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The natural modes and frequencies of an elastic ring fixed at a point are determined by numerically solving a boundary-value problem for a differential operator of the sixth order. The ring models a large circular antenna that slowly expands under zero gravity. The in-plane flexural vibrations of the ring are analyzed. Numerical results are presented

A conjugate electroelastic field in a piezoceramic cylinder with a parabolic crack under static loading is investigated. Uniformly tensile stresses and an electric potential are applied to the end faces of the cylinder. The following two types of electric conditions are considered at the crack boundary: the electric potential is continuous across the crack and the normal component of the electric-displacement vector on the crack surface is equal to zero. For each of these cases, expressions for some quantities characterizing the disturbed field in the crack plane and formulas to calculate the stress intensity factors are presented.

The solution of the problem of a rigid punch with a parabolic cross-section and flat base that is forced into an elastic piezoelectric ceramic half-space is derived in explicit form. The punch is somewhat displaced, being parallel to the isotropy plane that coincides with the boundary surface of the half-space. The symmetry axis coincides with the direction of the force lines of the field with the previous polarization. Formulas are derived to determine the stresses on the surface of the half-space under the punch and the components of the conjugate electric field for certain boundary conditions on the contact area.

The stress-strain state of an elastic piezoceramic halfspace under the action of a rigid elliptical die with a convex base is considered, in the case where the symmetry axis of the body is in the direction of the preliminary-polarization field. The contact area is within the isotropy plane. Attention is confined to the case of die translation. Expressions are obtained for the semimajor axis and eccentricity of the contact area and the translational points of the die base under different electric boundary conditions.

UDC 539.3 An exact solution is constructed for the problem of the stressed state of an elastic tramversally isotropic half-space affected by a nonplane elliptical die when the die is subjected to compressive forces and bending moments. The problem is solved in the absence of frictional forces. Expressions are given for determining the compressive load, the transition of points in the die bottom, projections of the rotation vector, the semimajor axis, and the eccentricity of the contact area. A large number of studies of contact problems for elliptical dies were maae by Lur'e [2], Galin [1, 4], and Mossakovskii [3]. Those studies, however, dealt mainly with the stresses in an isotropic solid. Such problems for a transversally isotropic half-space were studied little. In this work we construct an exact solution for problems of the stressed state of an elastic transversally isotropic halfspace under the action of a nonplane elliptical die. The bottom of the die is assumed to be absolutely smooth. The die is considered as an absolutely hard solid subjected to compressive forces and bending moments. The surface of the die bottom in the region of contact with the bourdary of the half-space is approximated by an elliptical paraboioid. The equation of the surface is represented by a power series expansion. The plane bounding the half-space is taken to be the xy plane. Suppose that the z axis is directed on the outside of the solid normal to the plane of isotropy and the x and y axes are oriented arbitrarily in that plane. For a nonplane elliptical die the contact area S is an elliptical region in the plane Z = 0

In this paper we examine an unbounded transversally isotropic medium containing a parabolic crack in the plane of isotropy. Let varying shear forces of the type be applied to the surface of the crack. In solving the problem, we can use the expression of the general solution of the equilibrium equations in displacements in terms of the potential functions.

We are studying the stress-strain state of an infinite, transversely isotropic medium containing a parabolic crack in the plane of isotropy. We assume that the surface crack is loaded by linearly changing pressure, and we will solve the problem with the use of an expression for the general solution of the equilibrium equations in displacements that employ potential functions.