移动荷载作用下弹性半空间Timoshenko梁的临界速度

根据梁的波速和半空间波速的相对关系,将Timoshenko梁-半空问系统分成四种不同情况。在梁与半空间相互作用的等效刚度和Timoshenko梁-半空间的弥散方程的基础上。利用弥散曲线，研究了移动荷载的临界速度。这四种情况分别为：软梁-硬半空间系统。次软梁-硬半空间系统，次硬梁-软半空间系统，硬梁-软半空间系统。研究表明，Timoshenko梁在移动荷载作用下的临界速度取决于梁的波速和半空间波速的相对关系；半空间的Rayleigh波波速始终是一个临界速度，当荷载速度达到Rayleigh波波速时．系统响应会趋于无穷大；对软梁-硬半空间系统，梁的剪切波速和压缩波速也是临界速度；对次软梁-硬半空间系统，梁的剪切波速是临界速度，并且还存在一个最小临界速度；对（次）硬梁-软半空间系统．粱的波速不再是临界速度。但也存在一个最小临界速度。     

Wave generation in an elastic half-space by a normal point load moving uniformly over the free surface

The motion is determined of an elastic, homogeneous and isotropic half-space, excited by a normal point load traveling uniformly over the free surface. Using the differential transform technique [9], exact, closed expressions in terms of algebraic functions are found for the displacements at any point of the half-space. The displacements appear as a superposition of a primary wave, i.e. The wave that would exist if the medium were unbounded, and a secondary wave accounts for the presence of the boundary. The primary wave has previously been given by Eason, Fulton and Sneddon.     

A thin cracked layer bonded to an elastic half-space under an antiplane concentrated load

The antiplane elasticity problem for a thin cracked layer bonded to an elastic half-space under an antiplane concentrated load is considered. The fundamental solution is obtained as a rapidly convergent series in terms of the complex potentials via iterations of Möbius transformation. The singular integral equation with a logarithmic singular kernel is derived to model a crack problem that can be solved numerically in a straightforward manner. The dimensionless mode-III stress intensity factors obtained for various crack inclinations and crack lengths are discussed in detail and provided in graphic form. A strip problem with an arbitrarily oriented crack is also considered.     

Surface-breaking crack in an elastic half-space

A semi-infinite crack terminating at the boundary of an elastic half-space is considered. It is assumed that the crack is subjected to a mode-I load applied in a finite region remote from the crack plane, and the boundary of the half-space and the crack surfaces are free of tractions. The problem is formulated in terms of a hypersingular integral equation with respect to the relative crack-face separation defined over the region occupied by the crack. The behaviour of the solution near the corner point where the crack edge intersects the boundary is analysed and results which show the dependence of the stress singularity exponent on the angle of inclination of the crack edge are presented.     

Tangential-displacement effects in the wedge indentation of an elastic half-space – an integral-equation approach

The idea of considering tangential-displacement effects in a classical elastostatic contact problem is explored in this paper. The problem involves the static frictionless indentation of a linearly elastic half-plane by a rigid wedge, and its present formulation implies that the tangential surface displacements are not negligible and should thus be coupled with the normal surface displacements in imposing the contact zone boundary conditions. L.M. Brock introduced this idea some years ago in treating self-similar elastodynamic contact problems, and his studies indicated that such a formulation strongly influences the contact-stress behavior at half-plane points making contact with geometrical discontinuities of the indentor. The present work again demonstrates, by studying an even more classical problem, that the aforementioned considerations eliminate contact-stress singularities and therefore yield a more natural solution behavior. In particular, the familiar wedge-apex logarithmic stress-singularity encountered within the standard formulation of the problem (i.e. by avoiding the tangential displacement in the contact boundary condition) disappears within the proposed formulation. The contact stress beneath the wedge apex takes now a finite value depending on the wedge inclination angle and the material constants. By utilizing pertinent integral relations for the displacement/stress field in the half-plane, an unusual mixed boundary-value problem results whose solution is obtained through integral equations.     

The interfacial waves launched by an explosive line-source in a submerged elastic half-space

The propagation of waves of small amplitude at the interface between an elastic half-space and a fluid half-space is investigated. The effects of an explosive line-source embedded in the elastic medium are studied, consideration being given to both dilatational and distortional cases, and a similar investigation is made for a compressive line-source in the fluid. The exact solutions for the displacement field are obtained. It is shown that for fluids of relatively low density, the interfacial waves are of two kinds. The relative efficiencies of the three sources for the launching of these waves are shown explicitly.     

Forced flexural vibrations of a Timoshenko column supported by an elastic half-space

The plane stress problem of forced flexural vibrations of an elastic column supported by an elastic half-space and subjected to a sinusoidally varying force at the free end is investigated analytically, by applying the Timoshenko theory to the column. Numerical results obtained from the Timoshenko theory are compared with those from the Bernoulli-Euler theory, and the effects of column slenderness and foundation stiffness on the column response curves and the resonant frequencies of the system are clarified.     

SH-waves at a corrugated interface between a dry sandy half-space and an anisotropic elastic half-space

Summary A problem of reflection and transmission of a plane SH-wave incident at a corrugated interface between a dry sandy half-space and an anisotropic elastic half-space is investigated. Rayleigh's method of approximation is applied to derive the reflection and transmission coefficients for the first and second order approximation of the corrugation. The expressions for reflection and transmission coefficients for the first order approximation of the corrugation are obtained in closed form for a special type of interface, and the energy partition relation is derived. It is found that these coefficients are proportional to the amplitude of corrugation and are functions of elastic properties of the half-spaces and also of the angle of incidence. Numerical examples illustrating the effects of the sandiness, the anisotropy, the corrugation of the interface, the frequency, and the angle of the incidence on the coefficients are presented.     

Surface waves in an elastic half-space with voids

Summary Surface waves of general type propagating in a plane-faced, homogeneous and isotropic linear elastic halfspace containing a distribution of vacuous pores (voids) are studied. Assuming that the face of the halfspace is free of external loads, it is found that the motion is not necessarily two-dimensional and that all physical variables associated with the waves are derivable from a single scalar function. The phase speed equation reveals that, unlike in the classical problem, the waves are dispersive, in general. If the frequency is very small, the motion is qualitatively similar to that in the classical problem, but the wave speed is modified due to the presence of voids.     

Second order elastic effects in an infinite,isotropic compressible medium with an elliptic hole subjected to a uniform tangential force at the boundary

Summary Second order elastic effects with respect to different materials are expected to give results which conform better to the observed results than those obtained in infinitesimal elasticity. The theory was developed byAdkins, Green, andShield [1], and subsequently applied to various simple problems by various authors [2], [3].Bhargava andPande [4], [5] after modifying the technique suggested byAdkins et al. have solved more general problems.In the present paper the complete elastic field has been determined for the case of an isotropic, infinite, compressible medium which has an elliptic hole whose boundary is acted upon by a uniform tangential force. The results differ significantly from those of the infinitesimal case. Some idea with respect to the distribution of the hoop stresses on the boundary can be obtained from the table given in appendix B. Hoop stresses for the infinitesimal case and the case with second order effects for incompressible and compressible materials are given for different ellipses.

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Zusammenfassung Die Betrachtung elastischer Effekte zweiter Ordnung läßt bei verschiedenen Materialien bessere Übereinstimmung mit den beobachteten Resultaten erwarten, als dies in der infinitesimalen Elastizitätstheorie möglich ist. Die Theorie wurde vonAdkins, Green undShield [1] entwickelt und in der Folge von verschiedenen Autoren [2], [3] auf verschiedene einfache Probleme angewendet.Bhargava undPande [4], [5] haben nach Änderung der vonAdkins und seinen Mitarbeitern vorgeschlagenen Methode allgemeinere Probleme gelöst.In der vorliegenden Arbeit wird das elastische Feld für den Fall eines unbegrenzten, isotropen, kompressiblen Mediums mit elliptischen Loch, an dessen Rand eine tangentiale Gleichlast angreift, bestimmt. Die Ergebnisse unterscheiden sich deutlich von jenen der infinitesimalen Theorie. Eine gewisse Vorstellung von der Verteilung der Umfangsspannungen am Lochrand gibt die Tabelle im Anhang B. Die Umfangsspannungen werden für den infinitesimalen Fall und für den Fall der Berücksichtigung der Effekte zweiter Ordnung sowohl für inkompensibles als auch für kompressibles Material unter Annahme verschiedener Ellipsen angegeben.

     

Transient behavior of a few dies on an elastic half-space

Summary An asymptotic approach to dynamic interaction between a few distant dies and an elastic half-space is proposed. The transient motion of the dies under low-frequency vertical load is under consideration. The explicit expression for the fundamental singular solution of Lamb's problem is used to derive the boundary integral equation of contact. Then this equation is asymptotically simplified and solved numerically in combination with equations of motion of the dies.Equations obtained in the asymptotic limit describe both the die-medium dynamic interaction and the interaction between dies through the elastic medium. These equations take into account the energy dissipation phenomenon associated with energy transfer deep into the medium by outgoing elastic waves, of so called geometrical damping.Equations proposed are asymptotically correct within the corresponding range of parameters, as such improving the state-of-the-art.     

A problem of Reissner-Sagoci type for an elastic cylinder embedded in an elastic half-space

The problem considered is that of the torsion of an elastic cylinder which is embedded in an elastic half-space of different rigidity modulus. It is assumed that there is perfect bonding at the common cylindrical surface and also that the torque is applied to the cylinder through a rigid disk bonded to its flat surface. The problem is reduced, by means of the use of integral transforms and the theory of dual integral equations to that of solving a Fredholm integral equation of the second kind. The results obtained by solving this equation are exhibited graphically in Fig. 2.