scholarly journals The stability of three-layer nonhomogeneous rectangular plates in anisotropic resisting medium

2015 ◽  
Vol 1 (7(73)) ◽  
pp. 4
Author(s):  
Биллура Элман кызы Исалы

The analysis of part I is extended to deal with the case of free-edged rectangular plates having an initial curvature about an axis parallel to one pair of opposite edges and loaded by distributed bending moments applied to the straight edges and compressive forces applied to the curved edges. In particular, the stability and post-buckling behaviour of such plates subjected to the compressive forces alone is studied. The axially symmetrical buckling of thin-walled circular tubes in axial compression is also considered. Experimental plates are found to buckle at loads rather lower than those predicted.


1831 ◽  
Vol 121 ◽  
pp. 17-66

In last April I had the honour of presenting to the Society a paper containing expressions for the variations of the elliptic constants in the theory of the motions of the planets. The stability of the solar system is established by means of these expressions, if the planets move in a space absolutely devoid of any resistance*, for it results from their form that however far the ap­proximation be carried, the eccentricity, the major axis, and the tangent of the inclination of the orbit to a fixed plane, contain only periodic inequalities, each of the three other constants, namely, the longitude of the node, the longitude of the perihelion, and the longitude of the epoch, contains a term which varies with the time, and hence the line of apsides and the line of nodes revolve continually in space. The stability of the system may therefore be inferred, which would not be the case if the eccentricity, the major axis, or the tangent of the inclination of the orbit to a fixed plane contained a term varying with the time, however slowly. The problem of the precession of the equinoxes admits of a similar solution; of the six constants which determine the position of the revolving body, and the axis of instantaneous rotation at any moment, three have only periodic inequalities, while each of the other three has a term which varies with the time. From the manner in which these constants enter into the results, the equilibrium of the system may be inferred to be stable, as in the former case. Of the constants in the latter problem, the mean angular velocity of rotation may be considered analogous to the mean motion of a planet, or its major axis ; the geographical longitude, and the cosine of the geographical latitude of the pole of the axis of instantaneous rotation, to the longitude of the perihelion and the eccentricity; the longitude of the first point of Aries and the obliquity of the ecliptic, to the longitude of the node and the inclination of the orbit to a fixed plane; and the longitude of a given line in the body revolving, passing through its centre of gravity, to the longitude of the epoch. By the stability of the system I mean that the pole of the axis of rotation has always nearly the same geographical latitude, and that the angular velocity of rotation, and the obliquity of the ecliptic vary within small limits, and periodically. These questions are considered in the paper I now have the honour of submitting to the Society. It remains to investigate the effect which is produced by the action of a resisting medium; in this case the latitude of the pole of the axis of rotation, the obliquity of the ecliptic, and the angular velocity of rotation might vary considerably, although slowly, and the climates undergo a con­siderable change.


Author(s):  
Yurii Kononov ◽  
Yaroslav Sviatenko

The conditions for asymptotic stability of uniform rotations in a resisting medium of two heavy Lagrange gyroscopes connected by an elastic spherical hinge are obtained in the form of a system of three inequalities. The bottom gyroscope has a fixed point. The rotation of the gyroscopes is maintained by constant moments in the inertial coordinate system. The influence of the elasticity of the hinge on the stability conditions is estimated. It is shown that for a sufficiently high rigidity of the hinge, the asymptotic stability conditions are determined by only one inequality, which coincides with the inequality obtained for the case of a cylindrical hinge. When the angular velocities of the gyroscopes' own rotations coincide, this inequality coincides with the well--known condition for one gyroscope. Cases of degeneration of an elastic spherical hinge into a spherical inelastic, cylindrical and universal elastic hinge (Hooke's hinge) are considered. For the Hooke hinge, it is shown that there is no asymptotic stability at a sufficiently high angular velocity of gyroscopes rotation.


1989 ◽  
Vol 56 (2) ◽  
pp. 375-381 ◽  
Author(s):  
Andrzej Tylikowski

The dynamic stability problem is solved for rectangular plates that are laminated antisymmetrically about their middle plane and compressed by time-dependent deterministic or stochastic membrane forces. Moderately large deflection equations taking into account a coupling of in-plane and transverse motions are used. The asymptotic stability and almost-sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunov’s direct method. A relation between the stability of nonlinear equations and linearized ones is analyzed. An influence on the number of orthotropic layers, material properties for different classes of parametric excitation on stability domains is shown.


2018 ◽  
Vol 931 ◽  
pp. 100-106
Author(s):  
Alexej I. Pritykin ◽  
Ilja E. Kirillov

In thin-walled structures, to which girders with slender web (GSW) are related, one of the weak links is their local stability. Girders with slender web are still buckling in elastic stage of loading under shear deformation. Increasing of their stability is possible to reach with installation of Analysis carried out in the work show that demands to appointment of optimum sizes of transverse stiffening ribs in Russian structural standard differ essentially from those of the foreign standards. The goal of the work is to find out the demands by which the standards are more well grounded and bring in suggestion on improving the Russian structural rules. The determined goal has been reached with GSW panels calculations FEM using the program complex ANSYS. The critical loads were determined in the shear of rectangular plates supported by transverse stiffening ribs of different sizes. The results of the FEM were compared with the calculations performed on the empirical dependencies of different standards. The result of the research was to make recommendations on the rational dimensions of the stiffening ribs, determined from the ratio of flexural stiffnesses of the reinforced plate and rib. It is noted that the presence of stiffening ribs can increase the stability of the beam wall by 15-30%. The results of the research can be used in design organisations.


1937 ◽  
Vol 4 (4) ◽  
pp. A177-A178
Author(s):  
S. Voinovsky-Krieger

Abstract The energy criterion of stability, investigated by G. N. Bryan and S. Timoshenko, has been applied with great success to numerous problems of buckling of thin elastic plates submitted to compressive or shearing forces in their own plane. The cases discussed up to the present have concerned almost exclusively rectangular plates, this form of the plate being practically the most important. The application of the energy method to plates bounded curvilinearly will now be illustrated by the case of the elliptic plate.


1984 ◽  
Vol 20 (2) ◽  
pp. 121-134 ◽  
Author(s):  
T. Chelladurai ◽  
B.P. Shastry ◽  
G.V. Rao

2012 ◽  
Vol 594-597 ◽  
pp. 2651-2654
Author(s):  
Yan Wang ◽  
Zhong Min Wang

The element-free Galerkin method is proposed to solve the stability of the moving rectangular plates. Utilizing the extended Hamilton’s principle for the elastic dynamics system, the variational expression of the moving thin plate are established. The dimensionless equations of motion of the moving thin plate are obtained by the element-free Galerkin method, and the complex eigenvalue equation is presented. Via numerical calculation, the variation relationship between the first three complex frequencies of the system and the moving speed is obtained. The effects of dimensionless moving speed on the stability and critical load of the thin plates are analyzed.


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