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Estimating free-body modal parameters from tests of a constrained structure

Hardware advances in suspension technology for ground tests of large space structures provide near on-orbit boundary conditions for modal testing. Further advances in determining free-body modal properties of constrained large space structures have been made, on the analysis side, by using time domain parameter estimation and perturbing the stiffness of the constraints over multiple sub-tests. In this manner, passive suspension constraint forces, which are fully correlated and therefore not usable for spectral averaging techniques, are made effectively uncorrelated. The technique is demonstrated with simulated test data.

Cooley, Victor M.↗

Analyzing Aeroelastic Stability of a Tilt-Rotor Aircraft

Proprotor Aeroelastic Stability Analysis, now at version 4.5 (PASTA 4.5), is a FORTRAN computer program for analyzing the aeroelastic stability of a tiltrotor aircraft in the airplane mode of flight. The program employs a 10-degree- of-freedom (DOF), discrete-coordinate, linear mathematical model of a rotor with three or more blades and its drive system coupled to a 10-DOF modal model of an airframe. The user can select which DOFs are included in the analysis. Quasi-steady strip-theory aerodynamics is employed for the aerodynamic loads on the blades, a quasi-steady representation is employed for the aerodynamic loads acting on the vibrational modes of the airframe, and a stability-derivative approach is used for the aerodynamics associated with the rigid-body DOFs of the airframe. Blade parameters that vary with the blade collective pitch can be obtained by interpolation from a user-defined table. Stability is determined by examining the eigenvalues that are obtained by solving the coupled equations of motions as a matrix eigenvalue problem. Notwithstanding the relative simplicity of its mathematical foundation, PASTA 4.5 and its predecessors have played key roles in a number of engineering investigations over the years.

Kvaternil, Raymond G.↗

Shockwave/Boundary-Layer Interaction Studies Performed in the NASA Langley 20-Inch Mach 6 Air Tunnel

This paper highlights results from a collaborative study performed by The University of Tennessee Space Institute (UTSI) and NASA Langley Research Center on the Shockwave/Boundary-Layer Interaction (SWBLI) generated by a cylindrical protuberance on a flat plate in a Mach 6 flow. The study was performed in the 20-Inch Mach 6 Air Tunnel at NASA Langley Research Center and consisted of two separate entries. In the first entry, simultaneous high-speed schlieren and high-speed pressure-sensitive paint (PSP) imaging – which was performed for the first time in the 20-Inch Mach 6 facility at NASA Langley – were performed as well as simultaneous high-speed schlieren and oil-flow imaging. In the second entry, the model configuration was modified to increase the size of the interaction region. High-speed schlieren and infrared thermography (IR) surface imaging were performed in this second entry. The goal of these tests was to characterize the SBLI in the presence of a laminar, transitional, and turbulent boundary layer using high-speed optical imaging techniques. AoA = sting angle-of-attack (°) dcylinder = cylinder diameter (mm) dtrip = cylindrical tripping element diameter (mm) Δshock = shock stand-off distance (mm) hcylinder = cylinder height (mm) htrip = cylindrical tripping element height (mm) HSS = high-speed schlieren M∞ = freestream Mach number PSP = pressure-sensitive paint Re∞ = freestream unit Reynolds number (m-1) SWBLI = shockwave/boundary-layer interaction θplate = model plate angle (°) Introduction his paper highlights two experimental entries performed in the 20-Inch Mach 6 Air Blowdown Tunnel at NASA Langley Research Center in collaboration with The University of Tennessee Space Institute (UTSI). The purpose of these entries was to characterize the dynamic shockwave/boundary-layer interaction (SWBLI) between a vertical cylinder on a flat plate and laminar, transitional (XSWBLI), and turbulent (SWTBLI) boundary layers with a freestream Mach number of 6 using non-intrusive optical diagnostics. Experiments performed by Murphree et al.1,2 were among the first to specifically characterize XSWBLI induced by a vertical cylinder on a flat plate geometry using several optical measurement techniques. Recent optical studies of XSWBLI phenomenon have been performed by UTSI at Mach 2 in their low-enthalpy blow wind tunnel3-8 and by Texas A&M University and UTSI at Mach numbers of 6 and 7 in their Adjustable Contour Expansion wind tunnel.9 The experiments described in this paper were intended to complement previous studies by expanding the freestream unit Reynolds number range, Re∞, over which the XSWBLI phenomena has been observed. Additionally these experiments, made possible under NASA’s new facility funding model under the Aeronautics Evaluation and Test Capabilities (AETC) project, promoted collaboration between university and NASA researchers. The initial entry in the 20-Inch Mach 6 Air Tunnel at NASA Langley occurred in December of 2016. Originally, testing was to occur in November of 2016 in the 31-Inch Mach 10 Air Tunnel at NASA Langley. This facility was chosen so that the XSWBLI phenomenon could be observed at much higher Mach numbers than had previously been attempted in ground test experiments. The model selected for this experiment, a 10° half-angle wedge with a sharp leading edge (described in detail in section II.B), had previously been used by Danehy et al. [10] for boundary layer transition studies using the nitric oxide planar laser-induced fluorescence (NO PLIF) flow visualization technique. In that work, it was determined that transition could be induced downstream of a single htrip = 1-mm tall, dtrip = 4-mm diameter cylindrical tripping element and that the streamwise location of the transition could be changed for a single Re∞ by changing the model angle-of-attack (AoA) (see Fig. A3 in Ref. [10] for more details). Based on the findings of that work, a decision was made to use the wedge model with the cylindrical tripping element to trip the boundary layer flow ahead of a cylindrical protuberance in order to achieve a XSWBLI. Unfortunately, the 31-Inch Mach 10 facility had been taken offline for repairs in October of 2016 and a decision was made to move the test to the 20-Inch Mach 6 facility. Since the behavior of the boundary layer with the chosen model configuration had not been studied before in that facility and the available test time was limited, the entry was considered to be exploratory and was used to collect spatially-resolved and time-resolved flow and surface visualization data that would be used to inform a second entry. Test techniques included simultaneous high-speed schlieren (HSS) captured at 160 kHz and high-speed pressure sensitive paint captured at 10 kHz as well as oil flow visualization, captured at 750 Hz. The second entry in the 20-Inch Mach 6 facility occurred in June and July of 2017. In this follow-on test, modifications to the wind tunnel model were made based on observations made during the first entry and included removing the cylindrical tripping element, increasing the size of the cylinder used to induce the SWBLI to increase the size of the interaction while simultaneously improving spatial resolution, and using a swept ramp array, similar to that described in Ref. [11], to trip the flow to turbulence. Simultaneous HSS (captured at 140 kHz, 100 kHz, and 40 kHz) and conventional IR thermography (captured at 30 Hz) imaging were performed simultaneously in this follow-on entry. This paper is intended to serve as a summary of the work performed during these two entries, to detail lessons learned from each entry, and to highlight some of the datasets acquired. Details on the experimental setup, model configuration, and techniques used are provided. Papers providing a more rigorous analysis of data acquired during the second entry, including statistical, spectral, and modal decomposition methods, can be found in Refs. [12,13]. An entry examining XSWBLI in the 31-Inch Mach 10 Blowdown Wind Tunnel facility is currently planned for mid-to-late calendar year 2019, pending the success of facility repairs. The work performed and described in this paper and the upcoming entry in the 31-Inch Mach 10 facility at NASA Langley have been made possible by NASA’s new facility funding model under the Aeronautics Evaluation and Test Capabilities (AETC) project. Wind Tunnel Facility All experiments discussed in this paper were performed in the 20-Inch Mach 6 Air Tunnel at NASA Langley Research Center. Specific details pertaining to this facility can be found in Refs. [14,15], with only a brief description of the facility provided here. For both entries, the nominal freestream unit Reynolds number was varied between 1.8×106 m-1 (0.5×106 ft-1) and 26.3×106 m-1 (8×106 ft-1). The nominal stagnation pressure was varied between 0.21 MPa and 3.33 MPa and the nominal stagnation temperature was varied between 480 K and 520 K to achieve the desired Re∞ condition. For all runs, the nominal freestream Mach number was 6. The nearly square test section is 520.7-mm (20.5-inches) wide by 508-mm (20-inches) high. Two 431.8-mm (17-inch) diameter windows made of Corning 7940, Grade 5F schlieren-quality glass serve as the side walls of the tunnel and provide optical access for the high-speed schlieren measurements. A rectangular window made of the same material as the side windows served as the top wall of the test section and provided optical access for the high-speed PSP and oil flow measurements. For the second entry, this top window was replaced with a Zinc Selenide (ZnSe) window with an anti-reflection coating capable of passing IR wavelengths between 8μm and 12μm with greater than 98% transmittance. The model was sting supported by a strut attached to a hydraulic system that allows for the model pitch angle to be adjusted between -5° to +55°. For the first entry, an initial pitch/pause sweep of the model AoA was performed to observe the resulting SWBLI. Ultimately, however, the sting pitch angle for this entry was fixed at +10.0° so that the angle of the top surface of the wedge relative to the streamwise axis of the tunnel (referred to herein as the plate angle, θplate), was θplate = 0°. For the second entry, θplate = 0° and θplate = -13.25° were initially tested with the swept ramp array (discussed in the following section) to determine which orientation produced conditions most favorable for XSWBLI to occur based on the heating signatures observed over the top surface of the model in the IR thermography images. Based on these initial tests, θplate = -13.25° was set for the remainder of the runs in the second entry. For both entries, any model changes were performed in a housing located beneath the closed test section. Prior to performing a run of the tunnel, the housing was sealed and the tunnel started. Once the appropriate freestream conditions were achieved, the model was injected into the test section using a hydraulic injection system. B. Model Geometry For all runs, a 10° half-angle (20° full-angle) wedge model with a sharp leading edge was used. The model is described in detail in Refs. [10,16]. The top surface of the sharp leading edge of the model extended 47.8 mm from its upstream-most edge to a junction with the upstream edge of a stainless steel top plate that then extended an (a) (c) (b) Fig. 1 (a) Schematic of top surface of wedge model with gas seeding insert, (b) perspective view of the model in the 20-Inch Mach 6 tunnel with centerline pressure orifices on sharp leading edge, and (c) a perspective view of the model with stainless steel (top) and SLA middle insert (bottom) during the first entry. Flow occurs from left to right.

Bathel, Brett F.↗

Relationship Between the Sub-Micron Fraction (SMF) and Fine-Mode Fraction (FMF) in the Context of AERONET Retrievals

The sub-micron (SM) aerosol optical depth (AOD) is an optical separation based on the fraction of particles below a specified cutoff radius of the particle size distribution (PSD) at a given particle radius. It is fundamentally different from spectrally separated FM (fine-mode) AOD. We present a simple (AOD-normalized) SM fraction versus FM fraction (SMF vs. FMF) linear equation that explains the well-recognized empirical result of SMF generally being greater than the FMF. The AERONET inversion (AERinv) products (combined inputs of spectral AOD and sky radiance) and the spectral deconvolution algorithm (SDA) products (input of AOD spectra) enable, respectively, an empirical SMF vs. FMF comparison at similar (columnar) remote sensing scales across a variety of aerosol types. SMF (AERinv-derived) vs. FMF (SDA-derived) behavior is primarily dependent on the relative truncated portion (ε c ) of the coarse-mode (CM) AOD associated with the cutoff portion of the CM PSD and, to a second order, the cutoff FM PSD and FM AOD (ε f ). The SMF vs. FMF equation largely explains the SMF vs. FMF behavior of the AERinv vs. SDA products as a function of PSD cutoff radius (“inflection point”) across an ensemble of AERONET sites and aerosol types (urban-industrial, biomass burning, dust, maritime and a mixed class of Arctic aerosols). The overarching dynamic was that the linear SMF vs. FMF relation pivots clockwise about the approximate (SMF, FMF) singularity of (1, 1) in a “linearly inverse” fashion (slope and intercept of approximately 1−ε c and ε c ) with increasing cutoff radius. SMF vs. FMF slopes and intercepts derived from AERinv and SDA retrievals confirmed the general domination of ε c over ε f in controlling that dynamic. A more general conclusion is the apparent confirmation that the optical impact of truncating modal (whole) PSD features can be detected by an SMF vs. FMF analysis.

Norman T. O'Neill↗

Determination of the effects of heating on modal characteristics of an aluminum plate with application to hypersonic vehicles

The structural integrity of proposed high speed aircraft can be seriously affected by the extremely high surface temperatures and large temperature gradients throughout the vehicle's structure. Variations in the structure's elastic characteristics as a result of thermal effects can be seen by changes in vibration characteristics. Analysis codes that predict these changes must be correlated and verified with experimental data. Analytical and experimental modal test results are given from uniform, nonuniform, and transient thermoelastic vibration tests of a 12 x 50 x 0.19 aluminum plate. The data show the effect of heat on the modal characteristics of the plate. The results showed that frequencies decreased, damping increased, and mode shapes remained unchanged as the temperature of the plate increased. Analytical predictions provided good correlation with experimental results.

Snyder, H. Todd↗

A Mixed Finite Analysis of Axial Foreshortening

In previous studies, a mixed finite element was derived and shown to be effective in facilitating accurate modal reduction of rotor blades. This study builds upon that earlier work through the development of algorithms that allow the element's Lagrangian axial displacement degrees of freedom to be eliminated in favor of the axial force degrees of freedom. This reduction process, which had been demonstrated previously for the case of a single mixed finite element, may be viewed as a generalization of the UMARC blade analysis methodology to arbitrary topologies. A unique strength of the method. developed here is that the model may consist of two dimensional or even three dimensional elements.

Ruzicka, Gene↗

Model verification of large structural systems

A computer program for the application of parameter identification on the structural dynamic models of space shuttle and other large models with hundreds of degrees of freedom is described. Finite element, dynamic, analytic, and modal models are used to represent the structural system. The interface with math models is such that output from any structural analysis program applied to any structural configuration can be used directly. Processed data from either sine-sweep tests or resonant dwell tests are directly usable. The program uses measured modal data to condition the prior analystic model so as to improve the frequency match between model and test. A Bayesian estimator generates an improved analytical model and a linear estimator is used in an iterative fashion on highly nonlinear equations. Mass and stiffness scaling parameters are generated for an improved finite element model, and the optimum set of parameters is obtained in one step.

Lee, L. T.↗

Calculating the Modal Mineralogy of Aubrite Meteorites Using X-Ray Computed Tomography

The aubrites are a group of differentiated meteorites that formed in extremely reducing conditions, with oxygen fugacities (ƒO2) ranging from ~2 to ~6 log units below the Iron-Wüstite buffer. At these extreme conditions, elements that are lithophile (silica-loving) on Earth can behave as chalcophiles (sulfur-loving) or siderophiles (metal-loving), and FeO-poor silicates and exotic sulfides can form. Elemental partitioning among minerals at these conditions are still not well understood, thus studying aubrites could help better constrain elemental behavior. Only 30 aubrites exist; however, they display various textures, which can be difficult to identify in small samples. Identifying composite clasts can help in understanding the igneous history of the aubrite parent bodies. In order to distinguish different minerals and textures in larger samples, we use X-ray computed tomography (XCT), which is a useful, non-destructive analysis that can produce a 3D representation of a meteorite's textures, structures, and modal mineralogy. This study investigates the Norton County aubrite using XCT. Norton County is a fragmental impact breccia aubrite, and was an observed fall with a main mass of 1.1 tons. This large amount of material offers an opportunity to investigate a great volume of reduced, aubritic sample and study a more diverse variety of clasts. Here we report XCT results of two samples of Norton County (NC 15417) in order to constrain the 3D modal mineralogy of silicates, sulfides, and metals, and to identify unique clasts within the matrix.

Wilbur, Zoe↗

Comparison and Limitations of DVH-Based NTCP Models Derived From 3D-CRT and IMRT Data for Prediction of Gastrointestinal Toxicities in Prostate Cancer Patients by Using Propensity Score Matched Pair Analysis

Purpose: This study compared normal tissue complication probability (NTCP) modeling of chronic gastrointestinal toxicities following prostate cancer treatment for 2 treatment modalities. Possible factors causing discrepancies in optimal NTCP model parameters between 3-dimensional conformal radiation therapy (3D-CRT) and intensity modulated RT (IMRT) were analyzed and discussed, including the impact of patient characteristics, image guidance, toxicity scoring bias, and NTCP model limitations. Methods and Materials: Rectal wall dose-volume histograms of 1115 patients treated for prostate cancer under an adaptive radiation therapy protocol were used to model gastrointestinal toxicity grade ≥2 (according to Common Terminology Criteria for Adverse Events). A total of 457 patients were treated with 3D-CRT and 658 with IMRT. 3D-CRT patients were matched to IMRT patients based on various patient characteristics, using a propensity score–based algorithm. Parameters of the Lyman equivalent uniform dose and cut-off dose logistic regression NTCP models were estimated for the 2 matched treatment modalities and the combined group. Results: After they were matched, the 3D-CRT and IMRT groups contained 275 and 550 patients with a large discrepancy of 28.7% versus 7.8% toxicities, respectively (P<.001). For both NTCP models, optimal parameters found for the 3D-CRT groups did not fit the IMRT patients well and vice versa. Models developed for the combined data overestimated NTCP for the IMRT patients and underestimated NTCP for the 3D-CRT group. Conclusions: Our analysis did not reveal a single definitive cause for discrepancies of model parameters between 3D-CRT and IMRT. Patient characteristics and bias in toxicity scoring, as well as image guidance alone, are unlikely causes of the large discrepancy of toxicities. Whether the cause was inherent to the specific NTCP models used in this study needs to be verified by future investigations. Because IMRT is increasingly used clinically, it is important that appropriate NTCP model parameters are determined for this treatment modality.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

SU-F-R-33: Can CT and CBCT Be Used Simultaneously for Radiomics Analysis

Purpose: To investigate whether CBCT and CT can be used in radiomics analysis simultaneously. To establish a batch correction method for radiomics in two similar image modalities. Methods: Four sites including rectum, bladder, femoral head and lung were considered as region of interest (ROI) in this study. For each site, 10 treatment planning CT images were collected. And 10 CBCT images which came from same site of same patient were acquired at first radiotherapy fraction. 253 radiomics features, which were selected by our test-retest study at rectum cancer CT (ICC>0.8), were calculated for both CBCT and CT images in MATLAB. Simple scaling (z-score) and nonlinear correction methods were applied to the CBCT radiomics features. The Pearson Correlation Coefficient was calculated to analyze the correlation between radiomics features of CT and CBCT images before and after correction. Cluster analysis of mixed data (for each site, 5 CT and 5 CBCT data are randomly selected) was implemented to validate the feasibility to merge radiomics data from CBCT and CT. The consistency of clustering result and site grouping was verified by a chi-square test for different datasets respectively. Results: For simple scaling, 234 of the 253 features have correlation coefficient ρ>0.8 among which 154 features haveρ>0.9 . For radiomics data after nonlinear correction, 240 of the 253 features have ρ>0.8 among which 220 features have ρ>0.9. Cluster analysis of mixed data shows that data of four sites was almost precisely separated for simple scaling(p=1.29 * 10{sup −7}, χ{sup 2} test) and nonlinear correction (p=5.98 * 10{sup −7}, χ{sup 2} test), which is similar to the cluster result of CT data (p=4.52 * 10{sup −8}, χ{sup 2} test). Conclusion: Radiomics data from CBCT can be merged with those from CT by simple scaling or nonlinear correction for radiomics analysis.

60 APPLIED LIFE SCIENCES↗

Dose Constraint for Minimizing Grade 2 Rectal Bleeding Following Brachytherapy Combined With External Beam Radiotherapy for Localized Prostate Cancer: Rectal Dose-Volume Histogram Analysis of 457 Patients

Purpose: To determine the rectal tolerance to Grade 2 rectal bleeding after I-125 seed brachytherapy combined with external beam radiotherapy (EBRT), based on the rectal dose-volume histogram. Methods and Materials: A total of 458 consecutive patients with stages T1 to T3 prostate cancer received combined modality treatment consisting of I-125 seed implantation followed by EBRT to the prostate and seminal vesicles. The prescribed doses of brachytherapy and EBRT were 100 Gy and 45 Gy in 25 fractions, respectively. The rectal dosimetric factors were analyzed for rectal volumes receiving >100 Gy and >150 Gy (R100 and R150) during brachytherapy and for rectal volumes receiving >30 Gy to 40 Gy (V30-V40) during EBRT therapy in 373 patients for whom datasets were available. The patients were followed from 21 to 72 months (median, 45 months) after the I-125 seed implantation. Results: Forty-four patients (9.7%) developed Grade 2 rectal bleeding. On multivariate analysis, age (p = 0.014), R100 (p = 0.002), and V30 (p = 0.001) were identified as risk factors for Grade 2 rectal bleeding. The rectal bleeding rate increased as the R100 increased: 5.0% (2/40 patients) for 0 ml; 7.5% (20/267 patients) for >0 to 0.5 ml; 11.0% (11/100 patients) for >0.5 to 1 ml; 17.9% (5/28 patients) for >1 to 1.5 ml; and 27.3% (6/22 patients) for >1.5 ml (p = 0.014). Grade 2 rectal bleeding developed in 6.4% (12/188) of patients with a V30 {<=}35% and in 14.1% (26/185) of patients with a V30 >35% (p = 0.02). When these dose-volume parameters were considered in combination, the Grade 2 rectal bleeding rate was 4.2% (5/120 patients) for a R100 {<=}0.5 ml and a V30 {<=}35%, whereas it was 22.4% (13/58 patients) for R100 of >0.5 ml and V30 of >35%. Conclusion: The risk of rectal bleeding was found to be significantly volume-dependent in patients with prostate cancer who received combined modality treatment. Rectal dose-volume analysis is a practical method for predicting the risk of development of Grade 2 rectal bleeding.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Involved-Field Radiation Therapy Prevents Recurrences in the Early Stages of Hodgkin Lymphoma in PET-Negative Patients After ABVD Chemotherapy: Relapse Analysis of GHSG Phase 3 HD16 Trial

The HD16 trial of the German Hodgkin Study Group (NCT00736320) demonstrated that radiation therapy in early-stage Hodgkin lymphoma without risk factors cannot be safely omitted, and therefore combined modality therapy (CMT) remains the standard treatment. To demonstrate the local effect of consolidating involved-field radiation therapy (IF-RT), we performed an analysis of the recurrence pattern of positron emission tomography (PET)-negative HD16 patients.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

SU-F-T-305: Clinical Effects of Dosimetric Leaf Gap (DLG) Values Between Matched Varian Truebeam (TB) Linacs

Purpose: The dosimetric leaf gap (DLG) is an important parameter to be measured for dynamic beam delivery of modern linacs, like the Varian Truebeam (TB). The clinical effects of DLG-values on IMRT and/or VMAT commissioning of two “matched” TB linacs will be presented.Methods and Materials: The DLG values on two TB linacs were measured for all energy modalities (filtered and FFF-modes) as part of the dynamic delivery mode commissioning (IMRT and/or VMAT. After the standard beam data was modeled in eclipse treatment planning system (TPS) and validated, IMRT validation was performed based on TG1191 benchmark, IROC Head-Neck (H&N) phantom and sample of clinical cases, all measured on both linacs. Although there was a single-set of data entered in the TPS, a noticeable difference was observed for the DLG-values between the linacs. The TG119, IROC phantom and selected patient plans were furnished with DLG-values of TB1 for both linacs and the delivery was performed on both TB linacs for comparison. Results: The DLG values of TB1 was first used for both linacs to perform the testing comparisons. The QA comparison of TG119 plans revealed a great dependence of the results to the DLG-values used for the linac for all energy modalities studied, especially when moving from 3%/3mm to 2%/2mm γ-analysis. Conclusion: The DLG-values have a definite influence on the dynamic dose, delivery that increases with the plan complexity. We recommend that the measured DLG-values are assigned to each of the “matched” linacs, even if a single set of beam data describes multiple linacs. The user should perform a detail test of the dynamic delivery of each linac based on end-to-end benchmark suites like TG119 and IROC phantoms.1Ezzel G., et al., “IMRT commissioning: Multiple institution planning and dosimetry comparisons, a report from AAPM Task Group 119.” Med. Phys. 36:5359–5373 (2009). partly supported by CAMC Cancer Center and Alliance Oncology.

60 APPLIED LIFE SCIENCES↗

Attitude stability of spinning flexible spacecraft

The stability of spinning flexible satellites in a force-free environment was analyzed. The satellite was modeled as a rigid core having attached to it a flexible appendage idealized as a collection of particles (point masses) interconnected by springs. Both Liapunov and Routh-Hurwitz stability procedures are used. In the former, the Hamiltonian of the system, constrained through the angular momentum integral so as to admit complete damping, is used as a testing function. Equations of motion are written using the hybrid coordinate formulation, which readily accepts a modal coordinate transformation ultimately allowing truncation to a level amenable to literal stability analysis. Closed form stability criteria are generated for the first mode of a restricted appendage model lying in a plane containing the system center of mass and orthogonal to the spin axis. The effects of spin on flexible bodies are discussed by considering a very elementary particle model. Control of passively unstable spacecraft is briefly considered.

Likins, P. W.↗

On-line structural parameter identification

Algorithms are presented for on-line parameter identification of structural dynamic systems. As an example, they are used to calculate the parameters of a modal model of a flexible beam. The algorithms are tested using hardware consisting of a 12 ft. beam with four voice coil actuators and nine noncontacting displacement sensors. They are programmed in a CDC Cyber 175 digital computer which provides input command signals for the actuators, reads the sensor data, and processes the algorithm to calculate consistent estimates of the modal parameters of the beam. Experimental results are compared with those of simulation analysis.

Thau, F. E.↗

Noise Transmission Loss of a Rectangular Plate in an Infinite Baffle

An improved analytical procedure was developed that allows for the efficient calculation of the noise transmission characteristics of a finite rectangular plate. Both isotropic and symmetrically laminated composite plates are considered. The plate is modeled with classic thin-plate theory and is assumed to be simply supported on all four sides. The incident acoustic pressure is assumed to be a plane wave impinging on the plate at an arbitrary angle. The reradiated pressure is assumed to be negligible compared with the blocked pressure, and the plate vibrations are calculated by a normal-mode approach. A Green's function integral equation is used to link the plate vibrations to be transmitted far-field sound waves, and transmission loss is calculated from the ratio of incident to transmitted acoustic powers. The result is a versatile research and engineering analysis tool that predicts noise transmission loss and enables the determination of the modal behavior of the plate.

Roussos, Louis A.↗

In-flight identification of the Galileo spacecraft flexible mode characteristics

The scan platform of the Galialan spacecraft is attached to a flexible stator structure that separates the actuator from the platform-mounted inartial sensor. A scheme to identify the flexible mode characteristics (frequency, damping, and modal coefficient) of the stator using flight data is presentevd. A frequency domain analysis approach is taken and the identified mode characteristics will be used for updating the scan platform controler parameters. The influence of structural flexibility to th s can controller design is explained and the constraints in experting the identification procedure in flight are discused. Computer simulation results of the identification scheme are presented. The scheme in further verified by DISCOS simulations, in conjunction witha full spacecraft dynamics model and the scan platform controllers.

Wang, F. C.↗

Estimation of blade airloads from rotor blade bending moments

A method is developed to estimate the blade normal airloads by using measured flap bending moments; that is, the rotor blade is used as a force balance. The blade's rotation is calculated in vacuum modes and the airloads are then expressed as an algebraic sum of the mode shapes, modal amplitudes, mass distribution, and frequency properties. The modal amplitudes are identified from the blade bending moments using the Strain Pattern Analysis Method. The application of the method is examined using simulated flap bending moment data that have been calculated for measured airloads for a full-scale rotor in a wind tunnel. The estimated airloads are compared with the wind tunnel measurements. The effects of the number of measurements, the number of modes, and errors in the measurements and the blade properties are examined, and the method is shown to be robust.

Bousman, William G.↗