ГИДРОУПРУГАЯ УСТОЙЧИВОСТЬ КОАКСИАЛЬНЫХ ЦИЛИНДРИЧЕСКИХ ОБОЛОЧЕК, ВЫПОЛНЕННЫХ ИЗ ПЬЕЗОЭЛЕКТРИЧЕСКОГО МАТЕРИАЛА

Abstract

The paper numerically investigates the dynamic behavior of electroelastic coaxial shells containing a compressible flowing fluid in the annular gap between them. The solution of the problem is carried out using a semi-analytical version of the finite element method. The shells are made of a material with piezoelectric properties, which is polarized in the radial direction. The behavior of the system is studied in the framework of the classical theory based on the Kirchhoff - Love hypotheses and equations of linear electroelasticity. The distribution of the electric potential through the thickness is assumed to be linear. The motion of a compressible non-viscous fluid is described by the wave equation, which, together with the impenetrability conditions and the corresponding boundary conditions, is transformed using the Bubnov - Galerkin method. The pressure exerted by the fluid on the deformable bodies is calculated from the linearized Bernoulli equation. The mathematical formulation of the problem of the thin-walled structure dynamics is based on the variational principle of virtual displacements. The stability estimate is obtained from the calculation and analysis of complex eigenvalues of a coupled system of equations, developed for unknown quantities of elastic and liquid media. The electrical variables are eliminated at the element level and produce an effect on the dynamic characteristics of the structure in the form of added stiffness. The reliability of the obtained results is evaluated by comparing them with the known data for isotropic shells. The estimation of the stability boundaries are carried out for systems with different geometrical dimensions, variants of kinematic boundary conditions (shells with simply supported edges, clamped at both edges and cantilevered) and different annular gap sizes. It has been shown that the critical velocities of the fluid flow and the form of the loss of stability depend on the electric boundary conditions set on the electrode surfaces of the inner and outer shells.