Applied Physics and Mathematics Annotation << Back VIBRATIONS OF MEMBRANE ON THE BORDER OF FLUID FLOW A.V. ZVYAGIN, N.E. SADYGOVA In this paper, we consider the problem of joint vibrations of a membrane and a moving liquid. The membrane is part of the fluid flow boundary. It is believed that the liquid is ideal, incompressible, and the flow is potential. The system of equations of the problem consists of the Laplace equation for the liquid potential, the equation of membrane vibrations and the boundary conditions connecting them. The potential of the liquid is searched for in the form of the real part of the analytical function-an integral of the Cauchy type. Taking into account the boundary conditions of the problem, using the Sohotsky-Plemel formulas, an integro-differential equation of membrane oscillations at the liquid boundary is obtained. The solution of the obtained equation is sought in the form of steady-state oscillations. The method of successive approximations allows us to find the natural oscillation frequencies of the membrane-liquid system with any given accuracy. The developed method allows us to study the dependence of the oscillation frequency on the main parameters of the problem-the density and velocity of the liquid, the elastic characteristics of the membrane. In this problem, the oscillation amplitudes increase over time. This means that the system is unstable in the linear approximation. Keywords: membrane oscillations, natural oscillation frequency, velocity potential, ideal fluid, Cauchy-type integral, Sohotsky-Plemel formula. DOI: 10.25791/pfim.06.2020.1182 Pp. 03-07.