Application of equations with deviating argument to mathematical modeling of pressure measurement systems in gas-liquid media

P. A. Vel'misov ; P. C. Matcenko ; Yu. A. Tamarova

Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 26 (2024) no. 4, pp. 442-457.

Résumé

This article discusses a mathematical model of a system for monitoring pressure changes in the combustion chamber of an aircraft engine, whose components are a pipeline and a sensor. The study of the original problem is reduced to solving a linear second-order differential equation with a deviating argument, which allows one to determine the pressure of the working medium in the combustion chamber at each moment of time basing on the deformation magnitude of the sensor's sensitive element. The aim of the work is to construct solutions to this equation and to use them in applied problems of aerohydroelasticity, namely, in studying the dynamics of elastic elements of pressure sensors interacting with gas or liquid. Some exact solutions are given for the equation with a deviating argument. A numerical method for studying this equation based on the Runge-Kutta method is proposed. Calculations are carried out in the Mathematica system; basing on their results graphs of changes in the elastic element deformation over the time are constructed. A numerical-analytical method for solving the equation with a deviating argument using the step method (the method of successive integration) is also considered. The research conducted in the article provides the opportunity to determine the optimal values for the parameters of mechanical pressure measurement systems at the design stage.

Détail

Keywords: differential-difference equations, Runge-Kutta method, pressure measurement system, aerohydroelasticity, dynamics

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