Disorder driven roughening transitions of elastic manifolds and periodic elastic media

The simultaneous effect of both disorder and crystal-lattice pinning on the equilibrium behavior of oriented elastic objects is studied using scaling arguments and a functional renormalization group technique. Our analysis applies to elastic manifolds, e.g., interfaces, as well as to periodic elastic media, e.g., charge-density waves or flux-line lattices. The competition between both pinning mechanisms leads to a continuous, disorder driven roughening transition between a flat state where the mean relative displacement saturates on large scales and a rough state with diverging relative displacement. The transition can be approached by changing the impurity concentration or, indirectly, by tuning the temperature since the pinning strengths of the random and crystal potential have in general a different temperature dependence. For D dimensional elastic manifolds interacting with either random-field or random-bond disorder a transition exists for 2<D<4, and the critical exponents are obtained to lowest order in . At the transition, the manifolds show a superuniversal logarithmic roughness. Dipolar interactions render lattice effects relevant also in the physical case of D=2. For periodic elastic media, a roughening transition exists only if the ratio p of the periodicities of the medium and the crystal lattice exceeds the critical value . For p<p _c the medium is always flat. Critical exponents are calculated in a double expansion in and and fulfill the scaling relations of random field models. Received 28 August 1998     

On the vibration of an elastic plate on an elastic foundation

The forced vibration of an elastic plate under a time harmonic point force is studied. The plate is infinite in extent and supported by an elastic foundation. This study is made on the basis of the improved (Timoshenko) plate theory. The mathematical problem is to seek a fundamental solution (the Green's function) of the time-reduced plate equation of the improved plate theory. Such a fundamental solution is constructed by the distributional Fourier transform method. From the explicit expressions of the fundamental solution, the behavior of the fundamental singularity as a function of the vibration frequency and the foundation stiffness is examined. Conditions under which plate resonance occurs are also determined.     

Role of elastic stress in statistical and scaling properties of elastic turbulence

The role of elastic stress in statistical and scaling properties of elastic turbulence in a polymer solution flow between two disks is discussed. The analogy with a small-scale magnetodynamics and a passive scalar turbulent advection in the Batchelor regime is used to explain the experimentally observed statistical properties, the flow structure, and the scaling of elastic turbulence. The emergence of a new length scale, namely, the boundary layer thickness, is observed and studied.     

Transition radiation of elastic waves at the interface of two elastic half-planes

Radiation of elastic waves is studied that is emitted by a point load that crosses the interface of two elastic half-planes. It is assumed that the load has a constant magnitude, moves along a straight line normal to the interface, and has a constant speed that is smaller than the minimum shear wave speed in the half-planes. In this case the mechanism of excitation of elastic waves is conventionally referred to as transition radiation. The adopted model allows to obtain an analytical expression for the elastic field excited by the load in the frequency-wavenumber domain. Using this expression, the energy of transition radiation is derived in a closed form. It is shown that transition radiation of the body waves occurs at any non-zero velocity of the load. Additionally, transition radiation of interface waves may occur provided that parameters of the half-planes allow existence of Stoneley waves. A parametric analysis of the directivity diagram of radiated body waves is accomplished focusing on dependence of the diagram on the load speed, load direction, and parameters of the half-planes. Using parameters that allow radiation of interface waves, the energy of this radiation is compared to that of the body waves. It is shown that the energy of the interface waves is greater unless the load velocity is close to the lowest body wave velocity.     

Formulation of elastic multi-structures

Based on the creative and groundbreaking work done by Feng and Shi, some further work has been carried out comprehensively by the first author on the formulation of elastic multi-structures. The main contribution of this paper can be summarized as follows: The work of Feng and Shi has been extended to an elastic multi-structures with nonlinear structural element: shell in both linear and nonlinear case. Three general combinations of multi-structures have been formulated, that is, Case 1: linear elements of 3-D body, 1-D bar/beam, 2-D plates and 2-D shell; Case 2: nonlinear elements of 3-D body, 1-D bar/beam, 2-D plates and 2-D shell; and Case 3: the linear-nonlinear mix problem of 3-D body (nonlinear), 1-D bar/beam (linear), 2-D plates (linear) and 2-D shell (linear). From the investigation, it has proved that the higher dimensional element will have a strong influence on the lower one with the inner linkage boundaries, and also proved that solution uniqueness of elastic multi-structures is different from a single 3-D body.     

Theory of elastic waves

Wave processes in real crystals are described by covariant first-order partial differential equations. Naimi and Khzardzhyan [1] have recently shown that the second-order equations $$\Delta u^{(n)} - c_n^{ - 2} \partial ^2 u^{(n)} /\partial t^2 = 0$$ ,     

Coiling of elastic ropes

A rope falling onto a solid surface typically forms a series of regular coils. Here, we study this phenomenon using laboratory experiments (with cotton threads and softened spaghetti) and an asymptotic "slender-rope" numerical model. The excellent agreement between the two with no adjustable parameters allows us to determine a complete phase diagram for elastic coiling comprising three basic regimes involving different force balances (elastic, gravitational, and inertial) together with resonant "whirling string" and "whirling shaft" eigenmodes in the inertial regime.     

Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface

In the current paper a general method is presented for the rigorous solution for the scattering of elastic waves by a cluster of elastic circular cylinders of infinite length. The interface separating the cylinder from the surrounding media is considered to be homogeneous imperfect. Specifically, the tractions are continuous but the displacements are discontinuous and proportional in terms of interface stiffness parameters to their respective traction components. Using the exact theory of multipole expansion, analytic solutions for the scattered and internal fields excited by an incident plane P-wave, an incident cylindrical P-wave and an incident plane SV-wave are derived.

Numerical results for directivity patterns and scattering cross-sections are presented for a finite hexagonal array of elastic circular inclusions with imperfect interface. The results show that the sequence of maxima and minima in the curves of scattered cross-sections becomes more undistinguishable as the interface becomes more imperfect. Also, the results reveal that large low-frequency peaks of the scattered cross-sections, which correspond to resonance scattering, can be observed for both the low-velocity and high-velocity elastic cylinders with extremely imperfect interface while the small high-frequency peaks of the scattered cross-sections can appear for low-velocity elastic cylinders with relatively perfect interface. Furthermore, the results clearly show that the interaction effects between cylinders cannot be ignored for an incident plane SV-wave as compared to an incident plane P-wave. More importantly is the fact that the reciprocity relations, which hold for elastic wave scattering by a single cylinder, no longer apply for elastic wave scattering by multiple cylinders.     

Scattering of time-harmonic elastic waves by an elastic inclusion with quadratic nonlinearity

This paper considers the scattering of a plane, time-harmonic wave by an inclusion with heterogeneous nonlinear elastic properties embedded in an otherwise homogeneous linear elastic solid. When the inclusion and the surrounding matrix are both isotropic, the scattered second harmonic fields are obtained in terms of the Green's function of the surrounding medium. It is found that the second harmonic fields depend on two independent acoustic nonlinearity parameters related to the third order elastic constants. Solutions are also obtained when these two acoustic nonlinearity parameters are given as spatially random functions. An inverse procedure is developed to obtain the statistics of these two random functions from the measured forward and backscattered second harmonic fields.     

Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface

In the current paper a general method is presented for the rigorous solution for the scattering of elastic waves by a cluster of elastic circular cylinders of infinite length. The interface separating the cylinder from the surrounding media is considered to be homogeneous imperfect. Specifically, the tractions are continuous but the displacements are discontinuous and proportional in terms of interface stiffness parameters to their respective traction components. Using the exact theory of multipole expansion, analytic solutions for the scattered and internal fields excited by an incident plane P-wave, an incident cylindrical P-wave and an incident plane SV-wave are derived.

Numerical results for directivity patterns and scattering cross-sections are presented for a finite hexagonal array of elastic circular inclusions with imperfect interface. The results show that the sequence of maxima and minima in the curves of scattered cross-sections becomes more undistinguishable as the interface becomes more imperfect. Also, the results reveal that large low-frequency peaks of the scattered cross-sections, which correspond to resonance scattering, can be observed for both the low-velocity and high-velocity elastic cylinders with extremely imperfect interface while the small high-frequency peaks of the scattered cross-sections can appear for low-velocity elastic cylinders with relatively perfect interface. Furthermore, the results clearly show that the interaction effects between cylinders cannot be ignored for an incident plane SV-wave as compared to an incident plane P-wave. More importantly is the fact that the reciprocity relations, which hold for elastic wave scattering by a single cylinder, no longer apply for elastic wave scattering by multiple cylinders.     

The elastic dielectric

Macroscopic field equations, boundary conditions and equations of state are derived for the non-linear, macroscopic elastic and dielectric response of an insulator. A centrosymmetric polynomial representation of order four is introduced for the energy density; the equations of state for the electric field and stress tensor are then deduced as polynomials of degree three in the displacement gradients and electric displacement field. The results are applied to the special case of m3m material symmetry.

A finite, point-charge model of a centrosymmetric ionic crystal is introduced and used to determine 0°K microscopic expressions for the electric field and stress tensor equation of state coefficients introduced in the macroscopic analysis. The results are used to calculate the full set of second and third-order non-linear coefficients for NaI, based on a Born-Mayer potential and the 4·2°K elastic stiffness data of Claytor and Marshall.     

Dynamic analysis of an elastic plate on a thin,elastic foundation

An improved theory for the motion of an elastic foundation is developed. Included is the interaction of two or more plates resting on a common foundation. A simplified model is deduced which appears useful for some applications.     

Angular distributions of elastic and quasi elastic heavy-ion collisions. pattern analysis

From classical in-beam spectroscopy on the¹⁰⁶Cd+¹²C reaction, unambiguousγ-ray assignments have been done for¹¹⁶Xe,¹¹⁶I and¹¹⁶Te nuclei. The ground band levels observed in¹¹⁶Xe have been compared to those of heavier even-even xenon isotopes and to the IBA theoretical predictions. In addition, using the newγ-ray assignments, evaporation cross-sections of the¹¹⁸Xe compound nucleus have been estimated and compared to the evaporation model calculations.     

Theories of elastic properties and elastic waves of equal phase velocities in crystals

A survey is made of pairs of heteronormal planar elastic waves, which can propagate in an unlimited crystal medium and have equal theoretical values of the phase velocity, using Voigt elastic moduli. Such pairs are chosen for which it is possible that the theoretical equality of velocities will be disturbed when using another theory of the elastic properties of crystals with generally different tensors of material constants (for example Kuvshinskij J. V., Aero E. L.: Fiz. tv. tela5 (1963), 2591). In such a case, a comparison of the measured velocities of a suitable pair of waves can help to decide between the two theories. Pairs of waves are found for 12 non-piezoelectric crystal classes. Among such pairs it is easy to find pairs of waves of the same properties for piezoelectric crystal classes.     

Pure elastic resonance scattering for submerged elastic objects with separable geometries

I.IntroductionTheResonanceScatteringTheory(RST)wasdevelopedasabasicmethodtoanalyzesoundscatteringfromelasticobjectsimmersedinwater.Itwasusedtocylindricalandspher-icalgeometries,includingsolidandshellobjects.TheRSTinvestigatesmainlytheresonancespectrumofscatteredwavefromanelasticobjectexcitedbytheincidentwave.Theresonallcespectrum,namedthe'AcousticSpectroscoPy',reflectsmaterialcharactersoftheobjectsandcanbeusedtoidentifythetarget.Theresonallcespectraareisolatedbysubtractingfromthescattere…