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Research and Applications in Aeroelasticity and Structural Dynamics at the NASA Langley Research Center

An overview of recently completed programs in aeroelasticity and structural dynamics research at the NASA Langley Research Center is presented. Methods used to perform flutter clearance studies in the wind-tunnel on a high performance fighter are discussed. Recent advances in the use of smart structures and controls to solve aeroelastic problems, including flutter and gust response are presented. An aeroelastic models program designed to support an advanced high speed civil transport is described. An extension to transonic small disturbance theory that better predicts flows involving separation and reattachment is presented. The results of a research study to determine the effects of flexibility on the taxi and takeoff characteristics of a high speed civil transport are presented. The use of photogrammetric methods aboard Space Shuttle to measure spacecraft dynamic response is discussed. Issues associated with the jitter response of multi-payload spacecraft are discussed. Finally a Space Shuttle flight experiment that studied the control of flexible spacecraft is described.

Abel, Irving↗

A Comparison of Combustion Dynamics for Multiple 7-Point Lean Direct Injection Combustor Configurations

The combustion dynamics of two 7-point lean direct injection (LDI) combustor configurations are compared. This 7-point LDI configuration has a circular cross section, with a center ("pilot") fuel-air mixer surrounded by six outer ("main") fuel-air mixers. Each fuel-air mixer consists of an axial air swirler followed by a converging-diverging venturi. A simplex fuel injector is inserted through the center of the air swirler, with the fuel injector tip located near the venturi throat. All 7 fuel-air mixers are identical except for the swirler blade angle. In the 'all-60' configuration, the swirler blade angle was 60 deg for all fuel-air mixers. In the '45-60' configuration, the swirler blade angle was 60 deg on the center and 45 deg on the outer fuel-air mixers. Testing was done in a 5-atm flame tube with inlet air temperatures from 630 to 830 F and equivalence ratios from 0.2 to 0.7. Combustion dynamics were measured using a cooled PCB pressure transducer flush-mounted in the wall of the combustor test section. Both configurations had large pressure fluctuations (greater than 2 psi peak-peak) near 730 Hz, the quarter-wave frequency. The all-60 configuration also had large pressure fluctuations near 1170 Hz; the 45-60 configuration did not. The 45-60 configuration had large pressure fluctuations near 480 Hz; the all-60 configuration did not.

combustion dynamics↗

Three-Dimensional Measurement of the Crater Formation During Plume–Surface Interactions Using Stereo-Photogrammetry

The present investigation focused on adapting and validating stereo-photogrammetry for obtaining 3-D, time-resolved, non-intrusive, full-domain measurements of crater evolution during the plume-surface interaction (PSI) process. An atmospheric experimental facility was designed and constructed to facilitate the development of the stereo-photogrammetry technique for PSI applications. Stereo-photogrammetry was then used to measure the dynamic crater evolution process at nozzle heights of 25, 40, 55, and 70 nozzle diameters above the sand simulant bed. From the stereo-photogrammetry data, time-resolved 3-D reconstructions of the crater geometry were generated, and crater depth, radius, and volume time histories were extracted. Crater depth was observed to grow logarithmically for the two highest nozzle heights, and the depth growth rate for the lower two nozzle heights was more rapid. Crater volume growth was well characterized by a power law fit. The slope of the collapsed crater post nozzle flow was found to increase with nozzle height, along with the final crater volume. The results show that stereo-photogrammetry can be used to successfully measure the crater geometry in cases where optical access to the crater is not completely degraded by ejected particles.

DC Stubbs↗

Quantification of energy and cost reduction from decreasing dissolved oxygen levels in full‐scale water resource recovery facilities

Abstract Aeration systems often lack the efficiency to maintain a desired residual dissolved oxygen (DO) concentration in the tank in part because little consideration is given to the dynamic daily and seasonal loading conditions. Although advanced aeration controllers exist, the majority of plants have DO set points typically based on common practice and literature values rather than site‐specific conditions, which can result in DO set points higher than those necessary to meet treatment objectives. DO set point reduction strategies have primarily been proposed through either static or dynamic simulations. In this study, the substantial improvements associated with DO set point reduction are demonstrated at full scale. A yearlong characterization of full‐scale aeration dynamics captured the effect of diurnal and seasonal fluctuations on oxygen transfer and energy demand and so facilitated the estimation of the potential savings of DO reduction strategies. Full‐scale validation provided direct evidence of DO reduction strategies inducing an overall enhancement of oxygen transfer efficiency along the different bioreactors, while confirming that energy savings as high as 20% were feasible. This study quantifies the influence of oxygen transfer efficiency on operating choices and site‐specific conditions (control strategy, loading conditions, and influent flow variability). Practitioner points We quantified the energy reduction and cost savings associated with a DO reduction in an aeration tank. For each 0.2 mg/L of DO decreased, the average power demand reduction per unit water treated exceeded 17%. Field measurements of dynamic alpha values eliminate the uncertainty in estimating aeration energy and cost savings from DO variations.

Pasini, Federico↗

Measurement of Photovoltaic Module Deformation Dynamics During Hail Impact Using Digital Image Correlation

Stereo high-speed video of photovoltaic modules undergoing laboratory hail tests was processed using digital image correlation to determine module surface deformation during and immediately following impact. The purpose of this work was to demonstrate a methodology for characterizing module impact response differences as a function of construction and incident hail parameters. Video capture and digital image analysis were able to capture out-of-plane module deformation to a resolution of ±0.1 mm at 11 kHz on an in-plane grid of 10 × 10 mm over the area of a 1 × 2 m commercial photovoltaic module. With lighting and optical adjustments, the technique was adaptable to arbitrary module designs, including size, backsheet color, and cell interconnection. Furthermore, impacts were observed to produce an initially localized dimple in the glass surface, with peak deflection proportional to the square root of incident energy. Subsequent deformation propagation and dissipation were also captured, along with behavior for instances when the module glass fractured. Natural frequencies of the module were identifiable by analyzing module oscillations postimpact. Limitations of the measurement technique were that the impacting ice ball obscured the data field immediately surrounding the point of contact, and both ice and glass fracture events occurred within 100 μs, which was not resolvable at the chosen frame rate. Increasing the frame rate and visualizing the back surface of the impact could be applied to avoid these issues. Applications for these data include validating computational models for hail impacts, identifying the natural frequencies of a module, and identifying damage initiation mechanisms.

14 SOLAR ENERGY↗

CDGPS-Based Relative Navigation for Multiple Spacecraft

This thesis investigates the use of Carrier-phase Differential GPS (CDGPS) in relative navigation filters for formation flying spacecraft. This work analyzes the relationship between the Extended Kalman Filter (EKF) design parameters and the resulting estimation accuracies, and in particular, the effect of the process and measurement noises on the semimajor axis error. This analysis clearly demonstrates that CDGPS-based relative navigation Kalman filters yield good estimation performance without satisfying the strong correlation property that previous work had associated with "good" navigation filters. Several examples are presented to show that the Kalman filter can be forced to create solutions with stronger correlations, but these always result in larger semimajor axis errors. These linear and nonlinear simulations also demonstrated the crucial role of the process noise in determining the semimajor axis knowledge. More sophisticated nonlinear models were included to reduce the propagation error in the estimator, but for long time steps and large separations, the EKF, which only uses a linearized covariance propagation, yielded very poor performance. In contrast, the CDGPS-based Unscented Kalman relative navigation Filter (UKF) handled the dynamic and measurement nonlinearities much better and yielded far superior performance than the EKF. The UKF produced good estimates for scenarios with long baselines and time steps for which the EKF would diverge rapidly. A hardware-in-the-loop testbed that is compatible with the Spirent Simulator at NASA GSFC was developed to provide a very flexible and robust capability for demonstrating CDGPS technologies in closed-loop. This extended previous work to implement the decentralized relative navigation algorithms in real time.

Mitchell, Megan Leigh↗

Evaluation of Start Transient Oscillations with the J-2X Engine Gas Generator Assembly

During development of the gas generator for the liquid oxygen/liquid hydrogen propellant J-2X rocket engine, distinctive and oftentimes high-amplitude pressure oscillations and hardware vibrations occurred during the start transient of nearly every workhorse gas generator assembly test, as well as during many tests of engine system hardware. These oscillations appeared whether the steady-state conditions exhibited stable behavior or not. They occurred similarly with three different injector types, and with every combustion chamber configuration tested, including chamber lengths ranging over a 5:1 range, several different nozzle types, and with or without a side branch line simulating a turbine spin start gas supply line. Generally, two sets of oscillations occurred, one earlier in the start transient and at higher frequencies, and the other almost immediately following and at lower frequencies. Multiple dynamic pressure measurements in the workhorse combustion chambers indicated that the oscillations were associated with longitudinal acoustic modes of the combustion chambers, with the earlier and higher frequency oscillation usually related to the second longitudinal acoustic mode and the later and lower frequency oscillation usually related to the first longitudinal acoustic mode. Given that several early development gas generator assemblies exhibited unstable behavior at frequencies near the first longitudinal acoustic modes of longer combustion chambers, the start transient oscillations are presumed to provide additional insight into the nature of the combustion instability mechanisms. Aspects of the steadystate oscillations and combustion instabilities from development and engine system test programs have been reported extensively in the three previous JANNAF Liquid Propulsion Subcommittee meetings (see references below). This paper describes the hardware configurations, start transient sequence operations, and transient and dynamic test data during the start transient. The implications of these results on previous analyses and understanding of the combustion instability observed during steady-state conditions, especially the effects of injector influences, is discussed.

Hulka, J. R.↗

Dynamic-mechanical response of graphite/epoxy composite laminates and neat resin

Dynamic mechanical measurement results are presented for the case of carbon fiber-reinforced, epoxy matrix composite laminates subjected to loading perpendicular to the lamination plane, as well as for neat epoxy resin under the same conditions, where temperatures ranged between 20 and 200 C and deformation levels lie within the linear viscoelastic region. In-phase and out-of-phase stiffnesses are found to become superposed, forming master curves that cover a 12-decade frequency range. The application of a master curve scaling procedure shows that the in-phase stiffness has the same shape, and out-of-phase stiffness has the same dispersion, for all laminates irrespective of stacking sequence and are, in turn, nearly identical to those for the neat epoxy resin. An empirical function is found for the relaxation modulus which, when converted to a dynamic modulus, yields good overall agreement for both of the dynamic stiffness components as a function of frequency.

Yang, P.↗

Bilinear modeling and nonlinear estimation

New methods are illustrated for online nonlinear estimation applied to the lateral deflection of an elastic beam on board measurements of angular rates and angular accelerations. The development of the filter equations, together with practical issues of their numerical solution as developed from global linearization by nonlinear output injection are contrasted with the usual method of the extended Kalman filter (EKF). It is shown how nonlinear estimation due to gyroscopic coupling can be implemented as an adaptive covariance filter using off-the-shelf Kalman filter algorithms. The effect of the global linearization by nonlinear output injection is to introduce a change of coordinates in which only the process noise covariance is to be updated in online implementation. This is in contrast to the computational approach which arises in EKF methods arising by local linearization with respect to the current conditional mean. Processing refinements for nonlinear estimation based on optimal, nonlinear interpolation between observations are also highlighted. In these methods the extrapolation of the process dynamics between measurement updates is obtained by replacing a transition matrix with an operator spline that is optimized off-line from responses to selected test inputs.

Dwyer, Thomas A. W., III↗

HydraGNN_Predictive_GFM_2024 - Ensemble of predictive graph foundation models for ground state atomistic materials modeling

We provide the ensemble of fifteen pre-trained graph foundation models (GFMs) for atomistic materials modeling applications. Each one of the fifteen GFMs has been trained on five open-source datasets that (once aggregated) amount to over 154 million atomistic structures, which cover over two-thirds of the natural elements of the periodic table and that comprises a broad set of organic and inorganic compounds. This vast set of atomistic structures comprises ground state configurations that are dynamically stable (i.e., equilibrated structures with atomic forces approximately close to zero values) as well as dynamically unstable structures (i.e., non-equilibrium structures with non-negligible non-zero values of atomic forces). The ensemble of datasets aggregated does NOT include excited states. The datasets have been curated to remove atomistic structures with spectral norm of the force tensor above 100 eV/angstrom. Moreover, a linear term of the energy was computed for each dataset using a linear regression model that uses the chemical concentration of each natural element as regressor. The linear term predicted by the linear regression model has been subtracted from each original energy value to perform a re-alignment of the energy values across different electronic structures approximation theories performed to generate the diverse multi-source, multi-fidelity datasets. The folder "ADIOS_files" contains the set of pre-processed datasets in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used for the development and training of GFMs in this work. The "ADIOS_files" directory contains 6 sub-directories named as follows: - ANI1x-v3.bp - MPTrj-v3.bp - OC2020-20M-v3.bp - OC2020-v3.bp - OC2022-v3.bp - qm7x-v3.bp Each sub-directory contains the pre-processed datasets converted in Adaptable I/O System (ADIOS) format (https://www.exascaleproject.org/research-project/adios/) that have been used to the development, training, and performance testing of the ensemble go predictive graph foundation models. Each GFM was developed using HydraGNN (https://github.com/ORNL/HydraGNN) as underlying graph neural network (GNN) architecture. The multi-task learning (MTL) capability of HydraGNN was used to simultaneously train the GFMs on labeled values for direct predictions of energy (a total system property of an atomistic structure that measures the chemical stability) and atomic forces (an atomic level property of an atomistic structure that measures the dynamical stability). The hyper parameters of the GFM have been tuned using scalable hyperparameter optimization (HPO) algorithms implemented in the software DeepHyper (https://github.com/deephyper/deephyper). The pre-training of each HPO trial was performed using distributed data parallelism (DDP) to scale the training across 128 compute nodes of the exascale OLCF supercomputer Frontier. Each HPO trial was trained only for 10 epochs and an early stopping was performed to avoid wasting significant computational resources on GNN architectures that were clearly underperforming. For each HPO trial, the 'omnistat' tool developed by (AMD Research - Advanced Micro Device) was used to measure the total energy consumption in kWh. The ensemble of GFMs was obtained by selecting the fifteen best performing HPO trials. Four models have been selected for their clear advantage in accuracy, and these are the GFMs with IDs 229, 156, 147, 260. Additional eleven models have been selected based on judicious balance between accuracy and energy consumption needed for training, and these are the GFMs with IDs 165, 78, 137, 1, 175, 171, 181, 67, 179, 167, 351. Each selected GFM of the ensemble was continued to cumulate a total of at most 30 epochs. In some cases, the total number of epochs actually performed was les than 30 due to two combined factors: (1) the size of the GFM (i.e., the number of model parameters to train) and (2) the total wall-clock time for which the computational resources could be allocated on OLCF-Frontier. The "Ensemble_of_models" directory contains 15 sub-directories named as follows: - gfm_0.229 - gfm_0.156 - gfm_0.147 - gfm_0.260 - gfm_0.165 - gfm_0.78 - gfm_0.137 - gfm_0.1 - gfm_0.175 - gfm_0.171 - gfm_0.181 - gfm_0.67 - gfm_0.179 - gfm_0.167 - gfm_0.351 Each one of these sub-directories refers to one of the fifteen HPO trials that have been selected to continue the pre-training with at most 30 epochs. With each sub-directory associated with a specific HPO trial, the following files can be found: - config.json: file for argument parsing to develop and train an HydraGNN architecture - gfm_0.ID_epoch_N.pk: file with model parameters for HPO ID trial after N epochs of training The ensemble of fifteen GFM architectures was used for (1) ensemble averaging to stabilize the predictions of energy and atomic forces after pre-training for post-processing analysis and (2) ensemble uncertainty quantification (UQ). The code used to develop, pre-train, and load the pre-trained models for post-processing analysis is available on the ORNL-GitHub at the following link: https://github.com/ORNL/HydraGNN/tree/Predictive_GFM_2024

36 MATERIALS SCIENCE↗

A Flat Analyzer Polycapillary Spectrometer for X-ray Absorption Spectroscopy of Dilute Transition Metals at X-ray-Free Electron Lasers

X-ray absorption spectroscopy (XAS) coupled with highly intense pulses from an X-ray-free electron laser (XFEL) can be used to track ultrafast chemical dynamics. Nonetheless, measurements for dilute samples (≤1 mM) have been exceptionally challenging, as scattering background signals dominate over the sample’s X-ray fluorescence. We show that femtosecond time-resolved XAS measurements of sub-millimolar transition metal solutions are now possible at the Linac Coherent Light Source (LCLS) using a high-throughput polycapillary XAS spectrometer, designed, developed, and commissioned at LCLS and the Stanford Synchrotron Radiation Lightsource (SSRL). The instrument integrates three polycapillary optics that collect and collimate X-ray fluorescence emitted from the interaction point with a high solid angle. X-ray collimated fluorescence is then selectively diffracted by coupled graphite analyzer crystals. As a result, the contribution of scattered photons is suppressed. Experiments at the Pt L 3 -edge on 0.1 mM aqueous K 2 PtCl 6 (delivered via a 100 μm liquid jet) were successfully performed in the laser pump X-ray probe configuration at the LCLS XCS and XPP instruments. We report the transient spectra of hexachloroplatinate within the first 10 ps after a 266 nm photoexcitation. We observed a short-lived reduced intermediate (≈2 ps). The polycapillary X-ray spectrometer at LCLS now enables the efficient study of the dynamics of ultradilute transition metals in solution. This capability opens the door to investigating plasmonic systems, photocatalysts, enzymes, and other scarce and dilute samples.

LCLS↗

Nature of Magnetic Excitations in the High-Field Phase of α–RuCl 3

We present comprehensive electron spin resonance (ESR) studies of in-plane oriented single crystals of α–RuCl 3 , a quasi-two-dimensional material with honeycomb structure, focusing on its high-field spin dynamics. The measurements were performed in magnetic fields up to 16 T, applied along the [110] and [100] directions. Several ESR modes were detected. Combining our findings with recent inelastic neutron- and Raman-scattering data, we identified most of the observed excitations. Most importantly, we show that the low-temperature ESR response beyond the boundary of the magnetically ordered region is dominated by single- and two-particle processes with magnons as elementary excitations. In conclusion, the peculiarities of the excitation spectrum in the vicinity of the critical field are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Measured Response to Wind-Induced Dynamic Loads of a Full-Scale Scout Vehicle Mounted Vertically on a Launching Tower

Winds blowing over a vehicle mounted in the launch position may induce dynamic loads which are large enough to cause structural damage. In an attempt to prevent the formation of excessive wind-induced loads on the Scout vehicle, spoiler strips of the type used on the.Vanguard vehicle were to be mounted along the upper two stages of the Scout. These spoilers were designed to blow off shortly after launch and might hit and damage the fins at the base of the Scout. In order to determine whether the spoilers planned for installation on the Scout were needed, measurements of the response to dynamic loads imposed by winds at average velocities up to approximately 33 mph were made on a full-scale Scout vehicle mounted vertically on the launching tower at the NASA Wallops Station. From these measurements, it has been concluded that the deflections and bending moments measured in response t o wind-induced dynamic loads were small and should present no structural problems to the vehicle. No significant difference exists between the responses measured with and without spoilers of the type used on the Vanguard vehicle.

Jones, George W., Jr.↗

Modal identification experiment

The Modal Identification Experiment (MIE) is a proposed on-orbit experiment being developed by NASA's Office of Aeronautics and Space Technology wherein a series of vibration measurements would be made on various configurations of Space Station Freedom (SSF) during its on-orbit assembly phase. The experiment is to be conducted in conjunction with station reboost operations and consists of measuring the dynamic responses of the spacecraft produced by station-based attitude control system and reboost thrusters, recording and transmitting the data, and processing the data on the ground to identify the natural frequencies, damping factors, and shapes of significant vibratory modes. The experiment would likely be a part of the Space Station on-orbit verification. Basic research objectives of MIE are to evaluate and improve methods for analytically modeling large space structures, to develop techniques for performing in-space modal testing, and to validate candidate techniques for in-space modal identification. From an engineering point of view, MIE will provide the first opportunity to obtain vibration data for the fully-assembled structure because SSF is too large and too flexible to be tested as a single unit on the ground. Such full-system data is essential for validating the analytical model of SSF which would be used in any engineering efforts associated with structural or control system changes that might be made to the station as missions evolve over time. Extensive analytical simulations of on-orbit tests, as well exploratory laboratory simulations using small-scale models, have been conducted in-house and under contract to develop a measurement plan and evaluate its potential performance. In particular, performance trade and parametric studies conducted as part of these simulations were used to resolve issues related to the number and location of the measurements, the type of excitation, data acquisition and data processing, effects of noise and nonlinearities, selection of target vibration modes, and the appropriate type of data analysis scheme. The purpose of this talk is to provide an executive-summary-type overview of the modal identification experiment which has emerged from the conceptual design studies conducted to-date. Emphasis throughout is on those aspects of the experiment which should be of interest to those attending the subject utilization conference. The presentation begins with some preparatory remarks to provide background and motivation for the experiment, describe the experiment in general terms, and cite the specific technical objectives. This is followed by a summary of the major results of the conceptual design studies conducted to define the baseline experiment. The baseline experiment which has resulted from the studies is then described.

Kvaternik, Raymond G.↗

Neural network for 3D inertial confinement fusion shell reconstruction from single radiographs

In inertial confinement fusion (ICF), x-ray radiography is a critical diagnostic for measuring implosion dynamics, which contain rich three-dimensional (3D) information. Traditional methods for reconstructing 3D volumes from 2D radiographs, such as filtered backprojection, require radiographs from at least two different angles or lines of sight (LOS). In ICF experiments, the space for diagnostics is limited, and cameras that can operate on fast timescales are expensive to implement, limiting the number of projections that can be acquired. To improve the imaging quality as a result of this limitation, convolutional neural networks (CNNs) have recently been shown to be capable of producing 3D models from visible light images or medical x-ray images rendered by volumetric computed tomography. Here, we propose a CNN to reconstruct 3D ICF spherical shells from single radiographs. We also examine the sensitivity of the 3D reconstruction to different illumination models using preprocessing techniques such as pseudo-flatfielding. To resolve the issue of the lack of 3D supervision, we show that training the CNN utilizing synthetic radiographs produced by known simulation methods allows for reconstruction of experimental data as long as the experimental data are similar to the synthetic data. We also show that the CNN allows for 3D reconstruction of shells that possess low mode asymmetries. Further comparisons of the 3D reconstructions with direct multiple LOS measurements are justified.

3D Reconstruction↗

Dynamic Regulation of Sub-Atmospheric Pressure for Constant and Cyclic Gas Loads During Testing of Spacesuit Components

New iterations of the various subsystems within the spacesuit will benefit from a new sorbent technology. For example, sorbents used in the Trace Contaminant Control (TCC) and the Rapid Cycle Amine (RCA) systems within the Exploration Portable Life Support System (xPLSS), part of the Extra-Vehicular Mobility Unit (xEMU). For proper validation, the sub-atmospheric pressure needs to be maintained within a simulated 2 ft 3 spacesuit volume. The traditional approach, which involves placing the entire vent loop within a hypobaric chamber, is not practical for the widespread testing of components and prototypes, as these specialized chambers are costly and not widely available. A two-stage regulator based sub-atmospheric pressure system is presented in this work. The method regulates the pressure based on pressure differentials between the pressure regulation pump, the test system, and the ambient environment. The performance of this system is demonstrated using data collected during a 150+ hour non-regenerative TCC sorbent evaluation, several 24-hour regenerative TCC sorbent evaluations with different regeneration cycles, and an 8-hour RCA sorbent evaluation, all under xEMU operating conditions. For regulation, the inlet regulator was set to propagate a small leak to increase the stability of the system as the gas load from the testing system changes. It was also found that controlling the input flow rate that replaces the material lost during regeneration is critical for ensuring the stability of the system. This system provided excellent pressure regulation, without adjustments, for constant loads during shorter time evaluations (hours), while longer time evaluations (days) are easily obtainable with periodic regulator adjustments. A second method is under development to address longer-term stability and to automate pressure regulation. It will incorporate flow and pressure measurements to dynamically control a set of electronically controlled proportional valves for adjusting the pumping speed and air bleed supply.

Nicholas F Materer↗

Forced Oscillations of Supported Drops

Oscillations of supported liquid drops are the subject of wide scientific interest, with applications in areas as diverse as liquid-liquid extraction, synthesis of ceramic powders, growing of pure crystals in low gravity, and measurement of dynamic surface tension. In this research, axisymmetric forced oscillations of arbitrary amplitude of viscous liquid drops of fixed volume which are pendant from or sessile on a rod with a fixed or moving contact line and surrounded by an inviscid ambient gas are induced by moving the rod in the vertical direction sinusiodally in time. In this paper, a preliminary report is made on the computational analysis of the oscillations of supported drops that have 'clean' interfaces and whose contact lines remain fixed throughout their motions. The relative importance of forcing to damping can be increased by either increasing the amplitude of rod motion A or Reynolds number Re. It is shown that as the ratio of forcing to damping rises, for drops starting from an initial rest state a sharp increase in deformation can occur when they are forced to oscillate in the vicinity of their resonance frequencies, indicating the incipience of hysteresis. However, it is also shown that the existence of a second stable limit cycle and the occurrence of hysteresis can be observed if the drop is subjected to a so-called frequency sweep, where the forcing frequency is first increased and then decreased over a suitable range. Because the change in drop deformation response is abrupt in the vicinity of the forcing frequencies where hysteresis occurs, it should be possible to exploit the phenomenon to accurately measure the viscosity and surface tension of the drop liquid.

Wilkes, Edward D.↗