Validation and Limits of Finite Inflatable Beam Elements

Although nowadays inflatable tubular beams are often used in the field of civil engineering, by now there are only few publications dealing with finite deformation inflatable beam elements, see e.g. [1], [2] and [3]. All formulations of inflatable beams have several assumptions in common, as constant cross sections throughout the deformation, a constant internal gas pressure and the negligence of circumferential stresses. These assumptions have to be validated either by experiments or numerical analysis. In the current contribution beam–like structures are investigated using a finite element shell or membrane formulation and featuring a volume dependent gas loading, see e.g. [5] and [4]. In general the formulation substitutes the internal gas pressure by an energetically equivalent volume dependent loading and thus enables to check for potential gas pressure changes during the deformation process of the inflated beam as a consequence of volume changes. Further local deformations as occurring in the vicinity of supports or almost single loads can be considered. In this paper the focus will be only on the initial assumption of the beam theory that the biaxial stress state is neglected. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gaussian Lenses Initiate Optical Vortices in LaserBeams During Self-action in Kerr-like Medium

It is shown that Gaussian lenses initiate closed line of dislocations in coherent beamswith initially smooth wavefront. The stigmatic lenses originate the circle line of edge dislocation,situated on the beam cross-section. In the case of astigmatic Gaussian lens this closed curve getsout from the plane and a quadruple of alternate single-charged optical vortices is born andannihilates in the beam cross-section. The distribution of topological charge signs in the quadruplealong z axis is defined by focusing or defocusing type of Gaussian lens. The model ofGaussian lenses explains self-action of fundamental mode laser beams transmitted by Kerr-likemedia. Two methods were used for study of optical singularities appearance: the geometricaloptics analysis for rapid qualitative location and numerical modeling of Kirchhoff-Fresnel integralfor exact solution.     

Electrostatics in a locally flat space with conical singularities

We calculate the potential of a pointlike source in a multicenter three-dimensional space-time and obtain general relations between the values of the regularized self-energy, force, and force moment. The self-action effects as well as the relative contribution of higher multipoles infinitely increase as the angle deficit increases. The results obtained are generalized to a system of parallel cosmic strings one of which carries a current. The case of string with a finite thickness is also considered. Translated from Teoreticheskaya i Matematicheskya Fizika, Vol. 123, No. 1, pp. 150–162, April, 2000.     

A Method for Solving the Inverse Problem in Soft Acoustic Scattering

The inverse problem considered is to determine the shape ofan acoustically soft obstacle in R³ from a knowledge of thetime-harmonic incident plane wave and the far-field patternof the scattered wave. To solve this inverse Dirichlet problemin acoustic scattering without requiring the solution of integralequations, a parametric representation is introduced in whichthe parameters are determined by a method of optimization. Directscattering can also be handled by this technique. Comparisonsreveal that results are obtained more easily than, and justas accurately as, in other methods.     

The optimum shape of a bending beam

The problem of minimizing the static deflection of an elastic beam of variable cross-section and fixed volume in the case of free supported and rigidly clamped ends is considered. In the first case it is proved that the solutions obtained earlier, based on the necessary conditions for an extremum, satisfy the sufficient conditions. In the case of clamped ends, which is of the most interest from the point of view of applications, it is proved that the optimum solutions must necessarily have points inside the solution range in which the distribution of the beam thicknesses degenerates to zero (“internal hinges”). A qualitative, analytical and numerical analysis of this phenomenon is given. In particular, in the case of clamped ends for a class of point loads, analytical solutions for which the beam splits into two cantilevers are obtained.     

3:1 Internal resonance of a string-beam coupled system with cubic nonlinearities

The dynamic behavior and chaotic motion of a string-beam coupled system subjected to parametric excitation are investigated. The case of three-to-one internal resonance between the modes of the beam and the string, in the presence of subharmonic resonance for the beam is considered and examined. The method of multiple scales is applied to study the steady-state response and the stability of the string-beam coupled system at resonance conditions. Numerical simulations illustrated that multiple-valued solutions, jump phenomenon, hardening and softening nonlinearities occur in the resonant frequency response curves. The effects of different parameters on system behavior have been studied applying frequency response function. Results are compared to previously published work.     

Flows op a reacting mixture in laval nozzles under conditions op a quasi-frozen process : PMM vol. 39, n 6, 1975, pp. 1068–1072

Flows of a chemically active gas mixture are considered in a small region of a La val nozzle, where their mode changes from subsonic to supersonic (the frozen speed of sound is considered) are analyzed. Continuous solutions and solutions with shock waves are derived. Conditions of shock-free flows are obtained.     

Reconstruction of an acoustically sound-soft obstacle from one incident field and the far-field pattern

The problem considered is that of determining the shape of aplane acoustically sound-soft obstacle from the knowledge ofthe far-field pattern for one time-harmonic incident field.An iterative procedure is proposed based on two boundary integralsrepresenting the incident field and the far-field pattern, respectively.Numerical examples are included which show that the proceduregives accurate numerical approximations in relatively few iterations.     

Self-action of a point charge in classical electrodynamics

A direct calculation demonstrates that the causal Green function for classical equations of an electromagnetic field contains an additional singular term cancelling the divergence in the self-action of a point charge. Thus, the problem of mass renormalization is avoided. An exact relativistic expression for the self-action force is presented as a sum of two terms. The first one gives the radiation damping and the second one describes the electromagnetic component of the particle momentum depending on its velocity and acceleration. Accordingly, the work of the force also consists of two terms: the radiation energy and the electromagnetic component of the particle energy. To perform the calculations, we have to extend the radial spherical coordinate in the -function argument to negative values.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 2, pp. 256–269, November, 1995.     

Resolving Controls for the Boundary Approximate Controllability of Sandwich Beams with Uncertainties the Green’s Function Approach

Mechanics of Composite Materials - The boundary approximate null-controllability of an Euler–Bernoulli sandwich beam subjected to a dynamically active distributed load is considered. The...     

Poincaré–Cosserat Equations for the Lighthill Three-dimensional Large Amplitude Elongated Body Theory: Application to Robotics

In this article, we describe a dynamic model of the three-dimensional eel swimming. This model is analytical and suited to the online control of eel-like robots. The proposed solution is based on the Large Amplitude Elongated Body Theory of Lighthill and a framework recently presented in Boyer et al. (IEEE Trans. Robot. 22:763–775, 2006) for the dynamic modeling of hyper-redundant robots. This framework was named “macro-continuous” since, at this macroscopic scale, the robot (or the animal) is considered as a Cosserat beam internally (and continuously) actuated. This article introduces new results in two directions. Firstly, it extends the Lighthill theory to the case of a self-propelled body swimming in three dimensions, while including a model of the internal control torque. Secondly, this generalization of the Lighthill model is achieved due to a new set of equations, which are also derived in this article. These equations generalize the Poincaré equations of a Cosserat beam to an open system containing a fluid stratified around the slender beam.     

Unlimited cumulation under one-dimensional unsteady compression of an ideal gas

Various methods of unlimited cumulation (UC) of an ideal (inviscid and non-heat-conducting) gas subject to one-dimensional unsteady compression by a plane, cylindrical, or spherical piston are considered. The most perfect method, namely, UC with isentropic compression from rest to rest, which is referred to as “ideal” (IUC), is compared with three other methods of UC, which correspond to well-known self-similar solutions of one-dimensional gas compression. The most effective of these is UC with a reflected shock wave, behind which the compressed gas is homogeneous and at rest, as in IUC. The efficiency of various methods of UC is estimated by the ratio of the work done during compression to the work in the case of IUC, the ratio of the internal energy to the total energy of the compressed gas, and the degree of gas homogeneity with respect to the Lagrangian variable. Computations of these characteristics are carried out for a perfect gas with various adiabatic exponents.     

Many-body wave scattering problems in the case of small scatterers

Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The case of transmission (interface) boundary conditions is also studied in detail. The limiting case is considered, when the size a of small particles tends to zero while their number tends to infinity at a suitable rate. Equations for the limiting effective (self-consistent) field in the medium are derived. The theory is based on a study of integral equations and asymptotics of their solutions as a→0. The case of wave scattering by many small particles embedded in an inhomogeneous medium is also studied.     

Positive definiteness of the gravitational radiation intensity in the theory of gravity with a nonzero graviton mass

A version of the theory of gravity is considered where the graviton mass is nonzero, and the gravitation radiation flux from an arbitrary spatially-bounded source is positive definite. The relation between energy losses by emission and the work of the source is established. It is shown that the total work includes the part produced by the interaction of the source with the radiation field and the part produced by the self-action of the field. The total work proves to be positive definite. The general form of the spectrum-angular distribution is obtained, accounting for the spin and polarization states. For spherically symmetric sources, the states with zero spin and zero projection of spin two on the momentum contribute to the emission.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 107, No. 2, pp. 329–343, May, 1996.Translated by V. I. Serdobol'skii.     

Periodic solutions of a periodically forced and undamped beam resting on weakly elastic bearings

We study the problem of existence of periodic solutions to a partial differential equation modelling the behavior of an undamped beam subject to an external periodic force. We assume that the ordinary differential equation associated to the first two modes of vibration of the beam has a symmetric homoclinic solution. By using methods borrowed by dynamical systems theory we prove that, if the period is non resonant with the (infinitely many) internal periods of the PDE, the equation has a weak periodic solution of the same period as the external force. In particular we obtain continua of periodic solutions for the undamped beam in absence of external forces. This result may be considered as an infinite dimensional analogue of a result obtained in [16] concerning accumulation of periodic solutions to homoclinic orbits in finite dimensional reversible systems. Matteo Franca: Partially supported by G.N.A.M.P.A. – INdAM (Italy).     

Internal gravity wave beams as invariant solutions of Boussinesq equations in geophysical fluid dynamics

It is shown that Lie group analysis of differential equations provides the exact solutions of two-dimensional stratified rotating Boussinesq equations which are a basic model in geophysical fluid dynamics. The exact solutions are obtained as group invariant solutions corresponding to the translation and dilation generators of the group of transformations admitted by the equations. The comparison with the previous analytic studies and experimental observations confirms that the anisotropic nature of the wave motion allows to associate these invariant solutions with uni-directional internal wave beams propagating through the medium. It is also shown that the direction of internal wave beam propagation is in the transverse direction to one of the invariants which corresponds to a linear combination of the translation symmetries. Furthermore, the amplitudes of a linear superposition of wave-like invariant solutions forming the internal gravity wave beams are arbitrary functions of that invariant. Analytic examples of the latitude-dependent invariant solutions associated with internal gravity wave beams that have different general profiles along the obtained invariant and propagating in the transverse direction are considered. The behavior of the invariant solutions near the critical latitude is illustrated.     

The interaction of electron beams and electromagnetic fields in relativistic Cerenkov generators

A method of numerical analysis of linear and nonlinear nonstationary processes in relativistic Cerenkov generators based on periodic superdimensional waveguides is proposed. The main idea lies in considering a nonregular waveguide as a sequence of wave transformers and using a cross-section method. Configurations of eigenwave fields of periodic waveguides with a high-current relativistic electron beam are considered. The processes of generation development in a section of a relativistic multiwave generator are studied. We show that the system frequency is proved to be determined by the longitudinal resonances of surface waves and internal feedback.     

Distributions of the high temperature and the high pressure inside a single acoustically driven bubble

The physical circumstances inside an acoustically driven single gas bubble in water has been intensively explored during the past few years. Starting from the results obtained for a typical case in a well known early paper (Wu, C. C., Roberts, P. H., Phys. Rev. Lett., 1993, 70(22): 3424) and introducing successively several corrections to the physical model, this paper computes in corresponding order the temporal and spatial distributions of significant physical parameters, including the temperature and the pressure, in the bubble around the moment of the bubble’s violent collapse, until expectations in consistence with the present points of view are procured. For the peak temperature our results agree with the prevailing belief that in a typical stable single bubble it is of the order of ten thousand degrees.     

Tropical topology

A space-periodic ground state is shown to exist for lattices of point ions in R³ coupled to the Schrödinger and scalar fields. The coupling requires renormalization due to the singularity of the Coulomb self-action. The ground state is constructed by minimizing the renormalized energy per cell. This energy is bounded from below when the charge of each ion is positive. The elementary cell is necessarily neutral.