# cylindrical shell

## Generalized model of nonlinear elastic foundation and longitudinal waves in cylindrical shells

A non-integrable quasi-hyperbolic sixth-order equation is derived that simulates the axisymmetric propagation of longitudinal waves along the generatrix of a cylindrical Kirchhoff – Love shell interacting with a nonlinear elastic medium. A six-parameter generalized model of a nonlinear elastic medium, which is reduced in particular cases to the models of Winkler, Pasternak, and Hetenyi, is introduced into consideration.

## Dynamical Simple Edge Effect in the Cylindrical Shell with the Edge of Arbitrary Form

The purpose of the article is to generalize the results derived in the cases of a circular shell and of a shell with a cut edge. Non-stationary wave process in a cylindrical shell with an arbitrary edge is considered. Half-geodesic frame is introduced on the middle surface of the shell and dynamical simple edge effect is studied. To find the solution Laplace transform is used while the inverse transform is realized via saddle-point method.

## The stability of the constructive-orthotropic heterogeneous cylindrical shell under uneven radial load

On the base haft-momentum Vlasov theory the problem of stability of cylindrical homogeneas shell with variation of thicknees atv radial symmetrical ractial pressure variated onalong axe distance. At one reletion between thickness and pressure values the accurate solution was produced for one values in pressure variation law when stability of shell is sailed.

## The Parametric Oscillations of Heterogeneous Round Cylindrical Shell of Variable Density on Different Boundary Conditions

We consider an isotropic cylindrical shell of varying thickness and density along the generatrix. Let the shell be under pressure, which is symmetric and also varying along the generatrix. We follow the polupostamenty theory by V. Z. Vlasov and consider the problem of the dynamical stability of the shell. We obtain the exact solution corresponding to the certain relation between thickness, pressure and density.

## Mathematical Models of Stability Loss of Nonuniform Cylindrical Shells Because of Nonuniform Radial Loading

The circular cylindrical shell with variable thickness along the axis of elongation is considered. The axisymmetric radial pressure along the axis of shell is suggested. The one of values (for the law of pressure variation) which effects the stability loss of shell is determinated.

## Finite Integral Transformations Method — Generalization of Classic Procedure for Eigenvector Decomposition

The structural algorithm of the finite integral transformation method is presented as a generalization of the classical procedure of eigenvector decomposition. The initial-boundary problems described with a hyperbolic system of linear partial second order differential equations are considered. The general case of non-self adjoint solution by expansion in the vector-functions is possible only by the use of biorthogonal of finite integral transformations.

## Theory of Vibrations of Carbon Nanotubes Like Flexible Micropolar Mesh Cylindrical Shells Taking into Account Shift

A theory of nonlinear dynamics of a flexible single-layer micropolar cylindrical shell of a network structure is constructed. The geometric nonlinearity is taken into account by the model of Theodor von Karman. We consider a nonclassical continuum shell model based on the Cosserat medium with constrained particle rotation (pseudocontinuum). It is assumed that the displacement and rotation fields are not independent. An additional independent material length parameter associated with the symmetric tensor of the rotation gradient is introduced into consideration.