Mechanics

Околорезонансные режимы в стационарной задаче о подвижной нагрузке в случае трансверсально изотропной упругой полуплоскости

Authors: Prikazchikov D. A.

A moving load problem on a transversely isotropic elastic half-plane is considered under steady-state assumption. The approach relies on the hyperbolic-elliptic asymptotic model for surface wave, allowing drastic simplifications. In particular, the formulation is reduced to a Dirichlet problem for a scaled Laplace equation having a straightforward solution in terms of elementary functions. The obtained approximate solutions are valid for loads travelling at speeds close to surface wave speed.

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

Authors: Mochalin A. A.

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.

Impulsive Action on the Three-layered Circular Cylindrical Shells in Elastic Media

Authors: Leonenko D. V., Starovoitov E. I.

The paper considers oscillations of three-layered cylindrical shells filled by an elastic medium. External loads are impulsive. The Kirchhoff – Love’s hypotheses are assumed for thin isotropic bearing layers. The work of the transverse shear and thickness reduction in the thick filler is taken into account. Variations in displacements in the transverse coordinate are assumed to be linear. The conditions of continuous displacements are used on the contact boundary. The reaction of the inertia-free elastic filler is described in terms of the Winkler’s model.

Nonlinear Deformation Waves in a Geometrically and Physically Nonlinear Viscoelastic Cylindrical Shell Containing Viscous Incompressible Fluid and Surrounded by an Elastic Medium

Authors: Blinkova A. Y., Blinkov Y. A., Ivanov S. V., Mogilevich L. I.

The present study is devoted to analysis of nonlinear deformation of longitudinal waves in a cylindrical shell surrounded by an elastic medium and containing viscous incompressible fluid inside. The physical properties of the shell are defined by the equations of quadratic theory of viscoelasticity, which takes into account the linear elastic volume strain.

Edge Waves in Plates with Fixed Faces and Various Boundary Conditions on the Front Edge

Authors: Ardazishvili R. V., Wilde M. V., Kossovich L. Y.

This paper is concerned with the propagation of surface waves in plates subject to free or mixed boundary conditions on the front edge. Symmetric and antisymmetric waves in plates with fixed faces are considered. Asymptotic analysis is performed, which shows that there is an infinite spectrum of higher order edge waves in plates. Asymptotics of phase velocity are obtained for large values of wave number.