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We solve a nonlinear orbital stability problem for a periodic motion of a homogeneous paraboloid of revolution over an immovable horizontal plane in a homogeneous gravity field. The plane is assumed to be absolutely smooth, and the body–plane collisions are assumed to be absolutely elastic. In the unperturbed motion, the symmetry axis of the body is vertical, and the body itself is in translational motion with periodic collisions with the plane.The Poincare´ section surfacemethod is used to reduce the problemto studying the stability of a fixed point of an area-preserving mapping of the plane into itself. The stability and instability conditions are obtained for all admissible values of the problem parameters.  相似文献   

3.
The translatory accelerating motion of a sphere due to an arbitrarily applied force in an unlimited Maxwell fluid is considered. The exact solutions for the velocity of the sphere for three particular types of accelerating motion are presented. The first is for a falling sphere; the second is for the decelerating motion of a sphere after the force which maintains the sphere with a constant velocity is removed; the third is for the motion of the sphere subjected to an impulsive force. The exact solutions are expressed in terms of real, regular, definite integrals which can be evaluated by numerical technique. Also presented are the asymptotic solutions for the velocity of the sphere in all three cases which are valid for small values of time.  相似文献   

4.
Kuang-Chong Wu   《Wave Motion》2004,40(4):359-372
The problem of a semi-infinite crack subjected to an incident stress wave in a general anisotropic elastic solid is considered. The plane wave impinges the crack at a general oblique angle and is of any of the three types propagating in that direction. A related problem of a semi-infinite crack loaded by a pair of concentrated forces moving along the crack surfaces is also considered. In contrast to the conventional approach by Laplace transforms, a Stroh-like formalism is employed to construct the solution directly in the time domain. The solution is shown to depend on a Wiener–Hopf factorization of a symmetric matrix. Closed-form solution of the stress intensity factors is derived. A remarkably simple expression for the energy release rate is obtained for normal incidence.  相似文献   

5.
An inplane problem for a crack moving with constant subsonic speed along the interface of two piezoelectric materials is considered. A mechanically frictionless and electrically permeable contact zone is assumed at the right crack tip whilst for the open part of the crack both electrically permeable and electrically insulated conditions are considered. In the first case a moving concentrated loading is prescribed at the crack faces and in the second case an additional electrical charge at the crack faces is prescribed as well. The main attention is devoted to electrically permeable crack faces. Introducing a moving coordinate system at the leading crack tip the corresponding inhomogeneous combined Dirichlet–Riemann problem is formulated and solved exactly for this case. All electromechanical characteristics at the interface are presented in a closed form for arbitrary contact zone lengths, and further, the transcendental equation for the determination of the real contact zone length is derived. As a particular case of the obtained solution a semi-infinite crack with a contact zone is considered. The numerical analysis performed for a certain piezoelectric bimaterial showed an essential increase of the contact zone length and the associated stress intensity factor especially for the near-critical speed region. Similar investigations have been performed for an electrically insulated crack and the same behavior of the above mentioned parameters is observed.  相似文献   

6.
This paper presents an analytical Buckley-Leverett-type solution for one-dimensibnal immiscible displacement of a Newtonian fluid by a non-Newtonian fluid in porous media. The non-Newtonian fluid viscosity is assumed to be a function of the flow potential gradient and the non-Newtonian phase saturation. To apply this method to field problems a practical procedure has been developed which is based on the analytical solution and is similar to the graphic technique of Welge. Our solution can be regarded as an extension of the Buckley-Leverett method to Non-Newtonian fluids. The analytical result reveals how the saturation profile and the displacement efficiency are controlled not only by the relative permeabilities, as in the Buckley-Leverett solution, but also by the inherent complexities of the non-Newtonian fluid. Two examples of the application of the solution are given. One application is the verification of a numerical model, which has been developed for simulation of flow of immiscible non-Newtonian and Newtonian fluids in porous media. Excellent agreement between the numerical and analytical results has been obtained using a power-law non-Newtonian fluid. Another application is to examine the effects of non-Newtonian behavior on immiscible displacement of a Newtonian fluid by a power-law non-Newtonian fluid.  相似文献   

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On the basis of the method of matched asymptotic expansions, the problem of the outflow of a nonswirling axisymmetric laminar jet from a hole in a plane is solved for large Reynolds numbers. Since directly matching the leading terms of the asymptotic expansions for the axial boundary layer and the main flow region is impossible, the problem is solved by introducing an intermediate region. In the axial region the solution is the Schlichting solution [1] for an axisymmetric jet in the boundary-layer approximation, in the intermediate region the solution is found analytically, and in the main flow region the problem is reduced to that of viscous flow induced by a sink line in the presence of a transverse wall [2].  相似文献   

9.
Summary  An exact, three-dimensional analysis is developed for a penny-shaped crack in an infinite transversely isotropic piezoelectric medium. The crack is assumed to be parallel to the plane of isotropy, with its faces subjected to a couple of concentrated normal forces and a couple of point electric charges that are antisymmetric with respect to the crack plane. The fundamental solution of a concentrated force and a point charge acting on the surface of a piezoelectric half-space is employed to derive the integral equations for the general boundary value problem. For the above antisymmetric crack problem, complete expressions for the elastoelectric field are obtained. A numerical calculation is finally performed to show the piezoelectric effect in piezoelectric materials. It is noted here that the present analysis is an extension of Fabrikant's theory for elasticity. Received 30 August 1999; accepted for publication 1 March 2000  相似文献   

10.
The problem of the interaction of a crack and a dislocation in a medium with a nonlinear stress-strain law is considered for the case of a semi-infinite crack in a displacement loaded strip under longitudinal shear deformation. A power law stress-strain relation is considered and the dislocation is assumed positioned so that the net effect of its interaction with the crack is to produce a zero stress intensity factor when combined with the effect of the applied displacements. Thus the Atkinson-Kay superdislocation model of a relaxed crack tip is extended to the situation where the material satisfies a power-law stress-strain relationship.  相似文献   

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