scholarly journals The gyroscopic forces influence on the oscillations of the rotating shafts

2020 ◽  
pp. 223-231
Author(s):  
Petro Lizunov ◽  
Valentyn Nedin
Keyword(s):  
Differential Equations ◽  
Computer Program ◽  
Block Diagram ◽  
Time Integration ◽  
Numerical Differentiation ◽  
Time Interval ◽  
Gyroscopic Forces ◽  
General Block Diagram ◽  
Inertia Forces ◽  
Transverse Oscillations

The results of numerical investigation of shafts transverse oscillations with account of gyroscopic inertia forces are presented. It is shown what the action and how the gyroscopic forces influence on the transverse oscillations of the shafts during rotation. The study has been done with computer program with a graphical interface that is developed by authors. The process of numerical solution of the differential equations of oscillations of rotating rods using the method of numerical differentiation of rod's bend forms by polynomial spline-functions and the Houbolt time integration method is described. A general block diagram of the algorithm is shown. This algorithm describes the process of repeated (cyclical) solving the system of differential equations of oscillations for every point of mechanical system in order to find the new coordinates of positions of these points in each next point of time t+Dt. The computer program in which the shown algorithm is realized allows to monitor for the behavior of moving computer model, which demonstrates the process of oscillatory motion in rotation. Moreover, the program draws the graphics of oscillations and changes of angular speeds and accelerations in different coordinate systems. Defines the dynamic stability fields and draw the diagrams of found fields. Using this program, the dynamics of a range of objects which are modeled by long elastic rods have been studied. For some objects is shown that on special rotational speeds of shafts with different lengths, in the rotating with shaft coordinate system, the trajectories of center of the section have an ordered character in the form of n-pointed star in time interval from excitation to the start of established circular oscillation with amplitude that harmoniously changes in time. It is noted that such trajectories are fact of the action of gyroscopic inertia forces that arise in rotation.

scholarly journals THE PARAMETRIC OSCILLATIONS OF ROTATING ELASTIC RODS UNDER THE ACTION OF THE PERIODIC AXIAL FORCES

2020 ◽  
pp. 56-64
Author(s):  
Petro Lizunov ◽  
Valentyn Nedin
Keyword(s):  
Differential Equations ◽  
Computer Program ◽  
Block Diagram ◽  
Time Integration ◽  
Numerical Differentiation ◽  
Oscillatory Motion ◽  
Elastic Rods ◽  
Axial Forces ◽  
General Block Diagram ◽  
Rotating Rods

The paper presents the results of numerical investigation of the periodic axial forces’ influence on the transverse oscillations of long rotating rods. The gyroscopic inertia forces are taken to account and space oscillating process of rotating rods is considered with account of geometric nonlinearity. The study has been done with computer program with a graphical interface that is developed by authors. The process of numerical solution of the differential equations of oscillations of rotating rods using the method of numerical differentiation of rod’s bend forms by polynomial spline-functions and the Houbolt time integration method is described. A general block diagram of the algorithm is shown. This algorithm describes the process of repeated (cyclical) solving of the system of differential equations of oscillations for every point of mechanical system in order to find the new coordinates of the positions of these points in each next point of time t+∆t. The computer program in which the shown algorithm is realized allows to monitor for the behavior of moving computer model, which demonstrates the process of oscillatory motion in rotation. Moreover, the program draws the graphics of oscillations and changes of angular speeds and accelerations in different coordinate systems. Using this program, the dynamics of a range of objects which are modeled by long elastic rods have been studied. For investigated objects is shown that on various rotational speeds and beat frequencies the oscillatory motion of the rods occurs with different character of behavior. On certain speeds with different frequencies of axial load the oscillations have definite periodicity and occur with beats of amplitude which are the result of the periodic axial force action.

AUTOMATIC PARALLELIZATION OF ELECTRO-MECHANICAL SYSTEMS GOVERNED BY ODEs

2002 ◽  
Vol 26 (3) ◽  
pp. 347-365
Author(s):  
C.A. Rabbath ◽  
A. Ait El Cadi ◽  
M. Abdonne ◽  
N. Lechevin ◽  
S. Lapierre ◽  
...  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Block Diagram ◽  
Time Integration ◽  
Mechanical Systems ◽  
Automatic Parallelization ◽  
Iteration Step ◽  
Control Laws ◽  
Loop Control ◽  
Novel Method

The paper proposes an effective approach for the automatic parallelization of models of electro-mechanical systems governed by ordinary differential equations. The novel method takes a nominal mathematical model, expressed in block diagram language, and portions in parallel the code to be executed on a set of standard microprocessors. The integrity of the simulations is preserved, the computing resources available are efficiently used, and the simulations are compliant with real-time constraints; that is, the time integration of the ordinary differential equations is performed within restricted time limits at each iteration step. The proposed method is applied to a two-degree-of-freedom revolute joint robotic system that includes an induction motor and two inner-outer loop control laws. Numerical simulations validate the proposed approach.

scholarly journals Finite-difference equations of quasistatic motion of the shallow concrete shells in nonlinear setting

2020 ◽  
Vol 7 (1) ◽  
pp. 48-55 ◽  
Author(s):  
Bolat Duissenbekov ◽  
Abduhalyk Tokmuratov ◽  
Nurlan Zhangabay ◽  
Zhenis Orazbayev ◽  
Baisbay Yerimbetov ◽  
...  
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Difference Equations ◽  
Constant Load ◽  
Time Interval ◽  
Test Case ◽  
Algebraic Equations ◽  
Nonlinear Properties ◽  
Finite Difference Equations ◽  
Concrete Shells

AbstractThe study solves a system of finite difference equations for flexible shallow concrete shells while taking into account the nonlinear deformations. All stiffness properties of the shell are taken as variables, i.e., stiffness surface and through-thickness stiffness. Differential equations under consideration were evaluated in the form of algebraic equations with the finite element method. For a reinforced shell, a system of 98 equations on a 8×8 grid was established, which was next solved with the approximation method from the nonlinear plasticity theory. A test case involved computing a 1×1 shallow shell taking into account the nonlinear properties of concrete. With nonlinear equations for the concrete creep taken as constitutive, equations for the quasi-static shell motion under constant load were derived. The resultant equations were written in a differential form and the problem of solving these differential equations was then reduced to the solving of the Cauchy problem. The numerical solution to this problem allows describing the stress-strain state of the shell at each point of the shell grid within a specified time interval.

scholarly journals Energy-efficient outdoor air flow control in ventilation systems

2021 ◽  
Vol 5 (2) ◽  
pp. 18-24
Author(s):  
A. B. Sulin ◽  
◽  
A. A. Nikitin ◽  
T. V. Ryabova ◽  
S. S. Muraveinikov ◽  
...  
Keyword(s):  
Carbon Dioxide ◽  
Block Diagram ◽  
Ventilation System ◽  
Flow Characteristics ◽  
Carbon Dioxide Concentration ◽  
Measured Parameter ◽  
Time Interval ◽  
Air Conditioning System ◽  
Control Zone ◽  
Exhaust Duct

A method for controlling the ventilation system flow characteristics is considered based on the forming principle an air temperature and carbon dioxide concentration predicted estimate in a room based on the changes dynamics analysis in these parameters in the supply and exhaust ducts. The expected microclimate parameters predicted assessment in real time opens up the possibility of using such elements and algorithms for controlling the ventilation and air conditioning system, which provide the required air quality with minimal energy consumption. The analysis calculates the finding probability the measured parameter inside or outside the control zone after a specified time interval. The algorithm for the control system actuators actuation for the channels of temperature and carbon dioxide concentration is presented in the block diagram form. The decision-making logic for actuating the actuators is based on the changes direction and intensity analysis in temperature and carbon dioxide concentration in the exhaust duct and the temperature difference between the supply and exhaust

A Method of Integrating the Equations of Motion in Special Coordinates and the Elimination of a Discontinuity in the Theory of the Motion of Periodic Comet Wolf

1972 ◽  
Vol 45 ◽  
pp. 95-102
Author(s):  
E. I. Kazimirchak-Polonskaya
Keyword(s):  
Differential Equations ◽  
Electronic Computer ◽  
Equations Of Motion ◽  
Close Approach ◽  
Time Interval ◽  
Variable Step ◽  
Rectangular Coordinates ◽  
Periodic Comet ◽  
Nongravitational Effects

From the integration formulae of Numerov and Subbotin we have developed and programmed for an electronic computer a particular method for integrating the differential equations of cometary motion in special rectangular coordinates, with a variable step and allowing for all planetary perturbations and nongravitational effects over a time interval of 400 yr. Application of this method and our set of programmes to the investigation of the motion of P/Wolf permits us to eliminate the discontinuity that has hitherto existed in the theory on account of the comet's close approach to Jupiter in 1922.

Numerical Computation of Differential-Algebraic Equations for the Approximation of Artificial Satellite Trajectories and Planetary Ephemerides

1999 ◽  
Vol 67 (3) ◽  
pp. 574-580 ◽  
Author(s):  
B. Fox ◽  
L. S. Jennings ◽  
A. Y. Zomaya
Keyword(s):  
Differential Equations ◽  
Virtual Work ◽  
Initial Conditions ◽  
Artificial Satellite ◽  
System Modeling ◽  
Differential Algebraic Equations ◽  
The Body ◽  
Time Interval ◽  
Differential Algebraic Equation ◽  
Generalized Coordinates

The principle of virtual work and Lagrange’s equations of motion are used to construct a system of differential equations for constrained spatial multibody system modeling. The differential equations are augmented with algebraic constraints representing the system being modeled. The resulting system is a high index differential-algebraic equation (DAE) which is cast as an ordinary differential equation (ODE) by differentiating the constraint equations twice. The initial conditions are the heliocentric rectangular equatorial generalized coordinates and their first time derivatives of the planets of the solar system and an artificial satellite. The ODE is computed using the integration subroutine LSODAR to generate the body generalized coordinates and time derivatives and hence produce the planetary ephemerides and satellite trajectories for a time interval. Computer simulation and graphical output indicate the satellite and planetary positions and the latter may be compared with those provided in the Astronomical Almanac. Constraint compliance is investigated to establish the accuracy of the computation. [S0021-8936(00)03403-6]

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