scholarly journals Buckling under the action of loading by aerodynamic and inertial forces during ground track tests of aviation equipment

2021 ◽  
Vol 13 (S) ◽  
pp. 5-12
Author(s):  
Sergey A. ASTAKHOV ◽  
Vasiliy I. BIRYUKOV
Keyword(s):  
Mathematical Modelling ◽  
Numerical Solution ◽  
Test Object ◽  
Propulsion System ◽  
Outer Shell ◽  
Inertial Forces ◽  
Longitudinal Stability ◽  
Outer Contour ◽  
Elastic Line ◽  
Aerodynamic Loading

The article analyses the choice of a rational layout of the test object with a propulsion system (PS). One of the design examples of calculating the longitudinal stability and strength of the structure is given. The purpose of the article is to solve the problem of bending the elastic line of a cantilever tubular rod with a hinged termination during tests of a propulsion system for various aircrafts. On the example, the estimates of the approximate test object, accelerated on the track to a speed of 1200 m/s, are carried out. The aerodynamic loading of the structure of the mobile track installation is considered using the methods of mathematical modelling and the development of an algorithm for the numerical solution of the problem of bending the elastic line of a cantilever tubular rod. The deflection from the forces of external and internal loads of the outer shell of a movable track installation is considered, provided that the diameter of the outer contour is equal to the minimum and it is constant along the entire length.

Mathematical Modelling the Power Supply-Load System for Electro-Discharge Polishing Process

2010 ◽  
Vol 159 ◽  
pp. 125-128
Author(s):  
A. Parshuta ◽  
V. Chitanov ◽  
Lilyana Kolaklieva ◽  
Roumen Kakanakov
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Power Supply ◽  
Equation System ◽  
Electrolyte Temperature ◽  
Polishing Process ◽  
The Real ◽  
Quadratic Interpolation ◽  
Runge Kutta

The real electro-discharge polishing (EDP) system has been presented by an equivalent electrical scheme and described by a corresponded equation system. The Runge-Kutta-Merson method with automatically changed step is used for the numerical solution the equation system. The current through the resistor equivalent to the steam gas wrapper is defined with an I-V characteristic obtained by the method of multi-interval quadratic interpolation-approximation. A mathematical model of the power supply-load system has been realized in Basic and Matlab® languages. On the base of the developed modelling conditions limiting the current and voltage overload in the EDP system have been determined depending on the maximum polished area and the electrolyte temperature.

The study and numerical solution of some inverse problems in simulation of hydrophysical fields in water areas with ‘liquid’ boundaries

2017 ◽  
Vol 32 (3) ◽  
Author(s):  
Valery I. Agoshkov ◽  
Tatiana O. Sheloput
Keyword(s):  
Data Assimilation ◽  
Inverse Problems ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Variational Data Assimilation ◽  
Open Boundaries ◽  
Solution Algorithms

AbstractSome inverse problems related to mathematical modelling of hydrophysical fields in water areas (seas and oceans) under the presence of ‘liquid’ (open) boundaries are studied and solved numerically in the paper. Numerical solution algorithms for these problems are based on procedures of variational data assimilation.

A Fluid Film Squeezed Between Two Rotating Parallel Plane Surfaces

1985 ◽  
Vol 107 (1) ◽  
pp. 110-115 ◽  
Author(s):  
E. A. Hamza
Keyword(s):  
Numerical Solution ◽  
Nonlinear Equations ◽  
Load Capacity ◽  
Equations Of Motion ◽  
Analytic Solutions ◽  
Parallel Plane ◽  
Fluid Film ◽  
Inertial Forces ◽  
Nonlinear Equations Of Motion ◽  
Radial Outflow

This paper is concerned with the motion of a fluid film squeezed between two rotating parallel plane surfaces. Attention is given to the case of impulsive squeezing and impulsive rotation. Approximate analytic solutions are obtained and a numerical solution to the full nonlinear equations of motion is presented. The results show that the centrifugal inertial forces increase the radial outflow and reduce considerably the load capacity while the noncentrifugal inertial forces increase the torque.

Mathematical modelling of the unified bipropellant propulsion system

1992 ◽  
Vol 26 (11) ◽  
pp. 779-798 ◽  
Author(s):  
V. Shankar ◽  
K. Anantha Ram ◽  
A.E. Muthunayagam
Keyword(s):  
Mathematical Modelling ◽  
Propulsion System

scholarly journals MATHEMATICAL MODELLING OF PROBLEM ON NON-LINEAR FLUTTER OF VISCO-ELASTIC SHELLS

2014 ◽  
pp. 94-98
Author(s):  
Bakhtiyar Khudayarov
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Viscoelastic Property ◽  
Critical Speed ◽  
Galerkin Methods ◽  
Basic Direction ◽  
Viscoelastic Cylindrical Shell ◽  
Current Value

In this work is investigated the flutter of viscoelastic cylindrical shell streamlined by gas current. The basic direction of work is consisted in taking into account of viscoelastic material’s properties at supersonic speeds. The vibration equations relatively of deflection are described by Integra-differential equations in partial derivatives. By Bubnov-Galerkin methods reduced the problems to investigation of system of ordinary Integro-Differential Equations (IDE). The IDE are solved by numerical method, which based on using of quadrature formula. The algorithm of the numerical solution on the basis of the method was described. Critical speeds for cylindrical shell flutter are defined. The influence of the viscoelastic property of the material, geometrical and aerodynamically non-linearity to the current value of critical speed and amplitude-frequency characteristics of the cylindrical shells was analyzed.

MATHEMATICAL MODELLING OF AN AUTOMATIC VOLTAGE REGULATOR

1996 ◽  
Vol 06 (01) ◽  
pp. 65-72 ◽  
Author(s):  
K. GREGORY ◽  
I.R. SMITH
Keyword(s):  
Mathematical Modelling ◽  
Numerical Solution ◽  
Digital Computer ◽  
System Model ◽  
Voltage Regulator ◽  
Automatic Voltage Regulator

This letter describes the mathematical modelling of an automatic voltage regulator (avr) in a form which is compatible with models developed for many other items of electrical plant. The corresponding equations are suitable for numerical solution on a digital computer, and results are presented to illustrate the performance when the avr program is added to an existing generator program to produce an overall system model.

scholarly journals Searching for the cost-optimal road trajectory on the relief of the terrain

2021 ◽  
Vol 17 (1) ◽  
pp. 4-12
Author(s):  
Majid E. Abbasov ◽  
◽  
Artyom S. Sharlay ◽  
◽  
Keyword(s):  
Differential Equation ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Calculus Of Variations ◽  
Optimality Condition ◽  
Optimal Trajectory ◽  
Computational Mathematics ◽  
Cost Functional ◽  
Integro Differential Equation ◽  
The Cost

The article analyzes the problem of obtaining the cost-optimal trajectory for building a road. Using the apparatus of mathematical modelling, the authors derive the cost functional, the argument of which is the function that describes the path trajectory. The resulting functional after some additional transformations is written in a simpler form. For the problem of the calculus of variations obtained in this manner, an optimality condition is derived. This condition takes into account the specifics of the constructed functional. Unlike the classical Euler—Lagrange condition, it leads not to a differential, but to an integro-differential equation. An illustrative example of the numerical solution of the obtained equation using the methods of computational mathematics is provided.

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