scholarly journals Bifurcation phenomena and statistical regularities in dynamics of forced impacting oscillator

2019 ◽  
Vol 98 (3) ◽  
pp. 1795-1806 ◽  
Author(s):  
Sergii Skurativskyi ◽  
Grzegorz Kudra ◽  
Krzysztof Witkowski ◽  
Jan Awrejcewicz
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Physical Model ◽  
Dry Friction ◽  
Stepper Motor ◽  
Nonlinear Phenomenon ◽  
Hertz Contact ◽  
Bifurcation Phenomena ◽  
Statistical Regularities ◽  
The Mathematical Model

Abstract The paper is devoted to the study of harmonically forced impacting oscillator. The physical model for oscillator is a cart on a guide connected to the support with springs and excited by the stepper motor. The support also is provided with limiter of motion. The mathematical model for this system is defined with the second-order piecewise smooth differential equation. Model’s nonlinearity is connected with the incorporation of dry friction and generalized Hertz contact law. Analyzing the classical Poincare sections and inter-impact sequences obtained experimentally and numerically, the bifurcations and statistical properties of periodic, multi-periodic, and chaotic regimes were examined. The development of impact-adding regime as a new nonlinear phenomenon when the forcing frequency varies was observed.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

A Meshless Method for Solving the Mathematical Model Associated the Leakage Problem in Gas Pipeline

2014 ◽  
Vol 986-987 ◽  
pp. 1418-1421
Author(s):  
Jun Shan Li
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Basis Function ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Gas Pipeline ◽  
The Mathematical Model

In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.

The Effect of Hertzian, Bending and Shearing Stiffness on Noise and Vibration

2001 ◽  
Author(s):  
Jamil Abdo ◽  
Kambiz Farhang ◽  
Mousa Mohsen
Keyword(s):  
Mathematical Model ◽  
Contact Stiffness ◽  
Hertzian Contact ◽  
Hertz Contact ◽  
Resonant Frequencies ◽  
Tangential Contact ◽  
Apparent Stiffness ◽  
Fundamental Understanding ◽  
The Mathematical Model ◽  
Friction Induced Vibration

Abstract Since the apparent stiffness due to contact of one surface on another relates directly to the localized resonant frequencies, it is believed that accurate account of this property will lead to the fundamental understanding of causes of friction-induced vibration and noise. The mathematical model of contact is utilized to develop formulae for normal and tangential contact stiffness. The inclusion of a study in which the various modes of elastic deflections of an asperity are also considered, as well as their effects. The bending, shear and Hertz contact modes of elastic deflection are assumed to simultaneously occur for an asperity. Investigation of the combined effect of bending, shear and Hertzian contributions to the contact stiffness is indicating that the equivalent contact stiffness is best represented, among the three types of stiffness, by that due to Hertzian contact.

Mathematical model of oil-containing water purification process in the volume of granulated media

2018 ◽  
Vol 233 (3) ◽  
pp. 879-885
Author(s):  
Valeriy Ivanovich Istomin ◽  
Elena Stanislavovna Solodova ◽  
Viktoria Valer’evna Khlebnikova
Keyword(s):  
Mathematical Model ◽  
Physical Model ◽  
Water Purification ◽  
Theoretical Research ◽  
Purification Process ◽  
Operational Parameters ◽  
Filtering Element ◽  
The Mathematical Model ◽  
First Time ◽  
Further Development

A mathematical model of oil-containing water purification process in the volume of granulated media is developed. On the basis of this model, the purifying ability of filtering unit with granulated coalescing media, which regenerates filtering media in the mode of pseudo liquefaction of granule without disassembling and replacement of filtering element, is studied. In the process of theoretical research, the physical model of oil-containing water purification process in the volume of granulated coalescing media is elaborated. The consistent patterns of the analysed process have gained further development. Due to these patterns, the factors which determine the effectiveneness of purification are established. After realization of the experiment plan for the first time, the mathematical model of a ship’s oil-containing water purification process in the volume of granulated media on the basis of the regression equation has been received. This model allows to calculate the rational constructive and operational parameters of the plant with granulated filter elements.

Attachment energy saving gripping device for chokerless timber skidding when thinning

10.12737/4537 ◽  
2014 ◽  
Vol 4 (2) ◽  
pp. 223-228
Author(s):  
Латышева ◽  
M. Latysheva ◽  
Зеликов ◽  
Vladimir Zelikov ◽  
Посметьев ◽  
...  
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Energy Saving ◽  
Hydraulic Cylinder ◽  
Equation Of Motion ◽  
The Mathematical Model ◽  
Attachment Energy

Hydrokinetic diagram of the device for chokerless skidding is presented. Chokerless device for logging includes a frame, capture with two jaws and hydraulic cylinder of jaw gripping attached to the hinged system of tractor, linked via a double-hinged capture unit to one end of the bell crank, and between the second end of the bell crank and the frame there is pivotally mounted hydraulic cylinder for additional amortization of oscillations of grapple. The mathematical model of the process of logging trees is made. It includes a differential equation of whips pack and differential equation of motion of the accumulator piston.

Dynamic Study on Vehicle Hydro-Pneumatic Suspension

2010 ◽  
Vol 139-141 ◽  
pp. 2653-2657
Author(s):  
Ling Xin Geng ◽  
Li Juan Zhang ◽  
Ren Zhi Wu
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Mathematical Models ◽  
Physical Model ◽  
Dynamic Load ◽  
Special Program ◽  
Vehicle Dynamic ◽  
Pneumatic Suspension ◽  
Working Principle ◽  
The Mathematical Model

The performance of HPS directly influences the comfort of vehicle, dynamic load of wheels and travel distance of suspension. In order to describe and evaluate the performance of HPS, the structure and working principle of main parts of the HPS are introduced and analyzed in this paper firstly. Then the physical model is founded by analyzing and simplifying the structure of HPS. According to the physical model, non-linear mathematical models of HPS with dual gas-accumulators are built up and a special program is composed. The results of computer simulation are carried out through the program. Then a testing rig for HPS is designed and manufactured after rebuilding cylinders and abundant experiments are performed on the testing rig. Comparisons are drawn between the results of simulation and testing, which manifest the mathematical model of HPS built in the thesis is feasible.

scholarly journals Modelling Fabric’s Optical Behaviors

2008 ◽  
Vol 575-578 ◽  
pp. 1266-1271 ◽  
Author(s):  
Hong Ying Yang ◽  
Su Kang Zhu ◽  
Ke Jing Li ◽  
Ning Pan
Keyword(s):  
Mathematical Model ◽  
Optical Properties ◽  
Physical Model ◽  
Structural Parameters ◽  
Incident Light ◽  
Optical Parameters ◽  
Light Component ◽  
Light Components ◽  
Improved Model ◽  
The Mathematical Model

In this paper, existing models of fabric’s optical behaviors are classified and estimated briefly. Then, basing on the optical theories, this paper abstracts the commonness of fabric’s optical behaviors and put forward an improved model of them, which includes a physical model and its corresponding mathematical model. The physical model describes the light falling on fabrics splits into six components, which compose another four components. The ten light components divided by the incident light yields ten light component parameters, which are functions of the wavelength. The mathematical model connects the ten light component parameters and gives formulas to calculate them. Thus, the light component parameters are connected with the basic optical parameters and structural parameters of fabric. This improved model provides a fundamental and theoretical guide for studying fabric’s optical properties systematically, which has been proved to be effective in solving some problems related fabric optical properties.

scholarly journals The predictability of seismicity and large earthquakes: Kamchatka 1962 to 2014

2019 ◽  
pp. 52-66
Author(s):  
A. I. Malyshev
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Nonlinear Differential Equation ◽  
Optimization Algorithm ◽  
Seismic Activity ◽  
Second Order ◽  
High Predictability ◽  
The Mathematical Model ◽  
Large Earthquakes ◽  
Over Time

This paper reports the estimation of the predictability of seismicity and large earthquakes in Kamchatka as inferred from data in the Kamchatka regional catalog for 1962–2014. The mathematical model uses a second-order nonlinear differential equation, while the optimization algorithm and the estimates of predictability are the author’s own. The estimates show a high predictability of seismicity; the extrema of prediction nonlinearity typical of large earthquakes usually occur simultaneously with similar extrema of seismicity as a whole. Overall, 220 large (K ≥ 13.3) Kamchatka earthquakes were analyzed to find that foreshock predictability was available for 200 earthquakes (~30000 determinations) and aftershock predictability for 215 earthquakes (~300000 determinations). The predictability related to large earthquakes began to be seen and was rapidly increasing at intermediate (7.5–30 km) radii of hypocenter samples. The prediction distances over time were some tens and hundreds of days for foreshock predictability and some hundreds and thousands of days for aftershock predictability. These results demonstrate very good promise for the approximation extrapolation approach to the prediction of both large earthquakes themselves and of subsequent aftershock decay of seismic activity.

scholarly journals Simulation of the Distribution of Nanoplates in a Liquid

2021 ◽  
Vol 27 (4) ◽  
pp. 647-655
Author(s):  
A. M. R. Al-Mashhadani ◽  
V. F. Pershin
Keyword(s):  
Mathematical Model ◽  
Physical Model ◽  
Critical Concentration ◽  
Solid Particles ◽  
The Real ◽  
Model Based ◽  
Real Process ◽  
Layered Crystals ◽  
The Mathematical Model

The general regularities of exfoliation of layered crystals are considered. A physical model based on the analogy of the spatial packing of polydisperse spherical solid particles is proposed to simulate the distribution of nanoplates in a liquid. Mathematical dependences have been obtained for calculating the critical concentration of aggregation of nanoplates, using graphene as an example. The verification of the adequacy of the mathematical model to the real process was carried out.

scholarly journals Measurement and improvement of efficiency of Library by mathematical modelling and finding reliability

2021 ◽  
Vol 7 (2) ◽  
pp. 1-5
Author(s):  
Yakshi Bahl ◽  
Tarun Kumar Garg
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Mathematical Modelling ◽  
Exponential Distribution ◽  
Death Process ◽  
Library System ◽  
The Mathematical Model ◽  
Server System ◽  
Birth Death

Here in this paper we have developed  the mathematical model of the library server using  Markov birth – death process assuming that library system server system is based on exponential distribution. The model so developed by victimisation Chapman Kolmogorov differential equation and is solved by using Mathematica. The solution so obtained is analysed for various rates of failures and repair. The finding so obtained are discussed with the concerned authorities of the library to boost the efficiency of the library.

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