On one class of initial-boundary-value problems in aerohydroelasticity

In this paper, we consider initial-boundary problems for systems of differential equations, which are mathematical models of the mechanical system “pipeline-pressure sensor” intended for controlling pressure in gas-liquid media. Based on the models proposed, we examine the joint dynamics of the sensitive element of the pressure sensor and the medium in the pipeline. To describe the dynamics of the medium and the dynamics of the sensitive element, we use linear models of fluid and gas mechanics and mechanics of solid deformable bodies. We obtain differential equations with deviating arguments that relate the displacement (deformation) of the sensitive element of the sensor with the pressure law of the medium in the engine. Also, we develop analytical and numerical methods for solving these initial-boundary problems.