Vibration analysis of fluid-conveying nanotubes embedded in an elastic medium considering surface effects

An analytical model is developed to study the surface effects on the vibration behavior including the natural frequency and the critical flow velocity of fluid-conveying nanotubes embedded in an elastic medium. The effects of surface elasticity and residual surface stress are accounted through the surface elasticity model and the Young-Laplace equation. A Winkler-type foundation is employed to model the interaction of nanotubes and the surrounding medium. The results show that the surface effects have more prominent influences on the nature frequency with smaller nanotube thickness, larger aspect ratio and larger elastic medium constants. Both surface layers and the elastic medium enhance the stability of nanotubes. This study might be helpful for designing the fluid-conveying nanotube devices in NEMS and MEMS systems.     

Motion of a thin plate in an elastic medium

A solution to the problem of motion of a thin rigid plate in an elastic medium is obtained using the Smirnov-Sobolev method for solving a two-dimensional wave equation.     

Vibration of an elastic tensegrity structure

The dynamic behavior of a simple elastic tensegrity structure is examined, in order to validate observations that the natural damping of the elastic elements in such a structure is poorly mobilized, due to the natural flexibility of the equilibrium position of the structure. It is confirmed, analytically and numerically, that the energy decay of such a system is slower than that of a linearly-damped system.     

Vibration effects of the dynamic interaction between a gas-liquid medium and elastic shells

The paper presents the results of experimental investigations of regimes of the nonlinear deformation of elastic shells filled with a liquid. These regimes are due to the interaction of local clusters of gas bubbles formed in a vibrating liquid with the vibration modes of an elastic shell excited in the circumferential and longitudinal directions. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 7, pp. 67–73, July, 2000.     

Eshelby tensor for a crack in an orthotropic elastic medium

In the present Note, we provide new analytical expressions of the components of Hill tensor $\mathbb{P}$ (or equivalently the Eshelby tensor $\mathbb{S}$) associated to an arbitrarily oriented crack in orthotropic elastic medium. The crack is modelled as an infinite cylinder along a symmetry axis of the matrix, with low aspect ratio. The three dimensional results obtained show explicitly the interaction between the primary (structural) anisotropy and the crack-induced anisotropy. They are validated by comparison with existing results in the case where the crack is in a symmetry plane. To cite this article: C. Gruescu et al., C. R. Mecanique 333 (2005).     

Coupled seismic vibrations of a pipeline in an infinite elastic medium

The exact solution of the problem of coupled seismic vibrations of an underground pipeline and an infinite elasticmediumis given. A method dramatically simplifying the solution of the exterior problem for themedium is proposed on the basis of the established theorem on the separation of the boundary conditions for the wave potentials on the surface of the cylinder. The obtained results permit improving the incorrect consideration of the problem accepted in the literature.     

Thermoelastic bending of a sandwich ring plate on an elastic foundation

The thermomechanical bending of an elastic sandwich ring plate with light core on an elastic foundation is considered. To describe the kinematics of the plate that is asymmetric across the thickness, broken-normal hypotheses are accepted. The foundation reaction is described by Winkler's model. A system of equilibrium equations is derived and solved for displacements. Numerical results for a sandwich ring plate in a temperature field are presented Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 94–103, September 2008.     

Formation of separation zones in an asymmetric motion of a body in an elastic medium

We obtain an analytical solution of the problem on the motion of a body with wedge-shaped nose in an elastic medium for the case in which a medium separation zone may occur near the nose owing to asymmetry. The character of the dependence of the separation region length on the body velocity, the nose opening angle, the motion asymmetry degree, and the friction coefficient is found. It is shown that if the body moves at a velocity greater than the transverse wave velocity, then there is a limit velocity at which the separation region near the nose of the body disappears.     

Torsional buckling of a double-walled carbon nanotube embedded in an elastic medium

The torsional buckling of a double-walled carbon nanotube embedded in an elastic medium is studied in this paper. The effects of surrounding elastic medium and van der Waals forces between the inner and outer nanotubes are taken into account. Using continuum mechanics, an elastic double-shell model is presented for the torsional buckling of a double-walled carbon nanotube. Based on the model, a condition is derived in terms of the buckling modes of the shell and the parameters describing the effect of van der Waals interaction and surrounding elastic medium. A simplified analysis is also carried out estimate the critical torque for torsional buckling of the double-walled carbon nanotube.