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Hierarchic Extensions in the Static and Dynamic Analysis of Elastic Beams

Approximate solutions of static and dynamic beam problems by the p-version of the finite element method are investigated. Within a hierarchy of engineering beam idealizations, rigorous formulations of the strain and kinetic energies for straight and circular beam elements are presented. These formulations include rotating coordinate system effects and geometric nonlinearities to allow for the evaluation of vertical axis wind turbines, the motivating problem for this research. Hierarchic finite element spaces, based on extensions of the polynomial orders used to approximate the displacement variables, are constructed. The developed models are implemented into a general purpose computer program for evaluation. Quality control procedures are examined for a diverse set of sample problems. These procedures include estimating discretization errors in energy norm and natural frequencies, performing static and dynamic equilibrium checks, observing convergence for qualities of interest, and comparison with more exacting theories and experimental data. It is demonstrated that p-extensions produce exponential rates of convergence in the approximation of strain energy and natural frequencies for the class of problems investigated.

Watson, Robert A.

Dynamic responses of graphite/epoxy laminated beam to impact of elastic spheres

Wave propagation in 90/45/90/-45/902s and 0/45/0/-45/02s laminates of a graphite/epoxy composite due to impact of a steel ball was investigated experimentally and also by using a high order beam finite element. Dynamic strain responses at several locations were obtained using strain gages. The finite element program which incorporated statically determined contact laws was employed to calculate the contact force history as well as the target beam dynamic deformation. The comparison of the finite element solutions with the experimental data indicated that the static contact laws for loading and unloading (developed under this grant) are adequate for the dynamic impact analysis. It was found that for the 0/45/0/-45/02s laminate which has a much larger longitudinal bending rigidity, the use of beam finite elements is not suitable and plate finite element should be used instead.

Sun, C. T.

Study of vibrations produced by a vibrating beam used for vibrating concretes

For compacting concretes in building, vibrating beams are used. The vibrations are generated by inertial vibrators, and the beam is normally displaced by the operator by means of a handle that is elastically fastened to the beam by means of rubber pads. Considered are vibrations transmitted to the operator, taking into account the beam's shock vibration motions. The steady state motion of a dynamic beam pattern is studied, and results of experimental tests with existing equipment are presented.

Silas, C.

Steerable Space Fed Lens Array for Low-Cost Adaptive Ground Station Applications

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.

Lee, Richard Q.

Demonstration of a 1-D Submillimeter-Wave Phased Array with MEMS Phase Shifters

At submillimeter-wave frequencies, due to the nonavailability of low-loss phase shifters, electronic antenna beam scanning is difficult to realize. Traditionally, power-hungry and bulky motors are used to mechanically scan the antenna beam. At lower-frequencies, phased array antennas are most commonly used where low-loss phase shifters are used with the array elements to accomplish beam steering. However, development of similar phased array antennas at submillimeter-waves has been challenging. Recently, we have developed a low-loss microelectromechanical systems (MEMS) based phased shifter in the 500-750 GHz band. In this work, we present a submillimeter-wave phased array antenna system with a cavity-backed double slot antenna architecture using the MEMS-based phase shifters. To demonstrate the concept, we developed two arrays: first one is a 8×1 linear antenna array with a fixed waveguide feeding network that achieved ±20◦ beam scanning, 18 dB directivity, and less than 1 dB scan loss over the design frequency of 500–570 GHz. The second one is a 4 × 1 linear antenna array with integrated MEMS-based phase shifters on each array element, achieving 15 dB directivity and capable of dynamic beam scanning over a range of ±9 ◦ . All the plots presented are simulated results since the parts are currently being fabricated. We hope to have access to our assembly and measurement facilities over the next few months and present measured performances at the conference.

Chattopadhyay, G.

Nonlinear equations for dynamics of pretwisted beams undergoing small strains and large rotations

Nonlinear beam kinematics are developed and applied to the dynamic analysis of a pretwisted, rotating beam element. The common practice of assuming moderate rotations caused by structural deformation in geometric nonlinear analyses of rotating beams was abandoned in the present analysis. The kinematic relations that described the orientation of the cross section during deformation are simplified by systematically ignoring the extensional strain compared to unity in those relations. Open cross section effects such as warping rigidity and dynamics are ignored, but other influences of warp are retained. The beam cross section is not allowed to deform in its own plane. Various means of implementation are discussed, including a finite element formulation. Numerical results obtained for nonlinear static problems show remarkable agreement with experiment.

Hodges, D. H.

Large Deformation Dynamic Bending of Composite Beams

Studies were conducted on the large deformation response of composite beams subjected to a dynamic axial load. The beams were loaded with a moderate eccentricity to promote bending. The study was primarily experimental but some finite element results were obtained. Both the deformation and the failure of the beams were of interest. The static response of the beams was also studied to determine potential differences between the static and dynamic failure. Twelve different laminate types were tested. The beams were loaded dynamically with a gravity driven impactor traveling at 19.6 ft/sec and quasi-static tests were conducted on identical beams in a displacement controlled manner. For laminates of practical interest, the failure modes under static and dynamic loadings were identical. Failure in most of the laminate types occurred in a single event involving 40% to 50% of the plies. However, failure in laminates with 30 deg or 15 deg off-axis plies occured in several events. All laminates exhibited bimodular elastic properties. Using empirically determined flexural properties, a finite element analysis was reasonably accurate in predicting the static and dynamic deformation response.

Derian, E. J.

Large Deformation Dynamic Bending of Composite Beams

Studies were conducted on the large deformation response of composite beams subjected to a dynamic axial load. The beams were loaded with a moderate eccentricity to promote bending. The study was primarily experimental but some finite element results were obtained. Both the deformation and the failure of the beams were of interest. The static response of the beams was also studied to determine potential differences between the static and dynamic failure. Twelve different laminate types were tested. The beams tested were 23 in. by 2 in. and generally 30 plies thick. The beams were loaded dynamically with a gravity-driven impactor traveling at 19.6 ft/sec and quasi-static tests were conducted on identical beams in a displacement controlled manner. For laminates of practical interest, the failure modes under static and dynamic loadings were identical. Failure in most of the laminate types occurred in a single event involving 40% to 50% of the plies. However, failure in laminates with 300 or 150 off-axis plies occurred in several events. All laminates exhibited bimodular elastic properties. The compressive flexural moduli in some laminates was measured to be 1/2 the tensile flexural modulus. No simple relationship could be found among the measured ultimate failure strains of the different laminate types. Using empirically determined flexural properties, a finite element analysis was reasonably accurate in predicting the static and dynamic deformation response.

Derian, E. J.

Shuttle flight control and structure interaction

A brief overview of the (DAP) Dynamic Autopilot is given. Results of the dynamic interaction study of the Orbiter with the General Dynamics Beam are presented. Preliminary results of the three degree of freedom payload parametric study are also presented.

Paluszek, M.

The impulsive hard X-rays from solar flares

A technique for determining the physical arrangement of a solar flare during the impulsive phase was developed based upon a nonthermal model interpretation of the emitted hard X-rays. Accurate values are obtained for the flare parameters, including those which describe the magnetic field structure and the beaming of the energetic electrons, parameters which have hitherto been mostly inaccessible. The X-ray intensity height structure can be described readily with a single expression based upon a semi-empirical fit to the results from many models. Results show that the degree of linear polarization of the X-rays from a flaring loop does not exceed 25 percent and can easily and naturally be as low as the polarization expected from a thermal model. This is a highly significant result in that it supersedes those based upon less thorough calculations of the electron beam dynamics and requires that a reevaluation of hopes of using polarization measurements to discriminate between categories of flare models.

Leach, J.

A comparison of the thick-target model with stereo data on the height structure of solar hard X-ray bursts

The thick target, hard solar X-ray source height structure is predicted for the case of a beam that is injected vertically downward, having a power law spectrum, being dominated by Coulomb collisional energy losses, and being structurally characterized by the ratio of hard X-ray flux from an upper part of the source to that from the entire source. These predictions are compared with the flux ratios at 150 and 350 keV which were observed by two spacecraft for five events in which the solar limb occults part of the source for one spacecraft. The energy dependence of the occultation ratio is found to be inconsistent with that predicted by the model, and it is concluded that noncollisional losses must be significant in beam dynamics.

Brown, J. C.

Experimental validation of structural optimization methods

The topic of validating structural optimization methods by use of experimental results is addressed. The need for validating the methods as a way of effecting a greater and an accelerated acceptance of formal optimization methods by practicing engineering designers is described. The range of validation strategies is defined which includes comparison of optimization results with more traditional design approaches, establishing the accuracy of analyses used, and finally experimental validation of the optimization results. Examples of the use of experimental results to validate optimization techniques are described. The examples include experimental validation of the following: optimum design of a trussed beam; combined control-structure design of a cable-supported beam simulating an actively controlled space structure; minimum weight design of a beam with frequency constraints; minimization of the vibration response of helicopter rotor blade; minimum weight design of a turbine blade disk; aeroelastic optimization of an aircraft vertical fin; airfoil shape optimization for drag minimization; optimization of the shape of a hole in a plate for stress minimization; optimization to minimize beam dynamic response; and structural optimization of a low vibration helicopter rotor.

Adelman, Howard M.

Nanoklystron: A Monolithic Tube Approach to THz Power Generation

The authors propose a new approach to THz power generation: the nanoklystron. Utilizing silicon micromachining techniques, the design and fabrication concept of a monolithic THz vacuum-tube reflex-klystron source is described. The nanoklystron employs a separately fabricated cathode structure composed of densely packed carbon nanotube field emitters and an add-in repeller. The nanotube cathode is expected to increase the current density, extend the cathode life and decrease the required oscillation voltage to values below 100 V. The excitation cavity is based on ridged-waveguide and differs from the conventional cylindrical re-entrant structures found in lower frequency klystrons. A quasi-static field analysis of the cavity and output coupling structure show excellent control of the quality factor and desired field distribution. Output power is expected to occur through an iris coupled matched rectangular waveguide and integrated pyramidal feed horn. The entire circuit is designed so as to be formed monolithically from two thermocompression bonded silicon wafers processed using deep reactive ion etching (DRIE) techniques. To expedite prototyping, a 600 GHz mechanically machined structure has been designed and is in fabrication. A complete numeric analysis of the nanoklystron circuit, including the electron beam dynamics has just gotten underway. Separate evaluation of the nanotube cathodes is also ongoing. The authors will describe the progress to date as well as plans for the immediate implementation and testing of nanoklystron prototypes at 640 and 1250 GHz.

Siegel, Peter H.

Integrated Antenna/Solar Array Cell (IA/SAC) System for Flexible Access Communications

Present satellite communications systems normally use separate solar cells and antennas. Since solar cells generally account for the largest surface area of the spacecraft, co-locating the antenna and solar cells on the same substrate opens the possibility for a number of data-rate-enhancing communications link architecture that would have minimal impact on spacecraft weight and size. The idea of integrating printed planar antenna and solar array cells on the same surface has been reported in the literature. The early work merely attempted to demonstrate the feasibility by placing commercial solar cells besides a patch antenna. Recently, Integrating multiple antenna elements and solar cell arrays on the same surface was reported for both space and terrestrial applications. The application of photovoltaic solar cell in a planar antenna structure where the radiating patch antenna is replaced by a Si solar cell has been demonstrated in wireless communication systems (C. Bendel, J. Kirchhof and N. Henze, 3rd Would Photovotaic Congress, Osaka, Japan, May 2003). Based on a hybrid approach, a 6x1 slot array with circularly polarized crossdipole elements co-located on the same surface of the solar cells array has been demonstrated (S. Vaccaro, J. R. Mosig and P. de Maagt, IEEE Trans. Ant. and Propag., Vol. 5 1, No. 8, Aug. 2003). Amorphous silicon solar cells with about 5-10% efficiency were used in these demonstrations. This paper describes recent effort to integrate advanced solar cells with printed planar antennas. Compared to prior art, the proposed WSAC concept is unique in the following ways: 1) Active antenna element will be used to achieve dynamic beam steering; 2) High efficiency (30%) GaAs multi-junction solar cells will be used instead of Si, which has an efficiency of about 15%; 3) Antenna and solar cells are integrated on a common GaAs substrate; and 4) Higher data rate capability. The IA/SAC is designed to operate at X-band (8-12 GH) and higher frequencies Higher operating frequencies enable greater bandwidth and thus higher data transfer rates. The first phase of the effort involves the development of GaAs solar cell MIMs (Monolithically Integrated Module) with a single patch antenna on the opposite side of the substrate. Subsequent work will involve the integration of MIMs and antennas on the same side of the substrate. Results from the phase one efforts will be presented.

Lee, Ricard Q.

Integrated Phase Array Antenna/Solar Cell System for Flexible Access Communication (IA/SAC)

This paper describes recent efforts to integrate advanced solar cells with printed planar antennas. Several previous attempts have been reported in the literature, but this effort is unique in several ways. It uses Gallium Arsenide (GaAs) multi-junction solar cell technology. The solar cells and antennas will be integrated onto a common GaAs substrate. When fully implemented, IA/SAC will be capable of dynamic beam steering. In addition, this program targets the X-band (8 - 12 GHz) and higher frequencies, as compared to the 2.2 - 2.9 GHz arrays targeted by other organizations. These higher operating frequencies enable a greater bandwidth and thus higher data transfer rates. The first phase of the effort involves the development of 2 x 2 cm GaAs Monolithically Integrated Modules (MIM) with integrated patch antennas on the opposite side of the substrate. Subsequent work will involve the design and development of devices having the GaAs MIMs and the antennas on the same side of the substrate. Results from the phase one efforts will be presented.

Clark, E. B.

Feasibility of Traveling Wave Direct Energy Conversion of Fission Reaction Fragments

Fission fragment direct energy conversion has been considered in the past for the purpose of increasing nuclear power plant efficiency and for advanced space propulsion. Since the fragments carry electric charge (typically in the order of 20 e) and have 100 MeV-range kinetic energy, techniques utilizing very high-voltage DC electrodes have been considered. This study is focused on a different approach: the kinetic energy of the charged fission fragments is converted into alternating current by means of a traveling wave coupling scheme (Traveling Wave Direct Energy Converter, TWDEC), thereby not requiring the utilization of high voltage technology. A preliminary feasibility analysis of the concept is introduced based on a conceptual level study and on a particle simulation model of the beam dynamics.

Tarditi, A. G.

Dynamics and control of orbiting grid and the synchronously deployable beam

The dynamic analysis of a grid structure hung from the ceiling by two steel wires is described. The method of approach uses the discrete mass model system. The concept of the bifilar pendulum is used in writing the equation of motion. Assumptions are made with regard to the bar stiffnesses in the vertical and horizontal planes. The discrete mases are assumed to be connected by inextensible massless strings that do not provide any torsion or bending. The modal frequencies obtained by this method are compared with those obtained from the finite element model.

Abu-Saba, E. G.