On the problem of axial tension of a circular inhomogeneous transversally isotropic shell

We consider the problem of axial tension of a circular inhomogeneous cylindrical shell by longitudinal forces. The determination of the stress-strain state of the shell is performed on the basis of a refined theory. The possibility of losing local stability under axial tension is discussed.     

On bending waves localized along the edge of a plate

We consider bending waves localized along the edge of a plate using nonclassical equations of motion and boundary conditions.Institute of Mechanics, Armenian Academy of Sciences, Erevan. Translated from Prikladnaya Mekhanika, Vol. 30, No. 2, pp. 61–68, February, 1994.     

Localized bending waves in a transversely isotropic plate

The problem of bending waves localized near the free edge of a transversely isotropic plate is investigated using the Ambartsumian higher-order plate theory which takes account of the transverse shears generated by flexural deformation. Unlike the first-order Reissner-Mindlin theory, which also takes account of transverse shears, Ambartsumian's analysis does not demand that plane normal cross-sections remain plane during bending. Within this analysis the existence of localized bending waves in transversely isotropic plates is established, and solutions of the dispersion equation obtained for different values of the elastic parameters.The analysis of frequencies of localized bending waves shows that for thick plates the effect of anisotropy can be considerable. For the particular case of vibrations of a narrow plate, from the long wave approximation a new beam vibration equation of the Timoshenko type is obtained for a transversally isotropic plate.     

Effect of the stiffness and inertia of a rib reinforcement on localized bending waves in semi-infinite strips

This paper reports an analytical and numerical study of localized bending waves in a thin elastic isotropic semi-infinite strip with a rib reinforment. Such waves can be considered as spatially non-uniform bending perturbations localized near free edges, similar to Rayleigh waves decaying exponentially with the distance. From the analysis of localized bending waves in thin elastic structures it may be possible to infer the presence of imperfections, cracks or inclusions, in the structure. In this study, a semi-infinite strip, simply supported on two edges and reinforced on the free one, is considered. A general solution is presented and the conditions under which localized bending waves exist are derived. The mathematical model, accompanied by numerical simulations, reveals that the presence of a reinforcement rib can suppress localized bending waves. This effect is mainly due to the stiffness coming from the rib, rather than from its added inertia terms.     

On Accounting for the Microrotation of Particles of an Elastic Medium According to Cosserat’s Simplified Theory During Electroelastic Wave Propagation in a 6mm Class Piezoelectric Crystal

Acoustical Physics - The article reveals how the micro polarity of a material influences the propagation of a one-dimensional electroelastic wave along different sections of a 6mm class...     

Axisymmetric vibrations of an orthotropic non-uniform cylindrical shell

The axisymmetric vibrations of a circular cylindrical shell of constant thickness, orthotropic along the principal geometrical directions and non-uniform along the generatrices, are considered. It is shown, using a particular problem as an example, that the non-uniform physical-mechanical characteristics of the shell material may lead to qualitatively new results in problems of shell dynamics.