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The purpose of this study was to investigate the strength of continuous beams after the elastic limit has been passed. As a result, a method of calculation, which is applicable to maximum load conditions, has been developed. The method is simpler than the methods now in use and it applies properly to conditions where the present methods fail to apply.
The one-sidedness, 'superluminal' motion, and detailed spectra observed for 3C 273 put significant constraints on continuous beam models for the source of the extended emission in 3C 273 A. The one-sidedness of the extended emission implies that the age of the radio-frequency cloud is probably about 3-5 Myr. The 'superluminal' motion observed with VLBI constrains the bulk Lorentz factor of the jet to be more than about 10. Finally, the observed X-ray emission from the jet provides a method for deciding the question of beam composition: for a given beam power, an electron-positron beam would produce a much higher (beamed) inverse-Compton X-ray flux off extended-jet optical photons than an electron-proton beam would, thus making the observed weak jet X-ray flux a strong indicator of a proton positive component to the jet. Remaining experimental uncertainties in the case of 3C 273 make it impossible to decide the question of beam composition at present, but the next generation of experiments may make this possible for 3C 273 and other 'superluminal' objects. The above arguments have the advantage of not depending on the details of the mechanism for producing the high-energy radio-cloud electrons.
The methods used to determine the lower natural frequencies and their corresponding mode shapes of the NASA-LSS Astromast (Unmodified Test Structure), and the mass integrals associated with the mode shapes are illustrated. The test structure is modeled as a cantilever beam with 91 lumped masses and without the tip mass on the free end of the bram. This uncouples the torsion and bending modes and allows for them to be determined separately. The frequency range was limited to an upper bound of 100 rad/sec (15.92 Hz.). In this range from 0.-100. rad/sec, three bending frequencies and one torsion frequency was found.
Optical communications to and from deep space probes will require beams possessing divergence on the order of a microradian, and must be steered with sub-microradian precision. Segmented liquid crystal spatial phase modulators, a type of optical phased array, are considered for this ultra-high resolution beam steering. It is shown here that in an ideal device of this type, there are ultimately no restrictions on the angular resolution. Computer simulations are used to obtain that result, and to analyze the influence of beam truncation and substrate flatness on the performance of this type of device.
Optical communications to and from deep space probes will require beams possessing divergence on the order of a microradian, and must be steered with sub-microradian precision. Segmented liquid crystal spatial phase modulators, a type of optical phased array, are considered for this ultra-high resolution beam steering. It is shown here that in an ideal device of this type, there are ultimately no restrictions on the angular resolution. Computer simulations are used to obtain that result, and to analyze the influence of beam truncation and substrate flatness on the performance of this type of device.
The buckling of infinite beams continuously supported by a semi-infinite elastic continuum is investigated. The buckling loads were determined when the beam rests on a two-dimensional elastic continuum and also when the foundation extends beyond the width of the beam. The effect of the outside foundation is shown by comparing the obtained buckling loads.
Numerical analysis of buckling of continuously infinite beams using Winkler model, Pasternak model, and elastic continuum
Distributed parameter modeling offers a viable alternative to the finite element approach for modeling large flexible space structures. The introduction of the transfer matrix method into the continuum modeling process provides a very useful tool to facilitate the distributed parameter model applied to some more complex configurations. A uniform Timoshenko beam model for the estimation of the dynamic properties of beam-like structures has given comparable results. But many aeronautical and aerospace structures are comprised of non-uniform sections or sectional properties, such as aircraft wings and satellite antennas. This paper proposes a piecewise continuous Timoshenko beam model which is used for the dynamic analysis of tapered beam-like structures. A tapered beam is divided into several segments of uniform beam elements. Instead of arbitrarily assumed shape functions used in finite element analysis, the closed-form solution of the Timoshenko beam equation is used. Application of the transfer matrix method relates all the elements as a whole. By corresponding boundary conditions and compatible conditions a characteristic equation for the global tapered beam has been developed, from which natural frequencies can be derived. A computer simulation is shown in this paper, and compared with the results obtained from the finite element analysis. While piecewise continuous Timoshenko beam model decreases the number of elements significantly; comparable results to the finite element method are obtained.
The optimal control of large angle rapid maneuvers and vibrations of a Shuttle mast reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam. The nonlinear terms in the equations come from the coupling between the angular velocities, the modal coordinates, and the modal rates. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem (TPBVP) is then solved by using the quasilinearization algorithm and the method of particular solutions. In the numerical simulations, the structural parameters and the control limits from the Spacecraft Control Lab Experiment (SCOLE) are used. In the 2-D case, only the motion in the plane of an Earth orbit or the single axis slewing motion is discussed. In the 3-D slewing, the mast is modeled as a continuous beam subjected to 3-D deformations. The numerical results for both the linearized system and the nonlinear system are presented to compare the differences in their time response.
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In this paper, the feasibility of orthogonal polynomials in the meshless local Petrov Galerkin method (MLPG) method is studied. The orthogonal polynomials, Chebyshev and Legendre polynomials, are used in this MLPG method as trial functions. The test functions used were power functions with smooth derivatives at their ends. The performance of these methods is studied by applying these methods to Euler-Bernoulli beam problems. The MLPG-Galerkin and Legendre methods passed all the patch tests for simple beam problems. Next the formulations are tested on complex beam problems such as beams with partial loadings and continuous beam problems. Problems with load discontinuities and additional supports require special attention. Near discontinuities, judicious choice of number of nodes and nodal placements are needed to obtain accurate deflections, slopes, moments and shear forces. As polynomial functions are used, the large number of nodes can create a transformation matrix that is ill-conditioned, resulting in problems with the inversion of the matrix. The conditioning worsens as the number of nodes are increased beyond 20. Quadruple precision was needed for models to obtain accurate solutions. Even with quadruple precision the accuracy of the method suffers as the number of nodes is increased beyond 20. This appears to be a drawback of the MLPG-Chebyshev and MLPG-Legendre methods.
A continuous beam model is developed for approximate analysis of a large, slender, beam-like truss. The model is incorporated in a multi-level optimization scheme for the weight minimization of such trusses. This scheme is tested against traditional optimization procedures for savings in computational cost. Results from both optimization methods are presented for comparison.
Graphite reinforced plastic strip transformed into continuous beam cap. Report describes machine that fabricates beam caps from graphite reinforced thermoplastic materials supplied as strip stock.
The dynamic behavior of flexible rotating beams continues to receive considerable research attention as it constitutes a fundamental problem in applied mechanics. Further, beams comprise parts of many rotating structures of engineering significance. A topic of particular interest at the present time involves the development of techniques for obtaining the behavior in both space and time of a rotor acted upon by a simple airload loading. Most current work on problems of this type use solution techniques based on normal modes. It is certainly true that normal modes cannot be disregarded, as knowledge of natural blade frequencies is always important. However, the present work has considered a computational structural mechanics (CSM) approach to rotor blade dynamics problems in which the physical properties of the rotor blade provide input for a direct numerical solution of the relevant boundary-and-initial-value problem. Analysis of the dynamics of a given rotor system may require solution of the governing equations over a long time interval corresponding to many revolutions of the loaded flexible blade. For this reason, most of the common techniques in computational mechanics, which treat the space-time behavior concurrently, cannot be applied to the rotor dynamics problem without a large expenditure of computational resources. By contrast, the integrating matrix technique of computational mechanics has the ability to consistently incorporate boundary conditions and 'remove' dependence on a space variable. For problems involving both space and time, this feature of the integrating matrix approach thus can generate a 'splitting' which forms the basis of an efficient CSM method for numerical solution of rotor dynamics problems.
Recent literature shows extensive research work on meshless or element-free methods as alternatives to the versatile Finite Element Method. One such meshless method is the Meshless Local Petrov-Galerkin (MLPG) method. In this report, the method is developed for bending of beams - C1 problems. A generalized moving least squares (GMLS) interpolation is used to construct the trial functions, and spline and power weight functions are used as the test functions. The method is applied to problems for which exact solutions are available to evaluate its effectiveness. The accuracy of the method is demonstrated for problems with load discontinuities and continuous beam problems. A Petrov-Galerkin implementation of the method is shown to greatly reduce computational time and effort and is thus preferable over the previously developed Galerkin approach. The MLPG method for beam problems yields very accurate deflections and slopes and continuous moment and shear forces without the need for elaborate post-processing techniques.
Simultaneous observations at about 22 MHz of an Io-unrelated component of Jovian decametric radiation from Voyagers 1 and 2 and from a ground-based observatory are analyzed to investigate the beam structure of the radiation and to locate the radio-emitting region. It is concluded that the radiation of this component is emitted in quasi-continuous beams that corotate with the Jovian inner magnetosphere and that each beam can be approximated by a sector of a hollow cone. The source locations are geometrically determined by fitting a hollow-cone beam model, based on the O4 magnetic field model, to the observations. The result indicates that the radio sources lie above the northern hemisphere and on the field lines that are connected with the ultraviolet aurora of the so-called active sector.
Simple and higher-order difference methods for the solution for the natural frequencies of vibration of a uniform beam are compared. The same basic higher-order method is used throughout for the interior cells, but three different methods of boundary-condition representation are given. Tables and graphs of the error in mode frequencies, as compared with a continuous beam, are given for the various methods as a function of the number of cells. It is concluded that higher-order methods improve accuracy for a given number of cells, with essentially no change in the quantity of computing equipment required.
The Space Fed Lens Array (SFLA) is an alternative to a phased array antenna that replaces large numbers of expensive solid-state phase shifters with a single spatial feed network. SFLA can be used for multi-beam application where multiple independent beams can be generated simultaneously with a single antenna aperture. Unlike phased array antennas where feed loss increases with array size, feed loss in a lens array with more than 50 elements is nearly independent of the number of elements, a desirable feature for large apertures. In addition, SFLA has lower cost as compared to a phased array at the expense of total volume and complete beam continuity. For ground station applications, both of these tradeoff parameters are not important and can thus be exploited in order to lower the cost of the ground station. In this paper, we report the development and demonstration of a 952-element beam-steerable SFLA intended for use as a low cost ground station for communicating and tracking of a low Earth orbiting satellite. The dynamic beam steering is achieved through switching to different feed-positions of the SFLA via a beam controller.