultaneously coupled mathematical model, which can describe the fully coupled process including seepage-damage coupling during hydraulic fracturing process and subsequent gas flow during gas drainage process, is established; its numerical implementation procedure is coded into a Matlab program to calculate the damage variables, and it partly uses COMSOL solver to obtain numerical solutions of governing equations with damage-flow coupling; the mathematical model and its implementation are validated for initial damage pressure and mode of a single solid model without considering flow-damage coupling, as well as fracture initiation pressure and influence of heterogeneity on damage evolution of hydraulic fracturing considering flow-damage coupling; and finally, based on an engineering practice of hydraulic fracturing with two boreholes, the mechanism of how hydraulic fracturing influences gas drainage is investigated, numerical simulation results indicate that coal-rock mass pore-fissure structure has been improved, and there would exist a gas migration channel with characteristics of higher porosity and lower stresses, which demonstrates significant effects and mechanism of hydraulic fracturing on improving coal-rock permeability and enhancing gas drainage. The research results provide a guide for operation of hydraulic fracturing and optimal layout of gas drainage boreholes.

scholarly journals 3D-SHELL ELEMENTS AND THEIR UNDERLYING MATHEMATICAL MODEL

2004 ◽  
Vol 14 (01) ◽  
pp. 105-142 ◽  
Author(s):  
D. CHAPELLE ◽  
A. FERENT ◽  
K. J. BATHE
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Engineering Practice ◽  
Finite Element Discretization ◽  
Finite Element Scheme ◽  
Element Discretization ◽  
Shell Elements ◽  
Shell Models ◽  
The Family ◽  
Model Features

We focus on a family of shell elements which are a direct generalization of the shell elements most commonly used in engineering practice. The elements in the family include the effects of the through-the-thickness normal stress and can be employed to couple directly with surrounding media on either surfaces of the shell. We establish the "underlying" mathematical model of the shell discretization scheme, and we show that this mathematical model features the same asymptotic behaviors — when the shell thickness becomes increasingly smaller — as classical shell models. The question of "locking" of the finite element discretization is also briefly addressed and we point out that, for an effective finite element scheme, the MITC approach of interpolation is available.

scholarly journals Modeling of Thermal Conductivity in a Medium with Phase Transition with a Moving Boundary of Phase Change

2021 ◽  
pp. 53-61
Author(s):  
Vadim Mizonov ◽  
◽  
Andrei Tikhonov ◽  
Elena Basova ◽  
Andrei Mitrofanov ◽  
...  
Keyword(s):  
Phase Transition ◽  
Thermal Conductivity ◽  
Heat Treatment ◽  
Mathematical Model ◽  
Numerical Experiments ◽  
Moving Boundary ◽  
Phase Interface ◽  
Significant Feature ◽  
Engineering Practice ◽  
Interface Motion

This work is devoted to the theoretical study of the effect of the phase interface motion on thermal conductivity in a liquid-solid nonlinear medium with a phase transition. The problem under consideration deals with the Stefan problems. Its most significant feature is the jump in the phase properties at separation of their moving boundaries. The objective was achieved by solving the following tasks: the construction of the process mathematical model based on its cell representation and with the use of the Markov chain theory mathematical apparatus, performing numerical experiments with the developed model, demonstrating its operability and the possibility to achieve the set goal. The most significant scientific results were as follows. First was an algorithm for the construction of a cell mathematical model of nonlinear thermal conductivity in a phase transitions medium with a moving phase interface for domains of a canonical shape (plane wall, cylinder, ball). Second, the results of the numerical experiments, showing that the jump of properties affected greatly the kinetics of the process. The significance of the results obtained consisted in the development of a simple but informative mathematical model of the media heat treatment kinetics with phase transformations, available for a direct use in the engineering practice. The proposed algorithm for constructing the model can be effectively used in prediction the open water pipes freezing in cold regions, in modeling the heat treatment of metals, in choosing the freezing modes of food products for a long-term storage, and other thermo-physical processes.

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