Mathematical modelling of the “Pipeline – pressure sensor” system

Abstract

A mathematical model of a mechanical system for measuring the pressure of the working medium in an engine is proposed. The system includes an axisymmetric pipe with fluid and a fluid pressure sensor. An integro-differential equation of the dynamics of the elastic element of the sensor is obtained, which relates its deformation to the pressure and temperature of the medium at the entrance to the pipeline (for example, at the exit from the engine combustion chamber). A numerical-analytical method for solving this equation is proposed and examples of numerical calculations of the element dynamics are given.

Non-Linear Oscillations of the Channel Wall Filled with a Viscous Liquid Induced by the Vibrating Foundation

“…Implementing the solution (10) taking into account the boundary conditions (11), we found an expression for the liquid pressure in the channel…”

“…Traditionally, when calculating the vibrations of the mechanical systems elements, they are limited to the linear theory for elastic elements [1,2]. For example, in this approach, the hydroelastic vibrations of plates and beams interacting with a liquid [3][4][5][6][7][8][9][10][11], as well as elastically fixed channel walls [12][13][14][15], are studied. In particular, in paper [3], a model was developed for studying the natural vibrations of a clamped circular plate, on one side of which there is an unlimited volume of an ideal liquid.…”

“…The dynamics interaction simulation for a circular plate with an ideal liquid as applied to a pressure sensor installed at the pipe end was performed in [10]. Reference [11] is devoted to the study of forced vibrations of a three-layer beam interacting with a layer of viscous liquid. In paper [12], the vibrations of a die supported by a linear spring and located at the channel bottom, during its interaction with an ideal liquid with a free surface, were studied.…”