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Simplified truss-beam modeling - Dynamic analysis

A model of the truss-beam has been developed and a set of algorithms provided to determine the flexibility matrix. Using lumped masses at the panel juncture, and applying the flexibility matrix in the equation of motion for the system, the dynamic characteristics are readily determined. An interactive computer program has been developed both in Basic and in Fortran for the IMB PC and other compatible micro-computers. This method is used to determine the lower natural frequencies of two truss-beams, and the results compared with those found by others.

Abu-Saba, Elias G.↗

Gamma-ray absorption for a beam model of NP0532.

The model involves an assessment of the effect of beaming as indicated by the pulsations themselves rather than by assuming gamma-ray absorption by interaction with an isotropic photon field. The chief absorption process to be taken into account is that of pair production in the intense photon field. Most important is the pair production in the intense photon field which occurs during the pulse.

Stecker, F. W.↗

Considerations for the application of finite element beam modeling to vibration analysis of flight vehicle structures

The manner of representing a flight vehicle structure as an assembly of beam, spring, and rigid-body components for vibration analysis is described. The development is couched in terms of a substructures methodology which is based on the finite-element stiffness method. The particular manner of employing beam, spring, and rigid-body components to model such items as wing structures, external stores, pylons supporting engines or external stores, and sprung masses associated with launch vehicle fuel slosh is described by means of several simple qualitative examples. A detailed numerical example consisting of a tilt-rotor VTOL aircraft is included to provide a unified illustration of the procedure for representing a structure as an equivalent system of beams, springs, and rigid bodies, the manner of forming the substructure mass and stiffness matrices, and the mechanics of writing the equations of constraint which enforce deflection compatibility at the junctions of the substructures. Since many structures, or selected components of structures, can be represented in this manner for vibration analysis, the modeling concepts described and their application in the numerical example shown should prove generally useful to the dynamicist.

Kvaternik, R. G.↗

Pulsar average waveforms and hollow cone beam models

An analysis of pulsar average waveforms at radio frequencies from 40 MHz to 15 GHz is presented. The analysis is based on the hypothesis that the observer sees one cut of a hollow-cone beam pattern and that stationary properties of the emission vary over the cone. The distributions of apparent cone widths for different observed forms of the average pulse profiles (single, double/unresolved, double/resolved, triple and multiple) are in modest agreement with a model of a circular hollow-cone beam with random observer-spin axis orientation, a random cone axis-spin axis alignment, and a small range of physical hollow-cone parameters for all objects.

Backer, D. C.↗

Gamma-ray absorption for a beam model of the Crab nebula pulsar NP0532

A model is discussed for determining gamma ray absorption from NP0532 by estimating the effect of beaming as indicated by the pulsations. The main absorption process is considered to be that of pair production in the intense photon field which occurs during the pulse. The results indicate that for this model, absorption does not occur below 10 GeV.

Stecker, F. W.↗

Equivalent beam modeling using numerical reduction techniques

Numerical procedures that can accomplish model reductions for space trusses were developed. Three techniques are presented that can be implemented using current capabilities within NASTRAN. The proposed techniques accomplish their model reductions numerically through use of NASTRAN structural analyses and as such are termed numerical in contrast to the previously developed analytical techniques. Numerical procedures are developed that permit reductions of large truss models containing full modeling detail of the truss and its joints. Three techniques are presented that accomplish these model reductions with various levels of structural accuracy. These numerical techniques are designated as equivalent beam, truss element reduction, and post-assembly reduction methods. These techniques are discussed in detail.

Chapman, J. M.↗

A beaming model of the Io-independent Jovian decameter radiation based on multipole models of the Jovian magnetic field

A geometrical model is presented in which the apparent source locations of the Io-independent decameter radiation are computed. The calculations assume that the radiation is produced by stably trapped electrons radiating near the electron gyrofrequency and that the emission is then beamed onto a conical surface. The maximum occurrence probability of noise storms is associated with regions in the Jovian magnetosphere where the axis of the emission cone is most inclined toward the Jovian equatorial plane. The calculations utilize and compare two of the octupole spherical harmonic expansions of the Jovian magnetic field constructed from data accumulated by the fluxgate and vector helium magnetometers on board Pioneer 11.

Goldstein, M. L.↗

A beaming model of the Io-independent Jovian decameter radiation based on multipole models of the Jovian magnetic field

A geometrical model is presented in which the apparent source locations of the Io-independent decameter radiation are computed. The calculations assume that the radiation is produced by stably trapped electrons radiating near the local electron gyrofrequency and that the emission is then beamed onto a conical surface. The maximum occurrence probability of noise storms is associated with regions in the Jovian magnetosphere where the axis of the emission cone is most inclined toward the Jovian equatorial plane. The calculations utilize and compare two of the octopole spherical harmonic expansions of the Jovian magnetic field constructed from data accumulated by the fluxgate and vector helium magnetometers on board Pioneer 11.

Goldstein, M. L.↗

Estimation of Boltzmann damping coefficients in beam models

A distributed parameter model of a flexible structure with Boltzmann type viscoelastic damping is discussed. A computational method for the estimation of the damping parameters is developed, and theoretical convergence results are given. An example is presented in which actual experimental data is used, demonstrating the efficacy of the computational method and the plausibility of the model for predicting response in damped structures.

Banks, H. T.↗

A fully Sinc-Galerkin method for Euler-Bernoulli beam models

A fully Sinc-Galerkin method in both space and time is presented for fourth-order time-dependent partial differential equations with fixed and cantilever boundary conditions. The Sinc discretizations for the second-order temporal problem and the fourth-order spatial problems are presented. Alternate formulations for variable parameter fourth-order problems are given which prove to be especially useful when applying the forward techniques to parameter recovery problems. The discrete system which corresponds to the time-dependent partial differential equations of interest are then formulated. Computational issues are discussed and a robust and efficient algorithm for solving the resulting matrix system is outlined. Numerical results which highlight the method are given for problems with both analytic and singular solutions as well as fixed and cantilever boundary conditions.

Smith, R. C.↗

Numerical recovery of material parameters in Euler-Bernoulli beam models

A fully Sinc-Galerkin method for recovering the spatially varying stiffness parameter in fourth-order time-dependence problems with fixed and cantilever boundary conditions is presented. The forward problems are discretized with a sinc basis in both the spatial and temporal domains. This yields an approximation solution which converges exponentially and is valid on the infinite time interval. When the forward methods are applied to parameter recovery problems, the resulting inverse problems are ill-posed. Tikhonov regularization is applied and the resulting minimization problems are solved via a quasi-Newton/trust region algorithm. The L-curve method is used to determine an appropriate value of the regularization parameter. Numerical results which highlight the method are given for problems with both fixed and cantilever boundary conditions.

Smith, R. C.↗

Build-up Approach to Updating the Mock Quiet Spike(TradeMark) Beam Model

A crucial part of aircraft design is ensuring that the required margin for flutter is satisfied. A trustworthy flutter analysis, which begins by possessing an accurate dynamics model, is necessary for this task. Traditionally, a model was updated manually by fine tuning specific stiffness parameters until the analytical results matched test data. This is a time consuming iterative process. NASA Dryden Flight Research Center has developed a mode matching code to execute this process in a more efficient manner. Recently, this code was implemented in the F-15B/Quiet Spike(TradeMark) (Gulfstream Aerospace Corporation, Savannah, Georgia) model update. A build-up approach requiring several ground vibration test configurations and a series of model updates was implemented in order to determine the connection stiffness between aircraft and test article. The mode matching code successfully updated various models for the F-15B/Quiet Spike(TradeMark) project to within 1 percent error in frequency and the modal assurance criteria values ranged from 88.51-99.42 percent.

Herrera, Claudia Y.↗

Build-up Approach to Updating the Mock Quiet Spike(TM)Beam Model

A crucial part of aircraft design is ensuring that the required margin for flutter is satisfied. A trustworthy flutter analysis, which begins by possessing an accurate dynamics model, is necessary for this task. Traditionally, a model was updated manually by fine tuning specific stiffness parameters until the analytical results matched test data. This is a time consuming iterative process. The NASA Dryden Flight Research Center has developed a mode matching code to execute this process in a more efficient manner. Recently, this code was implemented in the F-15B/Quiet Spike (Gulfstream Aerospace Corporation, Savannah, Georgia) model update. A build-up approach requiring several ground vibration test configurations and a series of model updates was implemented to determine the connection stiffness between aircraft and test article. The mode matching code successfully updated various models for the F-15B/Quiet Spike project to within 1 percent error in frequency and the modal assurance criteria values ranged from 88.51-99.42 percent.

Herrera, Claudia Y.↗

Build-Up Approach to Updating the Mock Quiet Spike Beam Model

When a new aircraft is designed or a modification is done to an existing aircraft, the aeroelastic properties of the aircraft should be examined to ensure the aircraft is flight worthy. Evaluating the aeroelastic properties of a new or modified aircraft can include performing a variety of analyses, such as modal and flutter analyses. In order to produce accurate results from these analyses, it is imperative to work with finite element models (FEM) that have been validated by or correlated to ground vibration test (GVT) data, Updating an analytical model using measured data is a challenge in the area of structural dynamics. The analytical model update process encompasses a series of optimizations that match analytical frequencies and mode shapes to the measured modal characteristics of structure. In the past, the method used to update a model to test data was "trial and error." This is an inefficient method - running a modal analysis, comparing the analytical results to the GVT data, manually modifying one or more structural parameters (mass, CG, inertia, area, etc.), rerunning the analysis, and comparing the new analytical modal characteristics to the GVT modal data. If the match is close enough (close enough defined by analyst's updating requirements), then the updating process is completed. If the match does not meet updating-requirements, then the parameters are changed again and the process is repeated. Clearly, this manual optimization process is highly inefficient for large FEM's and/or a large number of structural parameters. NASA Dryden Flight Research Center (DFRC) has developed, in-house, a Mode Matching Code that automates the above-mentioned optimization process, DFRC's in-house Mode Matching Code reads mode shapes and frequencies acquired from GVT to create the target model. It also reads the current analytical model, as we11 as the design variables and their upper and lower limits. It performs a modal analysis on this model and modifies it to create an updated model that has similar mode shapes and frequencies as those of the target model. The Mode Matching Code output frequencies and modal assurance criteria (MAC) values that allow for the quantified comparison of the updated model versus the target model. A recent application of this code is the F453 supersonic flight testing platform, NASA DFRC possesses a modified F-15B that is used as a test bed aircraft for supersonic flight experiments. Traditionally, the finite element model of the test article is generated. A GVT is done on the test article ta validate and update its FEM. This FEM is then mated to the F-15B model, which was correlated to GVT data in fall of 2004, A GVT is conducted with the test article mated to the aircraft, and this mated F-15B/ test article FEM is correlated to this final GVT.

Herrera, Claudia Y.↗

The Effect of Beam Loading on Water Impact Loads and Motions

An investigation of the effect of beam loading on impact loads and motions has been conducted in the Langley impact basin. Water impact tests of flat-bottom 5-inch-and 8-inch-beam models having beam-loading coefficients C(sub Delta) from 62.5 to 544 and a 30 deg dead-rise 5-inch-beam model A having beam-loading coefficients from 208 to 530 are described and the results analyzed to show trends of these heavy-beam-loading data with initial flight-path angle, trim angle, dead-rise angle, and time through- out the impact. Data from flat-bottom model tests, C(sub Delta) = 4.4 to 36.5, and from 30 deg dead-rise model tests, C(sub Delta) = 0.58 and 18.8, are included, along with the heavy-beam-loading data; and variations of these data with beam-loading coefficients are shown. Each of the load and motion coefficients is found to be directly proportional to a power factor of C(sub Delta). For instance, the maximum impact lift coefficient is found C(sub L,max) to be directly proportional to C(sub Delta, exp 0,33) for the flat-bottom model and C(sub Delta, exp 0,45) for the 30 deg dead-rise model. These variations of C(sub L, max) with C(sub Delta) are found to be in agreement with theoretical variations. Finally, an empirical equation for the prediction of C(sub L,max) is presented and is shown to give good agreement with experimental C(sub L, max) for about 500 fixed-trim smooth-water impacts. The range of variables included dead-rise angles from 0 deg to deg, beam-loading coefficients from o.48 to 544, trim angles from 3 deg to deg, and initial flight-path angles from about 2 deg to about deg.

Mixson, John S.↗

The Effect of Beam Loading on Water Impact Loads and Motions

An investigation of the effect of beam loading on impact loads and motions has been conducted in the Langley impact basin. Water impact tests of flat-bottom 5-inch- and 8-inch-beam models having beam-loading coefficients C(sub Delta) from 62.5 to 544 and a 30 0 dead-rise 5-inch-beam model A having beam-loading coefficients from 208 to 530 are described and the results analyzed to show trends of these heavy-beam-loading data with initial flight-path angle, trim angle, dead-rise angle, and time throughout the impact. Data from flat-bottom model tests, C(sub Delta) = 4.4 to 36.5, and from 300 dead-rise model tests, C(sub Delta)A = 0.58 and 18.8, are included, along with the heavy-beam-loading data; and variations of these data with beam-loading coefficients are shown. Each of the load and motion coefficients is found to be directly proportional to a power factor ofC(sub Delta). For instance, the maximum impact lift coefficient C(sub L,max)is found to be directly proportional to C(sub Delta)(sup 0.33) for the flat-bottom model and C(sub Delta)(sup 0.45) for the 30 deg dead-rise model. These variations of C(sub L,max) C(sub Delta) are found to be in agreement with theoretical variations. Finally, an empirical equation for the prediction of C(sub L,max) is presented and is shown to give good agreement with experimental C(sub L,max) for about 500 fixed-trim smooth-water impacts. The range of variables included dead-rise angles from 0 deg to 30 deg, beam-loading coefficients from 0.48 to 544, trim angles from 3 deg to 45 deg and initial flight-path angles from about 2 deg to about 27 deg.

Mixson, John S.↗