Flutter of a viscoelastic plate in a supersonic gas flow

The flutter of a viscoelastic plate in a supersonic gas flow is studied. A technique and algorithm for numerical solution of nonlinear integro-differential equations with weakly singular kernels are elaborated. The critical flutter speed of viscoelastic plates is determined     

Similarity parameters and simulation of plate vibrations in a supersonic gas flow

A number of rules are proposed to convert the parameters characterizing the plate vibrations in a model experiment to the corresponding parameters in a full-scale process (or in another experiment). The plate material is orthotropic and viscoelastic. The flutter model is based on the piston theory or on the linearized theory of supersonic potential flow.     

Stability of a thin panel with added elements in a supersonic gas flow

Thin elastic panels subjected to compression in the median plane and to supersonic gas flow are considered. An element is attached to the panel by an elastic spring and linear dashpot. The stability of the initial planar state of the panel is studied as a function of the main control parameters—such as the gas velocity and membrane force—and the parameters of the attached element. The evolution of the stability regions in the control-parameter plane is considered. Special attention is paid to compound bifurcation points and stabilization islets. Institute of Machine Science, Russian Academy of Sciences, Moscow, Russia. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 3–10, December, 1999.     

Aeroelastic stability of a cantilevered plate in yawed subsonic flow

The aeroelastic stability of cantilevered plates with their clamped edge oriented both parallel and normal to subsonic flow is a classical fluid–structure interaction problem. When the clamped edge is parallel to the flow the system loses stability in a coupled bending and torsion motion known as wing flutter. When the clamped edge is normal to the flow the instability is exclusively bending and is referred to as flapping flag flutter. This paper explores the stability of plates during the transition between these classic aeroelastic configurations. The aeroelastic model couples a classical beam structural model to a three-dimensional vortex lattice aerodynamic model. The aeroelastic stability is evaluated in the frequency domain and the flutter boundary is presented as the plate is rotated from the flapping flag to the wing configuration. The transition between the flag-like and wing-like instability is often abrupt and the yaw angle of the flow for the transition is dependent on the relative spacing of the first torsion and second bending natural frequencies. This paper also includes ground vibration and aeroelastic experiments carried out in the Duke University Wind Tunnel that confirm the theoretical predictions.     

Stability analysis of a fractional viscoelastic plate strip in supersonic flow under axial loading

The stability of a viscoelastic plate strip, subjected to an axial load with the Kelvin–Voigt fractional order constitutive relationship is studied. Based on the classical plate theory, the structural formulation of the plate is obtained by using the Newton’s second law and the aerodynamic force due to the fluid flow is evaluated by piston theory. The Galerkin method is employed to discretize the equation of motion into a set of ordinary differential equations. To determine the stability margin of plate the obtained set of ordinary differential equations are solved using the Laplace transform method. The effects of variation of the governing parameters such as axial force, retardation time, fractional order and boundary conditions on the stability margin of fractional viscoelastic panel are investigated and finally some conclusions are outlined.     

Stability of compressed continuously inhomogeneous plate

The action of an external reactive medium on the components of operational structures often changes the physicomechanical properties of the material, which markedly affects its carrying capacity. This means that the real properties of the material, including the formation of such inhomogeneities, must be taken more thoroughly into account. In the present work, the stability of an isotropic plate whose elastic characteristics are continuous functions of the Cartesian coordinate is investigated.L'vov University, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 30, No. 2, pp. 84–89, February, 1994.     

Fluctuations in cavities in a supersonic gas flow

Numerical calculations are carried out within the framework of the ideal compressible gas model for the unsteady flows in rectangular cavities exposed to a supersonic external stream. The Euler equations are integrated by means of Godunov's finite-difference method [6]. On the basis of an analysis of the calculation results an expression is proposed for determining the possible frequencies of the flow rate oscillations in the cavity as a function of the free-stream Mach number M and the geometry of the cavity. The results obtained are compared with the experimental data and calculations of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 121–127, March–April, 1990.     

Stability of an inhomogeneous vibrationally-nonequilibrium flow in a waveguide

The stability of an inhomogeneous subsonic vibrationally-nonequilibrium flow is examined in the linear approximation. It is shown that the nonequilibrium flow stability is reduced with increase in the initial flow velocity and the energy pumping zone width. This is attributed to the effect of the feedback due to acoustic disturbances propagating counter to the flow. Calculations are carried out for different pumping models.     

Penetration of a plate into the half-plane of a supersonic flow

We consider the two-dimensional self-similar problem of uniform entry of a profile with plane nose section into a half-plane of a homogeneous stream of an ideal perfect gas. For the flow scheme with a single detached shock wave and a parabolic degeneration line emanating from the corner of the body, a numerical solution is obtained for the problem in the elliptic region using the method of integral relations.The author wishes to thank A. N. Minailos for helpful discussions of this study.     

Investigation of supersonic rarefied gas flow in a cylindrical gap

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 185–187, May–June, 1989.     

Drag of a slender cone in a supersonic rarefied gas flow

On the basis of an analysis of experimental data, obtained by the authors or taken from the literature, on the drag of a slender cone with half-angle =2.5–20° an average correlation curve is proposed for the range of flow regimes extending from continuum to free molecular flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 187–189, January–February, 1987.     

Equilibrium of a flexible permeable shell in a supersonic gas flow

The plane steady-state regime of uniform supersonic ideal-gas flow around a uniaxial absolutely flexible open permeable shell is investigated numerically [1]. The effect of the angle of attack and the degree of nonuniformity of the permeability distribution on the aerodynamic characteristics and the equilibrium shape of the shell is determined for various methods of shell attachment. Approximate localization relations, which take into account the dependence of the distributed load on a concave permeable screen on its degree of permeability and the free-stream parameters, are formulated. An example of the application of these relations to the solution of three-dimensional problems of the equilibrium of permeable shells of the circular dome type in a supersonic flow [2] is given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 152–158, September–October, 1989.     

Stability of a viscoelastic plate in fluid flow

The stability of an infinite viscoelastic plate on an elastic foundation in a viscous incompressible flow is studied. The Navier-Stokes system is linearized for an exponential velocity profile. The problem is reduced by a Fourier-Laplace transform to a system of ordinary differential equations, whose solution is found in the form of convergent series. The roots of the dispersion relation that characterize the stability of the system are found numerically. The effect of the viscosities of the fluid and the plate on the stability of the waves propagating upstream and downstream is studied. The results are compared with available data on the stability of a viscoelastic plate in an ideal fluid flow. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 66–74, July–August, 2006.