Free and Forced Longitudinal Vibrations of Rods

2018 ◽  
Vol 931 ◽  
pp. 47-53 ◽  
Author(s):  
Khusen P. Kulterbaev ◽  
Lyalusya A. Baragunova ◽  
Maryana M. Shogenova
Keyword(s):  
Mathematical Model ◽  
Numerical Methods ◽  
Free Vibration ◽  
Cross Section ◽  
Forced Oscillations ◽  
Constant Cross Section ◽  
Longitudinal Vibrations ◽  
Numerical Examples ◽  
The Mathematical Model ◽  
Forced Longitudinal Oscillations

Free and forced longitudinal oscillations of homogeneous rods of constant cross section are considered. Analytical and numerical methods for solving problems are used. With free vibration, numerical examples are shown for a rod with a jammed and free end and for a rod with a concentrated non-deformable mass at the end, due to which the mathematical model accordingly changes. Forced oscillations are considered for distributed and concentrated loads. The eigenmodes of oscillations characteristic for continually discrete sisites are obtained.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Development of a Mathematical Model for a Workpiece Heating and Cooling in a Protective Medium while Treatment under Pressure

2021 ◽  
Vol 410 ◽  
pp. 115-122
Author(s):  
Victoria V. Devyatiarova ◽  
Eugenia E. Balakhnina ◽  
Lilya M. Valeeva
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Arbitrary Shape ◽  
Thermal Conductivity Coefficient ◽  
Regression Equations ◽  
Heating And Cooling ◽  
Temperature Problem ◽  
Protective Medium ◽  
Computer Calculations ◽  
The Mathematical Model

The paper reviews and develops the mathematical model of plastic flow during the hot-forming processes. A flat non-stationary temperature problem for a cross-section of a long solid (rolled product) of arbitrary shape with different heat transfer conditions along the perimeter of the cross-section was considered. Equations for calculation of the thermal conductivity coefficient and heat capacity of tungsten billets were obtained in the temperature range of 700 - 1500°C, based on the literature data. Analytical dependences in form of regression equations were obtained, allowing for computer calculations of physical specifications of 11x11 mm VA grade tungsten billets in form of temperature functions with accuracy sufficient for practical calculations.

Mobile Robots Characterized by Kinematic and Dynamic Equations: Motion Planning, Trajectory Tracking, and Group Control

2008 ◽  
Author(s):  
Amit Ailon
Keyword(s):  
Mathematical Model ◽  
Motion Planning ◽  
Mobile Robots ◽  
Dynamic Equations ◽  
Kinematics And Dynamics ◽  
Control Problems ◽  
Reference Trajectory ◽  
Numerical Examples ◽  
Group Control ◽  
The Mathematical Model

The paper solves some control problems of mobile robots as both kinematics and dynamics are intertwined in the mathematical model. The problems of driving the vehicle to a desired configuration in a specified time and tracking a reference trajectory are considered. The control problems associated with motion in convoy and rigid formations of a group of vehicles are studied and some results are demonstrated by numerical examples.

scholarly journals Bore formation, evolution and disintegration into solitons in shallow inhomogeneous channels

2003 ◽  
Vol 10 (4/5) ◽  
pp. 407-424 ◽  
Author(s):  
J.-G. Caputo ◽  
Y. A. Stepanyants
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Vries Equation ◽  
Spatial Inhomogeneity ◽  
Hydraulic Jumps ◽  
Variable Depth ◽  
Nonlinear Surface Waves ◽  
Nonlinear Surface ◽  
The Mathematical Model ◽  
Riemann Waves

Abstract. The propagation of nonlinear surface waves in channels of smoothly variable in space cross section is studied theoretically and by means of numerical computations. The mathematical model describing wave evolution is based on the generalized Korteweg-de Vries equation with additional terms due to spatial inhomogeneity and energy dissipation. Specifically we consider channels of variable depth and width. The breaking of Riemann waves and the disintegration of hydraulic jumps into trains of solitons have been examined. The results obtained can be useful in particular for the understanding some peculiarities of bore (mascaret) formation, viscous evolution and disintegration into solitons in inhomogeneous channels or rivers.

Random Oscillations of the Vertical Continual and Discrete Rod under Seismic Influences

2018 ◽  
Vol 931 ◽  
pp. 66-71
Author(s):  
Khusen P. Kulterbaev ◽  
Lyalusya A. Baragunova ◽  
Maryana M. Shogenova
Keyword(s):  
Numerical Methods ◽  
Random Processes ◽  
Longitudinal Vibrations ◽  
Numerical Examples ◽  
Stochastic Formulation ◽  
Deterministic Problem ◽  
The Subject ◽  
Joint Examination ◽  
Additional Reason

Stationary longitudinal vibrations of the vertical rod, kinematically excited by deterministic and random processes, are considered. In a joint examination, these tasks have many similarities. An additional reason for considering both problems was that the results obtained in the deterministic problem can be used to study the problem in stochastic formulation. In solving specific examples, analytical and numerical methods of solution are used. The amplitudes and variances of the oscillations are found. Numerical examples show the effect of broadband input random processes on the dispersion of oscillations. It is pointed out that it is necessary to expand the subject of studying random oscillations taking into account the results obtained.

A Study of the Effects of Baffles on Rotating Compressible Flows

1989 ◽  
Vol 56 (3) ◽  
pp. 710-712
Author(s):  
Max D. Gunzburger ◽  
Houston G. Wood ◽  
Rosser L. Wayland
Keyword(s):  
Fluid Dynamics ◽  
Mathematical Model ◽  
Compressible Flows ◽  
Numerical Examples ◽  
Thermal Boundary Conditions ◽  
Gas Centrifuge ◽  
Mass Injection ◽  
Flow Domain ◽  
The Mathematical Model ◽  
Element Algorithm

Onsager’s pancake equation for the fluid dynamics of a gas centrifuge is modified for the case of centrifuges with baffles which render the flow domain doubly connected. A finite element algorithm is used for solving the mathematical model and to compute numerical examples for flow fields induced by thermal boundary conditions and by mass injection and extraction.

scholarly journals Improving the Dynamic Characteristics of Precision Lathes Used in the Repair of Agricultural Machinery

2021 ◽  
pp. 36-39
Author(s):  
D.E. Molochnikov ◽  
◽  
R.Sh. Halimov ◽  
N.P. Ayugin ◽  
I.R. Salakhutdinov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Dynamic Characteristics ◽  
Low Frequency ◽  
Frequency Component ◽  
Honeycomb Structure ◽  
Friction Unit ◽  
Agricultural Machinery ◽  
Longitudinal Vibrations ◽  
Model Of Friction ◽  
The Mathematical Model

A model of a friction unit of a lathe in the form of a thin layer of material of a honeycomb structure is described to determine the dynamic characteristics of a movable carriage to guide joint. The analysis of the mathematical model of friction for different sliding pairs with varying load and sliding speed is performed. It is shown that the presence of an abrasive impurity in the lubrication of the guide enhances the effect of the low-frequency component of the carriage vibrations on the dynamics of the machine tool and the presence of pockets for retaining the lubricant in the joint of the guide makes it possible to reduce the amplitude of the longitudinal vibrations of the carriage to 30-50 %.

Mathematical Modelling of Thin-Walled Cold-Rolled Cross-Section

2014 ◽  
Vol 617 ◽  
pp. 171-174 ◽  
Author(s):  
Jakub Flodr ◽  
Martin Krejsa ◽  
David Mikolášek ◽  
Oldrich Sucharda ◽  
Libor Žídek
Keyword(s):  
Mathematical Model ◽  
Static Analysis ◽  
Cross Section ◽  
Wind Engineering ◽  
Thin Wall ◽  
Software Applications ◽  
Extreme Loads ◽  
Load Carrying ◽  
Cold Rolled ◽  
The Mathematical Model

The purpose of the paper is to perform a static analysis of a thin-wall cold-rolled steel cross-section of a trapezoidal sheet by means of a mathematical model developed in ANSYS, commercially available software applications. The trapezoidal sheets are used typically as an external cladding which covers the structures of steel halls. Investigating into behaviour of the trapezoidal sheets subjected to extreme loads represents an urgent issue in wind engineering. A physical tension test has been performed in order to verify and confirm the mathematical model. Experiments have been performed to prove results of the static analysis into the behaviour of a load-carrying structure formed by a thin-wall cross-section.

scholarly journals Longitudinal oscillations of the sugar beet root crop body at vibrational digging up from soil

2012 ◽  
Vol 51 (No. 3) ◽  
pp. 99-104
Author(s):  
V. Bulgakov ◽  
I. Holovach ◽  
M. Berezovyy
Keyword(s):  
Sugar Beet ◽  
Cross Section ◽  
Forced Oscillations ◽  
Oscillatory Process ◽  
Longitudinal Vibrations ◽  
Beet Root ◽  
Fundamental Frequencies ◽  
Sugar Beet Root ◽  
Definition Of ◽  
Analytical Expressions

The longitudinal vibrations theory of a continuous elastic body with one fixed extremity is designed. The Ostrogradskii–Hamilton principle of a stationary operation is applied. By Ritz’s method the Ritz’s equation of frequencies for viewed oscillatory process is obtained. In particular analytical expressions for definition of the first and second fundamental frequencies of body oscillations and forced oscillations amplitude of its any cross-section are obtained.

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