Mechanics

2007, No. 2

A.G. Bagdoev, A.V. Vardanyan, S.V. Vardanyan

ON DETERMINATION OF LINEAR FREQUENCIES OF BENDING VIBRATIONS OF PIEZOELECTRIC SHELLS AND PLATES BY EXACT AND AVERAGED TREATMENT

In this paper the derivation and numerical solution of disspersion relations for frequencies of free bending vibrations for piezoelectric cylindrical thin shells with longitudinal polarization and plates with normal polarization is made. Solution is done by exact space treatment and by Kirchhoff hypothesis. Comparision of obtained tables shows that frequencies by exact and based on Kirchhoff hypothesis are quite different.

V.V. Zuev, A.G. Shmeleva

AXISYMMETRIC SHOCK LOADING ELASTIC-PLASTIC MEDIUM WITH WORK-SOFTENING AND VARIABLE ELASTIC PROPERTIES

In the paper a mathematical model of wave motion in elasticplastic bodies complicated properties (work-softening, variable elastic modules, presence of irreversible volume strains) is considered. Supporting by the constitutive proposed by one of the authors [1], the closed system of the allowing equations presenting dynamic processes in case of generalized model Mises—Schleikher due to work-softening and variable elastic properties is obtained. In view of specified above features of deformation behaviour of materials the two-dimensional axisymmetric problem on a shock loading of a plate is numerically resolved. It is shown, that the proposed model allows to reveal peculiarities of mechanical behaviour of elastic-plastic bodies at dynamic processes.

S.V. Mathveev

ELASTIC-PLASTIC STATE OF SPACE WEAKENED BY A HORIZONTAL CYLINDRICAL CAVITY

In the paper the effect of gravity on elastic-plastic state of space weakened by a longitudinal cylindrical cavity (case of plane deformation) is considered. It is proposed, that initial viscoelastic intense and deformed state caused by all-round pressure of external environment, is axial-symmetric. The effect of gravity on elastic-plastic state of space is carried out at the first approximation.

S.V. Pavlikov

STABILITY TO PART OF THE VARIABLES MECANICAL CONTROL SYSTEM WITH DELAYED FEEDBACK

In the paper the asymptotic stability of the trivial solution of a functional- differential equation of delay type relative to part of the variables is studied. The Lyapunov functional whose derivative is sign-definite is used. There is no need the assumption of the solutions to be bounded as functions of the non-controllable coordinates. The obtained theorem is used to solve the problem of stabilizing mechanical control system with delayed feedback.