Asymptotic study of the normal-mode vibrations of a cylindrical shell

Dnepropetrovsk Civil Engineering Institute, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 29, No. 11, pp. 63–67, November, 1993.     

Forced vibrations of a boxed shell of square cross-section

We construct the solution of the problem on the steady-state vibrations of a finite boxed shell of square cross-section with symmetry conditions at the shell ends. We present the dispersion curves, find the natural frequencies, and study the stress distribution in the shell. We obtain a simple formula for the approximate analysis of the shell in the case of low-frequency vibrations on the basis of the expansion of the solution in two small parameters and on the Lagrange interpolation formula.     

Asymptotic form of the solution to the problem of multicomponent mixture flow through a porous medium with a boundary layer

In problems of two-phase mixture flow through a porous medium in a subterranean stratum a boundary layer phenomenon arises caused by the fact that relative phase motion exists in the system, and so having no analogy with the single-phase case. The physical nature of boundary layer phenomena is explained, and an asymptotic solution is constructed for the self-similar problem with an arbitrary number of components in the system, by using the method of matched asymptotic forms. The conditions are established for the motions of a multicomponent and a binary mixture to be equivalent, and a study is made of the role of convective factors in the formation of averaged working indices for the stratum.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 94–100, July–August, 1985.     

Natural vibrations of a cylindrical shell reinforced with rectangular plates

This paper outlines a technique of determining the natural frequencies and modes of an elastic structure consisting of a cylindrical shell and noncrossing rectangular plates inserted into it. The influence of the position, number, and thickness of the plates on the natural frequencies and modes is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 89–96, March 2006.     

Natural vibrations of a cantilever thin elastic orthotropic cylindrical shell

The natural vibrations of a cantilever thin elastic orthotropic circular cylindrical shell are studied. Dispersion equations for the determination of possible natural frequencies of cantilever closed shells and open shells with Navier hinged boundary conditions at the longitudinal edges are derived from the classical dynamic theory of orthotropic cylindrical shells. It is proved that there are asymptotic relationships between these problems and the problems for a cantilever orthotropic strip plate and for a cantilever rectangular plate and the eigenvalue problem for a semi-infinite closed orthotropic cylindrical shell with free end and for the same but open shell with Navier hinged boundary conditions at the longitudinal edges. A procedure to identify types of vibrations is presented. Orthotropic cylindrical shells with different radii and lengths are used as an example to find approximate values of the dimensionless natural frequency and damping factor for vibration modes __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 68–91, May 2008.