Showing papers on "Beam (structure) published in 1983"

Linear elastic materials with voids

Abstract: A linear theory of elastic materials with voids is presented. This theory differs significantly from classical linear elasticity in that the volume fraction corresponding to the void volume is taken as an independent kinematical variable. Following a discussion of the basic equations, boundary-value problems are formulated, and uniqueness and weak stability are established for the mixed problem. Then, several applications of the theory are considered, including the response to homogeneous deformations, pure bending of a beam, and small-amplitude acoustic waves. In each of these applications, the change in void volume induced by the deformation is determined. In the final section of the paper, the relationship between the theory presented and the effective moduli approach for porous materials is discussed. In the two year period between the submission of this manuscript and the receipt of the page proof, there have been some extensions of the results reported here. In the context of the theory described, the classical pressure vessel problems and the problem of the stress distribution around a circular hole in a field have uniaxial tension have been solved [19,22]. The solution given in the present paper for the pure bending of a beam when the rate effect of the theory is absent is extended to case when the rate effect is present in [21]. The various implications of the rate effect in the void volume deformation are pursued all the subsequent works [19,20,21,22].

Magnetic field paralleliser for 2π electron-spectrometer and electron-image magnifier

Abstract: An electron-optical device has been constructed in which electrons originally emitted over 2 pi steradians from a region of small volume are formed into a beam of half-angle 2 degrees . The instrument makes use of a magnetic field that diverges from 1 to 10-3 Tesla. The energies of the electrons parallelised in this way have been measured with a time-of-flight technique, giving energy resolutions as low as 15 meV. Electrons of energy 0-3 eV, formed in multiphoton ionisation, were used for these tests. The device can also act as an electron-image magnifier, giving a spatial resolution of a few mu m in the source plane. Detailed theoretical and computational results on the properties of the new apparatus are given.

Stochastic finite element analysis of simple beams

Abstract: A method of stochastic finite element analysis is developed for solving a variety of engineering mechanics problems in which physical properties exhibit one-dimensional spatial random variation. The method is illustrated by evaluating the second-order statistics of the deflection of a beam whose rigidity varies randomly along its axis. A key component of the approach is a new treatment of the correlation structure of the random material property in terms of the variance function and its principal parameter, the scale of fluctuation. The methodology permits efficient evaluation of the matrix of covariances between local spatial averages associated with pairs of finite elements. Numerical results are presented for a cantilever beam, with deformation controlled by shear, subjected to a concentrated force at its free end or to a uniformly distributed load.

The dynamic behaviour of slender structures with cross-sectional cracks

Abstract: A dynamic model for beams with cross-sectional cracks is discussed. It is shown that a crack can be represented by a consistent, static flexibility matrix. Two different methods for the determination of the flexibility matrix are discussed. If the static stress intensity factors are known, the flexibility matrix can be determined from an integration of these stress intensity factors. Alternatively, static finite element calculations can be used for the determination of the flexibility matrix. Both methods are demonstrated in the present paper. The mathematical model was applied to an edge-cracked cantilevered beam and the eigenfrequencies were determined for different crack lengths and crack positions. These results were compared to experimentally obtained eigenfrequencies. In the experiments, the cracks were modelled by sawing cuts. The theoretical results were, for all crack lengths, in excellent agreement with the experimental data. The dynamic stress intensity factor for a longitudinally vibrating, centrally cracked bar was determined as well. The results compared very well with dynamic finite element calculations. The crack closure effect was experimentally investigated for an edge-cracked beam with a fatigue crack. It was found that the eigenfrequencies decreased, as functions of crack length, at a much slower rate than in the case of an open crack.

Chaotic vibrations of a beam with non-linear boundary conditions

Abstract: Forced vibrations of an elastic beam with non-linear boundary conditions are shown to exhibit chaotic behavior of the strange attractor type for a sinusoidal input force The beam is clamped at one end, and the other end is pinned for the tip displacement less than some fixed value and is free for displacements greater than this value The stiffness of the beam has the properties of a bi-linear spring The results may be typical of a class of mechanical oscillators with play or amplitude constraining stops Subharmonic oscillations are found to be characteristic of these types of motions For certain values of forcing frequency and amplitude the periodic motion becomes unstable and nonperiodic bounded vibrations result These chaotic motions have a narrow band spectrum of frequency components near the subharmonic frequencies Digital simulation of a single mode mathematical model of the beam using a Runge-Kutta algorithm is shown to give results qualitatively similar to experimental observations

Theory of beam induced current characterization of grain boundaries in polycrystalline solar cells

Abstract: A theoretical analysis is given of the induced current profiles at grain boundaries in polycrystalline solar cells, as obtained by light or electron beam excitation. The area A and the variance σ2 of the contrast profile of a grain boundary are calculated for realistic generations as functions of the interface recombination velocity vs and the minority carrier diffusion length L. A graphical new procedure is proposed which allows the simultaneous determination of vs and L from the measured values of A and σ. The evaluation of an experimental electron beam induced current profile illustrates the applicability of the theory.

Polycrystalline Silicon Micromechanical Beams

Abstract: Using the conventional MOS planar process, miniature cantilever and doubly supported mechanical beams are fabricated from polycrystalline silicon. Poly‐Si micromechanical beams having thicknesses of 230 nm to 2.3 μm and separated by 550 nm to 3.5μm from the substrate are made in a wide range of lengths and widths. Two static mechanical properties are investigated: the dependences of maximum free‐standing length and beam deflection on the thickness of the beam. By annealing the poly‐Si prior to beam formation, both of these properties are improved. Nonuniform internal stress in the poly‐Si is apparently responsible for the beam deflection.

Beam elements on two-parameter elastic foundations

Abstract: Two-parameter elastic foundations are more accurate than a one-parameter (Winkler) foundation and are simpler than semi-infinite elastic continuum foundation models. Two kinds of finite elements are formulated in this paper to analyze beams on one-or two-parameter foundations. Models include Winkler, Filonenko-Borodich, Pasternak, generalized, and Vlasov foundations. One of the two kinds of elements is based on the exact displacement function. The other is based on a cubic displacement function. The stiffness matrix and consistent load vector is derived for each. Numerical tests show that the element based on the exact displacement function can give exact numerical results even if the number of elements is very small. The element based on a cubic function may require a fine mesh to give acceptable results.

Theory of mode-induced beam-particle loss in tokamaks

Abstract: Large‐amplitude rotating magnetohydrodynamic modes are observed to induce significant high‐energy beam particle loss during high‐power perpendicular netural beam injection on the poloidal divertor experiment (PDX). A Hamiltonian formalism for drift orbit trajectories in the presence of such modes is used to study induced particle loss analytically and numerically. Results are in good agreement with experiment.

Uniformity of Energy Deposition for Laser Driven Fusion

Abstract: Laser driven fusion requires a high degree of uniformity in laser energy deposition in order to achieve the high density compressions required for sustaining a thermonuclear burn. The characteristic nonuniformities produced by laser irradiation, with multiple overlapping beams, are examined for a variety of laser-target configurations, Conditions are found for which the rms variation in uniformity is less than 1%. The analysis is facilitated by separating the contributions from (1) the geometrical effects related to the number and orientation of the laser beams and (2) the details of ray trajectories for the overlapping beams. Emphasis is placed on the wavelength of the nonuniformities in addition to their magnitudes, as the shorter wavelength nonuniformities are more easily smoothed by thermal conduction within the target. It is demonstrated how the geometrical symmetry of the laser system effectively eliminates the longer wavelengths, and how shorter wavelength nonuniformities can be “tuned out” by varying parameters such as the focal position and the radial intensity profile of the beam. The distance required for adequate thermal smoothing of the irradiation nonuniformities is found to be 2 to 3 times smaller than previously estimated due mainly to the relatively small spatial wavelength of the nonuniformities. This is a consequence of the geometrical symmetry of the laser system and is relatively insensitive to the details of overlapping beam profiles. The results are particularly important for irradiation with short wavelength laser light (e.g. 0.35 µm), as the small smoothing distances anticipated for moderate laser intensities are found to still produce adequate attenuation of the calculated nonuniformities. The effect of irradiation nonuniformity on target dynamics is illustrated by an implosion simulation using laser-target conditions anticipated for near-term high-density experiments.

Beam propagation in uniaxial anisotropic media

Abstract: Paraxial wave equations are derived for the propagation of beams in uniform uniaxial anisotropic media. The equations are generalized to the case of nonuniform media with weakly varying refractive indices. An ordinary wave beam is governed by a standard paraxial equation, whereas an extraordinary wave beam is governed by a paraxial wave equation, which involves both a displacement relative to the position of an ordinary wave beam and a rescaling of one transverse coordinate. The solution to the latter equation for a propagating Gaussian beam displays a distortion of both shape and phase front. Numerical results for diffraction by a uniformly illuminated circular aperture in a calcite medium display various anomalies ascribable to a loss of circular symmetry.

Direct inelastic scattering Ar from Pt(111)

Abstract: High resolution angularly resolved time of flight distributions are presented for a supersonic argon beam scattering from a clean well‐characterized Pt(111) single crystal. A novel presentation of the resulting velocity and angular flux information in terms of iso‐flux contour maps in Cartesian velocity space allows the scattering process to be decomposed into three mutually independent directions defined by the surface normal (z), parallel to the surface and in the scattering plane (y), and parallel to the surface but perpendicular to y and z(x). The iso‐flux contour maps appear as nested ovals with principal axes oriented parallel to the above defined directions; axis length decreases in the order z, y, x. The corresponding variances in the x, y, and z velocities vary directly with the surface temperature. Three beam energy regimes are evident and are discussed in terms of the diminishing effect of the attractive well which occurs for increasing beam energies and the increasing effect of short range phenomena prevalent at high incident beam energies. Accomodation coefficients were defined and measured for the y and z directions and were 0.1 and 0.45, respectively, indicating the degree to which parallel and perpendicular momenta are not conserved in a single collision. Geometric scattering by instantaneous surface roughness is experimentally shown to be negligible for this system for beam energies <20 000 K indicating that the scattering is by the finite momentum of the surface.

An Emittance Scanner for Intense Low-Energy Ion Beams

Abstract: An emittance scanner has been developed for use with low-energy H- ion beams to satisfy the following requirements: (1) angular resolution of ± 1/2 mrad, (2) small errors from beam space charge, and (3) compact and simple design. The scanner consists of a 10-cm-long analyzer containing two slits and a pair of electric deflection plates driven by a ±500-V linear ramp generator. As the analyzer is mechanically driven across the beam, the front slit passes a thin ribbon of beam through the plates. The ion transit time is short compared with the ramp speed; therefore, the initial angle of the ions that pass through the rear slit is proportional to the instantaneous ramp voltage. The current through the rear slit then is proportional to the phase-space density d2i/dxdx. The data are computer-analyzed to give, for example, rms emittance and phase-space density contours. Comparison of measured data with those calculated from a prepared (collimated) phase space is in good agreement.

Diffraction of an Atomic Beam by Standing-Wave Radiation

Abstract: Preliminary experimental results are reported for the deflection of Na atoms in an atomic beam by a transverse standing-wave laser field whose frequency is tuned between the two ground-state hyperfine components of the ${D}_{2}$ line In contrast to the two experiments done previously, a splitting of the beam into two symmetric peaks whose separation increases with the electric-field is seen here In addition, the data show evidence for atomic diffraction: a tendency for scattered atoms to acquire momentum in multiples of $2\ensuremath{\hbar}k$

State resolved rotational excitation in D2+H2 collisions

Abstract: In a crossed molecular beam experiment time‐of‐flight distributions of ortho D2 molecules scattered from normal H2 (nH2) and para H2 (pH2) have been measured in a center‐of‐mass angular range of 75° to 180° The collision energies were 841 and 872 meV, respectively In all spectra the rotational excitation of D2 from j=0 to j=2 has been resolved With pH2 as secondary beam the same transition could also be observed for H2 The measurements show that the probability for rotational excitation of D2 depends on whether the scattering partner H2 is rotating (nH2) or not (pH2) In the first case the cross sections are larger by a factor of approximately 2 The reason for this behavior is the presence of an additional interaction term which is at long range distances, identical to the quadrupole–quadrupole interaction and which is absent if H2 is in the j=0 state The experimentally derived differential cross sections for the rotational excitation of D2 and H2 are compared with theoretical results obtained by

A Focusing Weissenberg Camera with Multi-Layer-Line Screens for Macromolecular Crystallography

Abstract: A conventional Weissenberg camera [Weissenberg (1924). Z. Phys. 23, 229–238] has been modified for macromolecular crystallography. This camera system consists of a doubly bent LiF monochromator, a newly designed Weissenberg goniometer with multi-layer-line screens and its controller. The camera is useful for recording many reflections up to high resolution on a film with high signal-to-background ratio from a crystal with large unit-cell dimensions without losing any of the diffracted beams by screens. The resulting photograph is very easy to index, and the ratio of partially recorded reflections to fully recorded reflections decreases in comparison with an oscillation camera. The multi-layer-line screens are especially practical with a continuous X-ray beam such as synchrotron radiation where both wavelength and band pass can be selected properly. The preparation of a point-focusing monochromator from a single-crystal of LiF is described, and the recording of anomalous dispersion profiles is discussed.

Direct Measurement of the Longitudinal Coherence Length of a Thermal Neutron Beam

Abstract: When a series of aluminum slabs are placed in one leg of a perfect-silicon-crystal neutron interferometer, a continuous and significant loss of contrast is observed. This observation is interpreted as being due to the finite length of the neutron wave packets.

Beam-propagation analysis of loss in bent optical waveguides and fibers

Abstract: We demonstrate that the beam-propagation method can be used to calculate accurately both the pure bending loss and the transition loss of bent single-mode optical waveguides and fibers. Our results allow us to establish the accuracy of several commonly used theories of bending loss and to investigate the degree to which theories of step-index monomode fiber losses can be used to predict the losses of graded-index monomode fibers.

Coupled vibrations of beams—an exact dynamic element stiffness matrix

Abstract: A uniform linearly elastic beam element with non-coinciding centres of geometry, shear and mass is studied under stationary harmonic end excitation. The Euler-Bernoulli-Saint Venant theory is applied. Thus the effect of warping is not taken into account. The frequency-dependent 12 × 12 element stiffness matrix is established by use of an exact method. The translational and rotational displacement functions are represented as sums (real) of complex exponential terms where the complex exponents are numerically found. Built-up structures containing beam elements of the described type can be analysed with ease and certainty using existing library subroutines.

Axial irradiance and optimum focusing of laser beams

Abstract: Using the Rayleigh-Sommerfeld theory of diffraction we obtain an exact expression for the axial irradiance of a focused annular laser beam valid for all axial points. Conditions for the validity of the Fresnel theory are obtained. We discuss why and how the depth of focus and asymmetry of focused fields about the focal plane depend on the Fresnel number of the beam aperture as observed from the geometric focus. When a beam is focused on a distant target so that the Fresnel number is small (≲5), the principal maximum of axial irradiance occurs at a point which is significantly away from the geometric focus in the direction of the aperture. We discuss how to optimally focus a beam to illuminate a moving distant target in terms of the encircled energy on it. We show that, to obtain the maximum possible concentration of energy on a target, the beam must be focused on it, thus requiring active focusing for a moving target. However, if energy concentration is adequate for a beam focused on a target at a certain distance, it is more than adequate for a considerable range of the distance of a moving target without active focusing. In a shared-aperture optical system the aperture used for focusing a beam on the target is also used for imaging the target. Hence, in such a system the optical transfer function is also more than adequate over a wide range of the target distance without active focusing.

Electro-optical switch for unpolarized optical signals

Abstract: An optical 1×N switch uses a polarizing beam splitter cube and a reflector to separate an arbitrarily polarized incident light beam into polarized components which propagate along parallel paths. A polarization rotator is positioned in the path of the reflected component to rotate the plane of polarization of the light beam component propagating therealong to be coplanar with that of the undeviated light beam in the parallel path. The two beams are simultaneously or individually deflected by selectively activating the electrodes of a liquid crystal nematic reflector/transmitter array confined between prismatic bodies to emerge at one or more of a plurality of desired outputs. In a second embodiment, a second polarization rotator and polarizing beam combiner assembly re-establishes the initial polarization and the beams are thereby combined to emerge from one or more selected output terminals as an arbitrarily polarized light beam. The switch exhibits extremely low crosstalk and insertion loss by utilizing the energy of both parallel and normal incidence polarization components and avoiding propagation of undesired stray polarization components as occurs with a liquid crystal polarizer.

Creation of a parting zone in a crystal structure

Abstract: A method of providing a thin parting zone in diamond and other crystal material is used to separate the crystal into multiple parts. The method comprises the following steps. An entrance window is prepared on the outer surface of the crystal. The window can transmit a beam of energy. An energy beam is focussed on a point zone of energy absorbing material which is spaced from the window in the crystal. The energy absorbing zone is generated at the focal point of the beam. The focal point of the beam is scanned through a succession of overlapping potential damage cells which lie along a predetermined parting zone within the crystal. The beam creates a plurality of actual damage cells comprised of shattered material which creates the parting surface. The succession of potential damage cell is such that the previously generated actual damage cells do not lie along the path of the beam between the actual damage cells being generated and the window.