scholarly journals Mathematical Modeling of Stress in Circuit Cards Represented by Mechanical Oscillatory Systems

2022 ◽  
Vol 16 (1) ◽  
pp. 303-315
Author(s):  
Igor Kovtun ◽  
Andrii Goroshko ◽  
Svitlana Petrashchuk
Keyword(s):  
Mathematical Modeling ◽  
Oscillatory Systems

scholarly journals MATHEMATICAL MODELING OF A MULTI-INERT OSCILLATORY MECHANISM

2020 ◽  
Vol 20 (1) ◽  
pp. 22-29
Author(s):  
I. P. Popov ◽  
Keyword(s):  
Mathematical Modeling ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Initial Conditions ◽  
Harmonic Oscillations ◽  
Modeling And Analysis ◽  
Main Research ◽  
Oscillatory Systems ◽  
Oscillatory Mechanism ◽  
Orbital Rotation

It is noted that the free harmonic vibrations of a classical pendulum are due to the mutual conversion of the kinetic energy of the load intothe potential energy of the spring. Oscillators with a different nature of energy exchange have been developed, for example, by converting the kinetic energy of a load into the energy of a magnetic field of a solenoid or the energy of an electric field of a capacitor. All these oscillatory systems and the like were a prerequisite for the creation of a biinert oscillator,in which the acceleration of one load occurs due to the braking of another, i. e. only kinetic energies are exchanged. The aim of the work is mathematical modeling of a multi-inert oscillatory mechanism. The main research methods in the framework of this work are methods of mathematical modeling and analysis. The methods used make it possible to obtain a reliable description of the studied objects. Inthe proposed multi-inert oscillator, inert bodies of mass m each carry out harmonic oscillations due to the mutual exchange of kinetic energy. The potential energy of the springs is not requiredfor this. Body vibrationsare free. A feature of a multi-inert oscillator is that the frequency of itsfree oscillations is not fixed and is determined mainly by the initial conditions. This feature can be very useful for technical applications, for example, for self-neutralization of mechanical reactive (inertial) power. n-gon, formed by inert bodies, carries out complex motion – orbital rotation around the center of coordinates and spin rotation around its axis passing through the center of the n-gon. Moreover, each load performs linear harmonic oscillations along its guide. With the arrangement of the guiding weights not in the form of a star, but in parallel to each other, the angles between the corresponding cranks must be 360/n degrees.

scholarly journals DIRECTIONS OF IMPROVING THE EFFICIENCY OF VIBRATION TECHNOLOGICAL MACHINES

2020 ◽  
pp. 49-58
Author(s):  
Oleg Omelyanov ◽  
Mykhailo Zamriі
Keyword(s):  
Mathematical Modeling ◽  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
New Technology ◽  
Oscillatory System ◽  
Simultaneous Action ◽  
Oscillatory Systems ◽  
Technical Developments ◽  
Vibration Field ◽  
Working Bodies

The article considers the directions of increasing the efficiency of vibrating technological machines. The processing of information on the development of vibration technologies is quite diverse and is represented by numerous scientific and technical developments related to improving the efficiency of vibration machines and ensuring the reliability of their work. The analytical basis for previous research in the creation of new technology are mathematical models that reflect the properties of mechanical oscillatory systems with several degrees of freedom, which perform small oscillations under the action of a system of periodic external perturbations that create vibration fields of one configuration. The dynamic properties of the working bodies of machines in a detailed form are revealed as the distribution of the amplitudes of oscillations of the points of the working bodies. In many cases, this distribution is linear, which is due to the manifestations of the properties of the simplest movements of the working bodies. Approaches are proposed in which the possible structural mathematical modeling is realized on the idea that a linear mechanical oscillatory system with concentrated parameters and several degrees of freedom can be compared with the structural scheme of the automatic control system. Particular attention is paid to the study and evaluation of the possibility of new dynamic effects associated with the simultaneous action of several working bodies of machines, as well as - modes of dynamic damping of oscillations. An important role in ensuring such developments is played by areas of research focused on the development of methods of mathematical modeling. Based on the research it is shown that the vibration field of the vibrating technological machine is formed under the influence of several factors, which are determined by the simultaneous action of several force perturbations, asymmetry of inertial and elastic properties of the mechanical system, the presence of additional connections. The introduction of additional links in the structure of the mechanical oscillating system of the vibrating machine, can significantly affect the structure of the vibration field, providing the choice of conditions for rational organization of the technological process of vibration processing, such as vibration hardening, crushing, transportation, screening.

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

MODELING THE HYDRAULIC CHARACTERISTICS OF DRAIN VALVE AND BURST FITTING OF AN AIRCRAFT ACCIDENT-RESISTANT FUEL SYSTEM

2020 ◽  
Vol 7 (3) ◽  
pp. 37-44
Author(s):  
KONSTANTIN NAPREENKO ◽  
◽  
ROMAN SAVELEV ◽  
ALEKSEY TROFIMOV ◽  
ANNA LAMTYUGINA ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Hydraulic Resistance ◽  
Hydraulic Calculation ◽  
Fuel System ◽  
Hydraulic Characteristics ◽  
System A ◽  
Ansys Cfx ◽  
Calculation Results ◽  
Scale Experiment ◽  
Aircraft Accident

The article discusses methods for determining the hydraulic resistance of units of an accident-resistant fuel system. A detailed description of the need to create such fuel systems for modern helicopters is given. The development of such systems today is impossible without the use of the method of mathematical modeling, which allows to qualitatively solve problems arising in the design process. To obtain accurate research results, it is necessary to have a complete description of all elements and assemblies of the system. Methods for determining the hydraulic characteristics of AFS elements using the drag coefficient, reference literature and CFD codes are considered. As the investigated AFS units, a drain valve and burst fitting were studied in the article. A hydraulic calculation of these AFS elements ware performed, the simulation results are presented in the ANSYS CFX software package. Also as the calculation results of bursting fitting, the pressure distribution fields of full and static pressure, velocity and streamlines are also shown. An experimental setup for validating the results obtained using the mathematical modeling method is considered, as well as a methodology for conducting a full-scale experiment to determine the hydraulic resistance of the unit. Materials have been prepared for inclusion in a one-dimensional mathematical model of an accident-resistant fuel system.

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