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Variations in the modal characteristics of different Space Shuttle Main Engines (SSMEs) are presented herein to study their structural dynamics vibrations, especially under fluid/structure interaction. The results of extensive modal survey tests and analysis relative to significant features in the modal characteristics of different powerheads and components are discussed.
Real disturbances and real sensors have finite bandwidths. The first objective of this paper is to incorporate this finiteness in the 'open-loop modal cost analysis' as applied to a flexible spacecraft. Analysis based on residue calculus shows that among other factors, significance of a mode depends on the power spectral density of disturbances and the response spectral density of sensors at the modal frequency. The second objective of this article is to compare performances of an optimal and a suboptimal output feedback controller, the latter based on 'minimum error excitation' of Kosut. Both the performances are found to be nearly the same, leading us to favor the latter technique because it entails only linear computations. Our final objective is to detect an instability due to truncated modes by representing them as a multiplicative and an additive perturbation in a nominal transfer function. In an example problem it is found that this procedure leads to a narrow range of permissible controller gains, and that it labels a wrong mode as a cause of instability. A free beam is used to illustrate the analysis in this work.
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The derivation and application of a Rayleigh-Ritz modal vibration analysis are presented for ring and/or stringer stiffened noncircular cylindrical shells with arbitrary end conditions. Comparisons with previous results from experimental and analytical studies showed this method of analysis to be accurate for a variety of end conditions. Results indicate a greater effect of rings on natural frequencies than of stringers.
To obtain a reduced model of a mechanical system, one can identify the dominant modes and retain those as the reduced model. Two widely used schemes for selection of dominant modes are modal cost analysis (MCA) and balancing, but neither of these methods guarantees that the model error is small, where model error measures the difference between the output of the full model and the output of the reduced model. The authors introduce a set of coordinates called pseudo uncorrelated modal coordinates (PUnc) that can be used in conjunction with component cost analysis to select dominant modes yielding a reduced model with minimum model error. Furthermore, unlike MCA and balancing, the accuracy of the reduced model (the model error) in PUnc coordinates can be evaluated before reduction.
A modal aeroelastic analysis combining structural and aerodynamic models is applied to counterrotating propfans to evaluate their structural integrity for wind-tunnel testing. The aeroelastic analysis code is an extension of the 2D analysis code called the Aeroelastic Stability and Response of Propulsion Systems. Rotational speed and freestream Mach number are the parameters for calculating the stability of the two blade designs with a modal method combining a finite-element structural model with 2D steady and unsteady cascade aerodynamic models. The model demonstrates convergence to the least stable aeroelastic mode, describes the effects of a nonuniform inflow, and permits the modification of geometry and rotation. The analysis shows that the propfan designs are suitable for the wind-tunnel test and confirms that the propfans should be flutter-free under the range of conditions of the testing.
Petrographic data form six size fractions for six samples of Apollo 16 drive tube section 64002 show source rocks similar to those of core 60009. Analysis of modal data from the 64002 core show that the upper three and lowest core soils are mature and have similar maturation histories, while the two middle soils are submature and have histories that are similar to each other but unlike those from the aforementioned soils. In all of these soils, mixing has dominated over reworking, and appears to involve two mature soils distinguished by differing source rocks and an immature, plagioclase-rich soil which is correlated with larger clasts of chalky, friable breccia. These breccias and the plagioclase-rich soil are tentatively associated with the Descartes Formation.
We present a generalized theoretical framework that allows the approximate but rapid analysis of residual couplings of arbitrary decoupling sequences in solid-state NMR under magic-angle spinning conditions. It is a generalization of the tri-modal Floquet analysis of TPPM decoupling [Scholz et al., J. Chem. Phys. 130, 114510 (2009)] where three characteristic frequencies are used to describe the pulse sequence. Such an approach can be used to describe arbitrary periodic decoupling sequences that differ only in the magnitude of the Fourier coefficients of the interaction-frame transformation. It allows a ∼100 times faster calculation of second-order residual couplings as a function of pulse sequence parameters than full spin-dynamics simulations. By comparing the theoretical calculations with full numerical simulations, we show the potential of the new approach to examine the performance of decoupling sequences. We exemplify the usefulness of this framework by analyzing the performance of commonly used high-power decoupling sequences and low-power decoupling sequences such as amplitude-modulated XiX (AM-XiX) and its super-cycled variant SC-AM-XiX. In addition, the effect of chemical-shift offset is examined for both high- and low-power decoupling sequences. The results show that the cross-terms between the dipolar couplings are the main contributions to the line broadening when offset is present. We also show that the SC-AM-XIX shows a better offset compensation.
The use of an orthogonal set of specially selected Ritz vectors is shown to be very effective in reducing the cost of dynamic analysis by modal superposition. Several mechanical structures are examined, and the Ritz vector approach is compared to the classical eigenvector approach on the basis of cost, accuracy and elapsed analysis (throughput) time. Mathematical proof of the completeness of orthogonal Ritz vectors is provided for the case of a positive definite mass matrix and a symmetric stiffness matrix.
The two-dimensional subsonic cascade unsteady aerodynamic theory of Jones and Rao (1975) has been modified to account for the variable sweep angles of the blades of advanced turbopropellers. The aerodynamics and the structural modal properties have been formally integrated to determine the generalized aerodynamic coefficients matrix for the blade modes. Modal flutter analysis has been conducted for two SR-5 five- and ten-blade propellers, and analytical results have been found to be in very good agreement with wind tunnel test data.
This report describes a computer program (program D2180) that has been prepared to implement the analysis described in (N71-10866) for calculating the aerodynamic forces on a class of harmonically oscillating planar lifting surfaces in supersonic potential flow. The planforms treated are the delta and modified-delta (arrowhead) planforms with subsonic leading and supersonic trailing edges, and (essentially) pointed tips. The resulting aerodynamic forces are applied in a Galerkin modal flutter analysis. The required input data are the flow and planform parameters including deflection-mode data, modal frequencies, and generalized masses.
We investigate the feasibility of beam position diagnostics using higher order mode (HOM) signals excited by an electron beam in the third harmonic 3.9 GHz superconducting accelerating cavities at FLASH. After careful theoretical and experimental assessment of the HOM spectrum, three modal choices have been narrowed down to fulfill different diagnostics requirements. These are localized dipole beam-pipe modes, trapped cavity modes from the fifth dipole band, and propagating modes from the first two dipole bands. These modes are treated with various data analysis techniques: modal identification, direct linear regression (DLR), and singular value decomposition (SVD). Promising options for beam diagnostics are found from all three modal choices. This constitutes the first prediction, subsequently confirmed by experiments, of trapped HOMs in third harmonic cavities, and also the first direct comparison of DLR and SVD in the analysis of HOM-based beam diagnostics.
An effective procedure for NASTRAN was developed that permits any number of substructures of any size to be synthesized for the purpose of developing normal modes of vibration of the complete structural system. The technique is extended to permit modal transient analysis of the subdivided system. This latter procedure permits the use of NASTRAN's ability to include nonlinear forces in the problem. The five-phase process is accomplished using standard NASTRAN rigid formats with problem-independent alter packages and DMAP sequences.
Purpose: This work proposes a new method of building 3D models of microcalcification clusters and describes the validation of their realistic appearance when simulated into 2D digital mammograms and into breast tomosynthesis images. Methods: A micro-CT unit was used to scan 23 breast biopsy specimens of microcalcification clusters with malignant and benign characteristics and their 3D reconstructed datasets were segmented to obtain 3D models of microcalcification clusters. These models were then adjusted for the x-ray spectrum used and for the system resolution and simulated into 2D projection images to obtain mammograms after image processing and into tomographic sequences of projection images, which were then reconstructed to form 3D tomosynthesis datasets. Six radiologists were asked to distinguish between 40 real and 40 simulated clusters of microcalcifications in two separate studies on 2D mammography and tomosynthesis datasets. Receiver operating characteristic (ROC) analysis was used to test the ability of each observer to distinguish between simulated and real microcalcification clusters. The kappa statistic was applied to assess how often the individual simulated and real microcalcification clusters had received similar scores (''agreement'') on their realistic appearance in both modalities. This analysis was performed for all readers and for the real and the simulated group of microcalcification clusters separately. ''Poor'' agreement would reflect radiologists' confusion between simulated and real clusters, i.e., lesions not systematically evaluated in both modalities as either simulated or real, and would therefore be interpreted as a success of the present models. Results: The area under the ROC curve, averaged over the observers, was 0.55 (95% confidence interval [0.44, 0.66]) for the 2D study, and 0.46 (95% confidence interval [0.29, 0.64]) for the tomosynthesis study, indicating no statistically significant difference between real and simulated lesions (p > 0.05). Agreement between allocated lesion scores for 2D mammography and those for the tomosynthesis series was poor. Conclusions: The realistic appearance of the 3D models of microcalcification clusters, whether malignant or benign clusters, was confirmed for 2D digital mammography images and the breast tomosynthesis datasets; this database of clusters is suitable for use in future observer performance studies related to the detectability of microcalcification clusters. Such studies include comparing 2D digital mammography to breast tomosynthesis and comparing different reconstruction algorithms.
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The effect of sweep on fan blade flutter is studied by applying the analytical methods developed for aeroelastic analysis of advance turboprops. Two methods are used. The first method utilizes an approximate structural model in which the blade is represented by a swept, nonuniform beam. The second method utilizes a finite element technique to conduct modal flutter analysis. For both methods the unsteady aerodynamic loads are calculated using two dimensional cascade theories which are modified to account for sweep. An advanced fan stage is analyzed with 0, 15 and 30 degrees of sweep. It is shown that sweep has a beneficial effect on predominantly torsional flutter and a detrimental effect on predominantly bending flutter. This detrimental effect is shown to be significantly destabilizing for 30 degrees of sweep.
The effect of sweep on fan blade flutter is studied by applying the analytical methods developed for aeroelastic analysis of advance turboprops. Two methods are used. The first method utilizes an approximate structural model in which the blade is represented by a swept, nonuniform beam. The second method utilizes a finite element technique to conduct modal flutter analysis. For both methods the unsteady aerodynamic loads are calculated using two dimensional cascade theories which are modified to account for sweep. An advanced fan stage is analyzed with 0, 15 and 30 degrees of sweep. It is shown that sweep has a beneficial effect on predominantly torsional flutter and a detrimental effect on predominantly bending flutter. This detrimental effect is shown to be significantly destabilizing for 30 degrees of sweep.
The Microwave Anisotropy Probe (MAP) is a follow-on to the Differential Microwave Radiometer (DMR) instrument on the Cosmic Background Explorer (COBE) spacecraft. The design and analysis of the MAP attitude control system (ACS) have been refined since work previously reported. The full spacecraft and instrument flexible model was developed in NASTRAN, and the resulting flexible modes were plotted and reduced with the Modal Significance Analysis Package (MSAP). The reduced-order model was used to perform the linear stability analysis for each control mode, the results of which are presented in this paper. Although MAP is going to a relatively disturbance-free Lissajous orbit around the Earth-Sun L(2) Lagrange point, a detailed disturbance-torque analysis is required because there are only a small number of opportunities for momentum unloading each year. Environmental torques, including solar pressure at L(2), aerodynamic and gravity gradient during phasing-loop orbits, were calculated and simulated. Thruster plume impingement torques that could affect the performance of the thruster modes were estimated and simulated, and a simple model of fuel slosh was derived to model its effect on the motion of the spacecraft. In addition, a thruster mode linear impulse controller was developed to meet the accuracy requirements of the phasing loop burns. A dynamic attitude error limiter was added to improve the performance of the ACS during large attitude slews. The result of this analysis is a stable ACS subsystem that meets all of the mission's requirements.