In this paper, we propose asymptotic expansions for the velocity potential and obtain asymptotic equations of gas dynamics for irrotational isentropic flows of an ideal gas: an equation of linear theory, a nonlinear equation for supersonic flows, and a nonlinear transonic equation. We construct some exact particular solutions for the asymptotic nonlinear transonic equation, which takes into account transverse perturbations. Based on a linear asymptotic equation, we examine the dynamic stability of an elastic deformable element of a channel at a subsonic flow rate of a gas or liquid. The study of stability is carried out in a statement corresponding to small perturbations of a homogeneous flow and small deformations of an elastic element, and is based on the construction of a positive definite functional. Sufficient stability conditions are obtained.
展开▼
