scholarly journals Mathematical modeling of forced oscillations of semidefinite vibro-impact system sliding along rough horizontal surface

2021 ◽  
Vol 39 ◽  
pp. 157-162
Author(s):  
Vitaliy Korendiy ◽  
Volodymyr Gursky ◽  
Oleksandr Kachur ◽  
Volodymyr Gurey ◽  
Oleksandr Havrylchenko ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Horizontal Surface ◽  
Forced Oscillations ◽  
Impact System

scholarly journals Vibro-Impact System Based on Forced Oscillations of Heavy Mass Particle along a Rough Parabolic Line

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Srdjan Jović ◽  
Vladimir Raičević ◽  
Ljubiša Garić
Keyword(s):  
Software Package ◽  
Nonlinear Differential Equations ◽  
Vertical Plane ◽  
Interpolation Polynomial ◽  
Primary Objective ◽  
Forced Oscillations ◽  
Single Frequency ◽  
Mass Particle ◽  
Impact System ◽  
Wolfram Mathematica

This paper analyses motion trajectory of vibro-impact system based on the oscillator moving along the rough parabolic line in the vertical plane, under the action of external single-frequency force. Nonideality of the bond originates of slidingCoulomb’stype friction force with coefficientμ=tgα0. The oscillator consists of one heavy mass particle whose forced motion is limited by two angular elongation fixed limiters. The differential equation of motion of the analyzed vibro-impact system, which belongs to the group of common second order nonhomogenous nonlinear differential equations, cannot be solved explicitly (in closed form). For its approximate solving, the software package WOLFRAM Mathematica 7 is used. The results are tested by using the software package MATLAB R2008a. The combination of analytical-numerical results for the defined parameters of analyzed vibro-impact system is a base for the motion analysis visualization, which was the primary objective of this analytic research. Upon the phase portrait of the heavy mass particle obtained, the energy of the considered vibro-impact system is analyzed. During the graphical visualization of the energetic changes, one of the steps is the process of the phase trajectory equations determination. For this determination, we have used interpolation process that utilizesLagrangeinterpolation polynomial.

scholarly journals Mathematical Modelling of a Specialized Vehicle Caterpillar Mover Dynamic Processes Under Condition of the Distributing the Parameters of the Caterpillar

2018 ◽  
Vol 7 (4.3) ◽  
pp. 40 ◽  
Author(s):  
Serhii Strutynskyi ◽  
Volodymyr Kravchu ◽  
Roman Semenchuk
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Mathematical Modelling ◽  
Mass Concentration ◽  
Forced Oscillations ◽  
Dynamic Processes ◽  
Random Loads ◽  
Distributed Parameters ◽  
The Mathematical Model ◽  
Transverse Oscillations

Features of a specialized vehicle caterpillar mover are considered. A dynamic model of caterpillar transverse oscillations as a system with distributed parameters is proposed. The differential equation in partial derivatives is obtained and its connection in the form of a decomposition by normal oscillation types is found. The analysis of frequencies and the type of caterpillar oscillations has been made. Inertial loads have been found. The mathematical model of forced oscillations of a caterpillar under the influence of random loads is developed and the mathematical modelling is executed. An analysis of the vibration movements and vibration velocities of the intersections of the caterpillar is carried out. The mathematical modeling of the caterpillar oscillations caused by stochastic discrete loads was carried out. A model of random discrete loads has been developed, calculations of the realization of random loads are performed. It was established that the transverse discrete loads occur in points of mass concentration on the caterpillar surface. 

Nonlinear Forced Oscillations and Stability Analysis of the Automotive Gearbox System

2010 ◽  
Author(s):  
Hamed Moradi ◽  
Hasan Salarieh
Keyword(s):  
Mathematical Modeling ◽  
Stability Analysis ◽  
Multiple Scale ◽  
Dynamic Parameter ◽  
Gear System ◽  
Forced Oscillations ◽  
Jump Phenomenon ◽  
Scale Method ◽  
Vibration Responses ◽  
Manufacturing Parameters

In this paper, nonlinear oscillation of the automobile gear system is studied. The backlash dynamic parameter is included in the nonlinear mathematical modeling of the problem. Using multiple scale method, forced vibration responses of the gear system including Primary, Sub-harmonic and Super-harmonic resonances are investigated. In each case, the jump phenomenon and stability analysis are studied. In addition, the effect of dynamic and manufacturing parameters of the gear system on the time responses are analyzed. Simulation and nonlinear analysis of the problem are developed in MAPLE and MATLAB environments.

Cerebral Blood Circulation in Premature Infants by Means of Mathematical Modeling

2015 ◽  
Vol 46 (S 01) ◽  
Author(s):  
R. Lampe ◽  
N. Botkin ◽  
V. Turova ◽  
T. Blumenstein ◽  
A. Alves-Pinto
Keyword(s):  
Mathematical Modeling ◽  
Premature Infants ◽  
Blood Circulation ◽  
Cerebral Blood Circulation

Study of the dynamics of ТПА 350 automatic mill working stand elements

2020 ◽  
Vol 76 (8) ◽  
pp. 830-840
Author(s):  
S. R. Rakhmanov ◽  
V. V. Povorotnii
Keyword(s):  
Mechanical System ◽  
Dynamic Model ◽  
Maximum Amplitude ◽  
Calculation Scheme ◽  
Dynamic Loads ◽  
Forced Oscillations ◽  
Mass Model ◽  
Automatic Mill ◽  
Hollow Billet ◽  
Oscillation Movement

To form a necessary geometry of a hollow billet to be rolled at a pipe rolling line, stable dynamics of the base equipment of the automatic mill working stand has a practical meaning. Among the forces, acting on its parts and elements, significant by value short-time dynamic loads are the least studied phenomena. These dynamic loads arise during transient interaction of the hollow billet, rollers, mandrel and other mill parts at the forced grip of the hollow billet. Basing of the calculation scheme and dynamic model of the mechanical system of the ТПА 350 automatic mill working stand was accomplished. A mathematical model of dynamics of the system “hollow billet (pipe) – working stand” within accepted calculation scheme and dynamic model of the mechanical system elaborated. Influence of technological load of the rolled hollow billet variation in time was accounted, as well as variation of the mechanical system mass, and rigidity of the ТПА 350 automatic mill working stand. Differential equations of oscillation movement for four-mass model of forked sub-systems of the automatic mill working stand were made up, results of their digital calculation quoted. Dynamic displacement of the stand elements in the inter-roller gap obtained, which enabled to estimate the results of amplitude and frequency characteristics of the branches of the mill rollers setting. It was defined by calculation, that the maximum amplitude of the forced oscillations of elements of the ТПА 350 automatic mill working stand within the inter-roller gap does not exceed 2 mm. It is much higher than the accepted value of adjusting parameters of the deformation center of the ТПА 350 automatic mill. A scheme of comprehensive modernization of the rollers setting in the ТПА 350 automatic mill working stand was proposed. It was shown, that increase of rigidity of rollers setting in the ТПА 350 automatic mill working stand enables to stabilize the amplitude of forced oscillations of the working stand elements within the inter-rollers gap and considerably decrease the induced nonuniform hollow billet wall thickness and increase quality of the rolled pipes at ТПА 350.

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