Wave Properties of Double One-Dimensional Periodic Sheet Grating

We show that the double one-dimensional periodic sheet gratings always have waveguide properties for acoustic waves. In general, there are two types of pass bands: i.e., the connected sets of frequencies for which there exist harmonic acoustic traveling waves propagating in the direction of periodicity and localized in the neighborhood of the grating. Using numerical-analytical methods, we describe the dispersion relations for these waves, pass bands, and their dependence on the geometric parameters of the problem. The phenomenon is discovered of bifurcation of waveguide frequencies with respect to the parameter of the distance between the gratings that decreases from infinity. Some estimates are obtained for the parameters of frequency splitting or fusion in dependence on the distance between the simple blade gratings forming the double grating. We show that near a double sheet grating there always exist standing waves (in-phase oscillations in the neighboring fundamental cells of the group of translations) localized near the grating. By numerical-analytical methods, the dependences of the standing wave frequencies on the geometric parameters of the grating are determined. The mechanics is described of traveling and standing waves localized in the neighborhood of the double gratings.     

Stability of the cylindrical flame front in an annular combustion chamber

Using small perturbations, within the framework of phenomenological theory of mixture combustion we study stability of the cylindrical front of deflagration combustion in an annular combustion chamber. The flame front is described as a discontinuity of gasdynamic parameters. It is discovered that the flame front is unstable for some types of small perturbations of the mainstream flow of the fuel mixture and the flame front. The mechanics of instability is examined using both numerical and analytical methods. The cases are presented of evolution of the instabilities rotating in the annular channel.     

Aeolian tones of a plate in a channel

The conditions of the onset of aeroacoustic resonance phenomena near a plate in a gas flow in a rectangular channel are studied theoretically and experimentally in a two-dimensional formulation. The eigenfrequency as a function of the plate's chord and its position in the channel, the shape of the eigenfunctions, and the effect of the Mach number of the basic gas flow versus the eigenfrequencies and eigenfunctions and the mechanism of self-excited oscillations are determined. A mathematical model by means of which the dependence of the resonance phenomena on the geometrical parameters of the structure were performed is proposed and substantiated. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 69–77, March–April, 1998.     

Acoustic oscillations near a thin-walled cylindrical obstacle in a channel

The problems of existence of eigenoscillations in infinite cylindrical regions comprising a thin cylindrical obstacle are studied. The existence criteria for eigenoscillations are obtained. For obstacles allowing axial symmetry, the dependence of eigenoscillation frequencies on the obstacle dimensions is studied. The form of eigenoscillations is studied for the first modes. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Science, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 133–142, July–August, 1999.     

Vibrations and vortices in combustion chambers

Computational and experimental studies have been made of large-scale vortex structures as sources of acoustic vibrations. Low-frequency sources of vibration in combustion chambers of solid propellant jet engines have been shown to be due to the hydrodynamic instability of large-scale vortex structures in the main gas flow.M. A. Lavrent'ev Institute of Hydrodynamics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 111–118, April, 1994.     

Investigation of stressed-strained state of three-layer cylindrical shells under the action of localized loads

The problem of the determination of the stressed-strained state of three-layer cylindrical shells with a light filler under the action of localized loads is solved by means of semimomentless hypotheses. By using single trigonometric series, the solution is reduced to integration of ordinary differential equation of the fourth order, similar to the Vlasov's equation. Decisive relationships were obtained for the components of the stressed-strained state of an asymmetric three-layer packet. A solution is given for a series of problems of the action of differently applied radial forces on a long cylindrical shell.Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 300–305, March–April, 1975.     

Discreteness of the eigenfrequencies of scattering by a periodic lattice

Questions of the uniqueness of the solution to problems of scattering by a periodic lattice of obstacles are studied. By means of an analytic Fredholm theorem, it is proved that the set of scattering eigenfrequencies with values of the parameter of the Helmholtz equation for which there is nonuniqueness of the solution is discrete on a certain Riemann surface.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 117, pp. 192–196, 1981.