“Volume trapping” of protons in the channeling regime in a bent crystal

A computer analysis of the “volume trapping” effect for 1 GeV protons in the planar channeling regime in a bent Si crystal has been performed. The dependences of the trapping efficiency on the beam incidence angle and the bending radius of the crystal have been obtained.     

Explication des anomalies observees dans une etude quantitative du rendement photoelectrique de l'argent par la non-localite de la reponse dielectrique

Discrepancies had been obtained for p polarization in the quantitative analysis of the photoemission yield of silver. They had been accounted in a semi-phenomenological way by introducing a “surface term”. It is shown here, that a non-local theory of the dielectric response introduces a term which is of the same form as the “surface term”. Therefore, the analysis of photoemission yields is an experimental test to prove the non-local character of the dielectric response.     

Bending,vibration and buckling of simply supported thick multilayered orthotropic plates: An evaluation of a new displacement model

Based upon a piecewise linear displacement field which allows the contact conditions for the displacements and the transverse shearing stresses at the interfaces to be satisfied simultaneously, the non-linear (in the von Kármán sense) equations of motion for thick multilayered orthotropic plates are developed. Successively, the equations are specified to the linear boundary value problem of the bending and to the linear eigenvalue problems of the undamped vibration and buckling of rectangular plates. In order to assess the accuracy of the proposed theory, the sample problem of the bending, free undamped vibration and buckling of a three-layered, symmetric cross-ply, square plate simply supported on all edges is investigated. For purposes of comparison, numerical results from the exact elasticity theory, the classical lamination (Kirchhoff) theory and the shear deformation theory (Timoshenko and Mindlin) with three different values of the shear correction factor are also presented. It is found that the proposed approach is very efficient in predicting the global responses (deflection, natural frequencies and buckling loads) of thick multilayered plates and models effects, such as the distortion of the deformed normals, not attainable from the classical lamination theory, as well as the shear deformation theory.     

An approximate method of predicting the response of periodically supported beams subjected to random convected loading

The space-averaged response of an infinite, elastically supported, periodic beam subjected to convected random loading has been studied by using an approximate “assumed mode” method. The complex wave motion in the beam is represented by any number of suitably chosen complex modes. With a good, yet simple, choice of mode which satisfies certain boundary conditions on one periodic beam element, a “single mode approximation” can yield very accurate values of the average response. This has been verified for a wide range of the support stiffnesses and loading convection velocities. Consideration has also been given to the ratio of the maximum response in the beam to the space-averaged response. The method has been applied only to uniform beams in this paper, but it should be readily applicable to periodic systems consisting of non-uniform beam elements.     

The infrared spectrum of HCCF around 17 μm

The absorption spectrum of HCCF in the region of the CH bending fundamental ν₄ has been studied at a resolution of about 0.03 cm^?1. In addition to the fundamental, the rotational analysis has been performed for six “hot” bands. Several molecular parameters have been derived. The effects of l-type resonances have been discussed. In particular, the influence of the resonance between the sublevels of ν₄ + ν₅ on the effective centrifugal distortion constants has been investigated.     

Generation of optical vortex light beams by volume holograms with embedded phase singularity

Special features of the optical-vortex (OV) beams generated by thick holographic elements (HE) with embedded phase singularity are considered theoretically. The volume HE structure is based on the 3D pattern of interference between an OV beam and a standard reference wave with regular wavefront. The incident beam diffraction is described within the framework of a linear single-scattering model in which the volume HE is represented by a set of parallel thin layers with the “fork” holographic structure. An explicit integral expression is derived for the complex amplitude distribution of the diffracted paraxial beam with OV. The numerical analysis demonstrates that the HE thickness may essentially influence not only selectivity and efficiency of the OV beam generation but also the amplitude and phase profile of the diffracted beam as well as regularities of its propagation. We have studied the generated OV morphology and laws of its evolution; in particular, the possibility of obtaining a circularly symmetric OV beam regardless of the diffraction angle is revealed.     

Transient response in flexure to general uni-directional loads of variable cross-section beam with concentrated tip inertias immersed in a fluid

This paper presents a method for solving problems of transient response in flexure due to general unidirectional dynamic loads of beams of variable cross section with tip inertias. An elastodynamic theory which includes effects of continuous mass and rigidity of the beam has been applied. In the analysis the general dynamic load is expanded into a Fourier series and the beam is divided into many small uniform thickness segments. The equation of motion of each segment is mapped onto the complex domain by use of the Laplace transform method. The solutions of each set of adjoining segments are related to each other at the boundaries by the use of the transfer matrix method. The displacement, the bending slope, the bending moment and the shearing force at each boundary and at arbitrary time are obtained from the Laplace transform inversion integral by using the residue theorem. The theoretical results given in this paper are applicable to problems of dynamic response due to arbitrary loads varying with time of beams of arbitrary shape with concentrated tip inertias. As applications of the present theoretical results, numerical calculations have been carried out for two cases: a uniform beam with a tip inertia and a non-uniform beam (a truncated cone) with a tip inertia. Both are immersed in a fluid and subjected to large waves such as cnoidal waves.     

Space charges can significantly affect the dynamics of accelerator maps

Space charge effects can be very important for the dynamics of intense particle beams, as they repeatedly pass through nonlinear focusing elements, aiming to maximize the beam's luminosity properties in the storage rings of a high energy accelerator. In the case of hadron beams, whose charge distribution can be considered as “frozen” within a cylindrical core of small radius compared to the beam's dynamical aperture, analytical formulas have been recently derived [C. Benedetti, G. Turchetti, Phys. Lett. A 340 (2005) 461] for the contribution of space charges within first order Hamiltonian perturbation theory. These formulas involve distribution functions which, in general, do not lead to expressions that can be evaluated in closed form. In this Letter, we apply this theory to an example of a charge distribution, whose effect on the dynamics can be derived explicitly and in closed form, both in the case of 2-dimensional as well as 4-dimensional mapping models of hadron beams. We find that, even for very small values of the “perveance” (strength of the space charge effect) the long term stability of the dynamics changes considerably. In the flat beam case, the outer invariant “tori” surrounding the origin disappear, decreasing the size of the beam's dynamical aperture, while beyond a certain threshold the beam is almost entirely lost. Analogous results in mapping models of beams with 2-dimensional cross section demonstrate that in that case also, even for weak tune depressions, orbital diffusion is enhanced and many particles whose motion was bounded now escape to infinity, indicating that space charges can impose significant limitations on the beam's luminosity.     

A SEMI-ANALYTICAL APPROACH TO THE NON-LINEAR DYNAMIC RESPONSE PROBLEM OF BEAMS AT LARGE VIBRATION AMPLITUDES, PART II: MULTIMODE APPROACH TO THE STEADY STATE FORCED PERIODIC RESPONSE

The semi-analytical approach to the non-linear dynamic response of beams based on multimode analysis has been presented in Part I of this series of papers (Azrar et al., 1999 Journal of Sound and Vibration224, 183-207 [1]). The mathematical formulation of the problem and single mode analysis have been studied. The objective of this paper is to take advantage of applying this semi-analytical approach to the large amplitude forced vibrations of beams. Various types of excitation forces such as harmonic distributed and concentrated loads are considered. The governing equation of motion is obtained and can be considered as a multi-dimensional form of the Duffing equation. Using the harmonic balance method, the equation of motion is converted into non-linear algebraic form. Techniques of solution based on iterative-incremental procedures are presented. The non-linear frequency and the non-linear modes are determined at large amplitudes of vibration. The basic function contribution coefficients to the displacement response for various beam boundary conditions are calculated. The percentage of participation for each mode in the response is presented in order to appraise the relation to higher modes contributing to the solution. Also, the percentage contributions of the higher modes to the bending moment near to the clamps are given, in order to determine accurately the error introduced in the non-linear bending stress estimated by different approximations. Solutions obtained in the jump phenomena region have been determined by a careful selection of the initial iteration at each frequency. The non-linear deflection shapes in various regions of the solution, the corresponding axial force ratios and the bending moments are presented in order to follow the behaviour of the beam at large vibration amplitudes. The numerical results obtained here for the non-linear forced response are compared with those from the linear theory, with available non-linear results, based on various approaches, and with the single mode analysis.     

Statistical analysis of parameter effects on bending angle in laser forming process by pulsed Nd:YAG laser

In recent years, laser application has been introduced for bending and forming as new processes in manufacturing. The capability of laser bending demands more studies to recognize parameters influencing bending angle of sheet metals. In this study the effects of parameters such as material, laser power, beam diameter, scan velocity, sheet thickness, pass number and pulse duration on bending angle were studied by FEM initially and then followed by experiments. Furthermore, the Taguchi experimental design method was employed to pin point parameters, which significantly affect the bending process of laser bending of St12 and 304 alloy steels, which have a wide range of applications in products manufacturing. A regression analysis was conducted and a closed form equation was derived. The closed form equation can be used in industry to determine which process parameters (factors) enhance the bending angle in laser bending process.     

Interface response theory of discrete composite systems

A general theory of “interface responses” in discrete composite d-dimensional systems for operators with two-body interactions is presented. It is shown that the “interface responses” of all the internal and external interfaces of any composite system are the linear superposition of the responses to a coupling operator of all individual interfaces and of the responses to a cleavage operator of the corresponding ideal free surfaces of the same but non-interacting subsystems. The response function and its elements between two space points of the system are given by a new simple general equation as a function of these “interface responses” and of the bulk response functions of each subsystem contained in the complete real system. The present paper establishes this new general two-body theory of interface responses for surfaces, interfaces, adsorbates, membranes, superlattices, defects of any kind and dimension, ... and for the first time, to the knowledge of the author, for any d-dimensional composite system. The presentation of the theory is followed here by a few general applications.     

Mono-coupled periodic systems with a single disorder: Response to convected loadings

This paper presents a general theory of the forced response under convected loading of mono-coupled periodic systems with a single disorder. The general expressions derived have been used to study the response of an infinite periodic beam on simple supports with one of the support spacings different from all the others. Convected harmonic pressure fields and frozen random pressure fields have been considered. Computer studies are presented showing the moment response at supports and the space-time-averaged responses in the disorder and in the nearby periodic beam elements. High response levels can occur due to (i) resonances of the beam length disorder against the stiffness of the attached periodic systems and (ii) hydrodynamic coincidence vibration occurring in the periodic beam. The frequency zones in which these high responses may occur are identified. The high response due to the resonance (ii) is restricted to the vicinity of the disorder, whereas that due to coincidence occurs throughout the system. Computed results show that the highest response levels do not necessarily occur in the beam length disorder, but may occur in one of the nearby periodic beam elements. The dependence of the maximum response levels on the magnitude of the disorder has been investigated. The conditions under which small disorders may be neglected have been pointed out.     

DLA光源质量对光栅-外腔谱合成系统光束质量的影响

在二极管激光阵列(DLA)光栅-外腔谱合成系统中,由于DLA存在子单元光束发散角、“smile”效应的位置偏差及指向性偏差等因素的综合作用,将导致合成光束的光束质量降低。综合考虑DLA子单元光束发散角、“smile”效应等因素对谱合成系统中光束传输特性的影响,建立了DLA光栅-外腔谱合成系统的光传输模型,进而对谱合成系统中DLA子单元光束发散角、“smile”效应的位置偏差及指向性偏差等因素对合成光束的光束质量影响进行了定量分析。结果表明,DLA光源质量会明显影响合成光束的光束质量：DLA子单元光束发散角和“smile”效应引入的指向性偏差越大,合成光束的光束质量就越差;“smile”效应引入的位置偏差在合束方向上对合成光束的光束质量没有影响,而在非合束方向上引入的位置偏差将会明显降低合成光束的光束质量。在实际工作应用中,需要采取措施提高DLA光源质量,以减小对合成光束的光束质量影响。     

On the two frequency spectra of Timoshenko beams

This paper is concerned with the question of whether there are, indeed, two distinct spectra of frequencies for the transverse vibrations of Timoshenko beams as has been claimed by a number of prior authors for the case of the simply supported beam and, more recently, for beams supported in an arbitrary manner. Elementary analysis leads to the conclusion that there is only a single frequency spectrum; in the particular case of the simply supported beam the “two frequency spectra” viewpoint may be expedient as a device to compute frequencies but does not serve otherwise to explain the complex, dynamical behavior of Timoshenko beams.     

Sound transmission at low frequencies through the walls of distorted circular ducts

A theoretical treatment of sound transmission through the walls of distorted circular ducts is given, for plane mode transmission within the duct. The transmission mechanism is essentially that of “mode coupling”, whereby higher structural modes in the duct walls are excited, because of the wall distortion, by the internal sound field. The theory is in two parts: an approximate analytical model for the structural response of the walls to the internal sound field, and a structural radiation model. Computed results, based on the theory, are compared to measurements on “long-seam” air conditioning ducts. Where the duct geometry can be reliably specified, reasonably good agreement is obtained between theoretical and experimental data. It is concluded that mode coupling effects serve to account for the discrepancies between ideal and observed behaviour in sound transmission through duct walls.     

Formulation and justification of the Wheeler-Feynman absorber theory

The “absorber theory” of Wheeler and Feynman is supposed to justify the use of retarded potentials in ordinary electromagnetic calculations despite a fundamentally time symmetric interaction. We restate the thesis of absorber theory as follows: here exist causal solutions of time symmetric electrodynamics. In our formulation, absorption need only take place in one direction of time (the future) rather than both, as seems to be required by Wheeler and Feynman. Even with complete absorption, however, the effects of advanced interactions are not entirely eliminated and a residual field may introduce a degree of indeterminacy into particle trajectories obtained using retarded potentials alone.     

Symmetric Talbot bands experiment

By impinging a step phase-shifted white light beam on a grating-based interferometer, one of diffraction orders is modulated and interference bands so-called “Talbot bands” are formed. Here, classical Talbot bands set up is generalized to the symmetry configuration, in which two glass plates of the same thickness instead of one plate, are inserted halfway into the grating interferometer aperture. Formation of Talbot bands were studied theoretically and experimentally. Frequency impulse response of the new Talbot bands setup was, also presented. It was demonstrated that symmetric set-up causes modulation of both of two opposite orders, according to the theory. In this manner, their visibility is the same. As a result, this similarity of the visibility is reduced while the symmetric arrangement of the glass plates with respect to the optical axis, is broken.     

Response of unconstrained layer panels to random excitation at a point

The acceleration response of unconstrained layer rectangular panels under random point force excitation has been investigated theoretically and experimentally. In the theory the layer material was assumed to be viscoelastic in nature. Generalized harmonic analysis was used to evaluate the power spectral density and the rms values of acceleration response analytically. The theoretical results are compared with the results obtained from experiments for “all edges simply supported” and “all edges clamped” panel boundary conditions.     

The rotation-inversion spectra and vibration-rotation interaction in NH2D

An additional 86 lines of the NH₂D rotation-inversion spectrum were measured between 7.5 and 850 GHz. These data and the existing NH₂D and ND₂H data are fitted to a Hamiltonian in which the vibration-rotation interaction is included in the form of an offdiagonal inertial tensor term. For comparison with the symmetric ammonias an oblate basis and a Watson-type reduced “S” set of distortion constants are used. A theory for the interaction term is given which is in excellent agreement with experiment. Structural parameters are derived. The magnitude and relative sign of the two dipole moment components of NH₂D are determined and previously measured nitrogen hyperfine structure for both species is reexamined using improved rotational wavefunctions.