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Preliminary Assessment of the Impact on the V-Band Oxygen Channels From Satellite Communication Uplinks

We calculate the percentage of time that an ATMS-like instrument [1] will be illuminated by the uplink beam of one of the proposed V-band communication system and estimate the damage resulting from such exposure. Using a combination of openly available information and educated guesses about the location and characteristics of the up/down link terminals, we constructed the ground segment of a hypothetical high-speed communication network. The space segment of the network was constructed from the orbital data of the existing Starlink constellation [2] of 6223 communication satellites (comsats) which is used as strawman to represent any other possible constellation of communication satellites. It is shown that without a very delicate balance of frequency allocations (science vs telecommunications), coupled with extremely steep and deep bandpass-defining filters, and strict adherence to the agreed limits (i.e. no out-of-band transmissions) the deployment of the telecommunication network leads to almost-complete loss of some important geophysical data. For the analysis we use the spectral characteristics of the ATMS instrument with the ephemeris for the NOAA-21 satellite [3]. The analysis is conducted for the USA and the simulation covers 8 consecutive days in July 2024. Effective and accurate microwave remote sensing of the atmosphere depends on the availability of interference-free spectrum windows at frequencies which are prescribed by physical processes [e.g. 4]. The family of resonant lines of the oxygen molecule near 60 GHz provides a unique opportunity to sample the vertical distribution of temperature and density from space, and it has been exploited for weather and climate studies from polar-orbiting satellites since 1978 (MSU on TIROS-N [5]). It remains a staple in the payloads operated by Russia, China, USA, Japan, France, India, UK, Ukraine [6] which are built around a common blueprint: a few wide-band (hundreds of MHz) channels around 50 GHz to sample the atmosphere and the surface while several more channels with high spectral resolution (few MHz) sample the individual resonant lines. Accurate retrieval of the environmental parameters depends upon the data provided by both sets of channels, and the their location in frequency space is not arbitrary and cannot be altered at will [7, 8]. The introduction of 5G technology in 2019 has driven telecommunication companies to request more bandwidth to be dedicated to their devices. This additional bandwidth is only available in spectral regions traditionally reserved for environmental and astrophysical research, such as the V-band between 50 and 60 GHz for up/downlink between satellites in low-earth orbits and terminals connected to fiberoptics network for distribution to high-speed local internet services. The power broadcast by the uplink communication leg is many orders of magnitude greater than the natural thermal signal emitted from the Earth scene. If the ground antenna were to perfectly align with the passive instrument’s antenna, the spaceborne receiver would suffer permanent, irreparable damage. While a direct boresight-to-boresight conjunction is extremely unlikely (even with a large constellation of satellites the fraction of the celestial sphere occupied by the satellites remains minuscule) the finite size of the ground station’s antenna beam in the sky suggests that the ATMS will be in the near background (as seen from the ground station) of one of the communication satellites and will be illuminated by either the main lobe or the near sidelobes of the uplink antenna more often than it is desirable. For our analysis we first calculate the position of the ATMS with respect to each of the ground stations at a resolution of 0.2 sec, then calculate the position of each of the comsats which are at least 25 deg above the station’s local horizon; finally we calculate the angle between the line-of-sight of the ATMS and the line-of-sight of the comsat. We assume that the gain pattern of the ground station is circularly symmetric; the angle-off-station-boresight then provides an attenuation of the uplink power which we use to assess the likely effect upon the passive instrument’s operations. We assume that each ground station can communicate with all the comsats in its field of view; this implies that, on average, a ground station can engage with 46 comsats simultaneously. The analysis is repeated for the case when the uplink broadcast within the ATMS passive channels (in-band scenario) and for the case when the uplink is limited to frequencies adjacent to the ATMS channels (out-of-band scenario). The antenna of the ground station is modelled as having a HPBW (Half-Power Beam Width) of 0.16 deg and EIRP (Equivalent Isotropic Radiated Power) of 70 dBW. We account for the geometric dissipation of the signal caused by the satellite orbital altitude, the attenuation induced by atmospheric gasses at 51 GHz and the mismatch between the circular polarization of the ground-based transmitting antenna and the linear polarization of the satellite-borne receiving antenna. The damages on ATMS are estimated from bench-level measurement conducted at the ATMS’ manufacturer facilities [unpublished].

passive microwave

Radio Metric Errors Due to Mismatch and Offset Between a DSN Antenna Beam and the Beam of a Troposphere Calibration Instrument

Two components of the error of a troposphere calibration measurement were quantified by theoretical calculations. The first component is a beam mismatch error, which occurs when the calibration instrument senses a conical volume different from the cylindrical volume sampled by a Deep Space Network (DSN) antenna. The second component is a beam offset error, which occurs if the calibration instrument is not mounted on the axis of the DSN antenna. These two error sources were calculated for both delay (e.g., VLBI) and delay rate (e.g., Doppler) measurements. The beam mismatch error for both delay and delay rate drops rapidly as the beamwidth of the troposphere calibration instrument (e.g., a water vapor radiometer or an infrared Fourier transform spectrometer) is reduced. At a 10-deg elevation angle, the instantaneous beam mismatch error is 1.0 mm for a 6-deg beamwidth and 0.09 mm for a 0.5-deg beam (these are the full angular widths of a circular beam with uniform gain out to a sharp cutoff). Time averaging for 60-100 sec will reduce these errors by factors of 1.2-2.2. At a 20-deg elevation angle, the lower limit for current Doppler observations, the beam-mismatch delay rate error is an Allan standard deviation over 100 sec of 1.1 x 10 -14 with a 4-deg beam and 1.3 x 10 -15 for a 0.5-deg beam. A 50-m beam offset would result in a fairly modest (compared to other expected error sources) delay error (less than or equal to 0.3 mm for 60-sec integrations at any elevation angle is greater than or equal to 6 deg). However, the same offset would cause a large error in delay rate measurements (e.g., an Allan standard deviation of 1.2 x 10 -14 over 100 sec at a 20-deg elevation angle), which would dominate over other known error sources if the beamwidth is 2 deg or smaller. An on-axis location is essential for accurate troposphere calibration of delay rate measurements. A half-power beamwidth (for a beam with a tapered gain profile) of 1.2 deg or smaller is desired for calibration of all types of radio metrics. A water-vapor radiometer calibration beam of this size with very low sidelobes would require a clear aperture antenna with a diameter of at least 1.5 m if the primary water vapor sensing channel were in the 20-22 GHz range.

R P Linfield

Spacecraft Conceptual Design for Returning Entire Near-Earth Asteroids

In situ resource utilization (ISRU) in general, and asteroid mining in particular are ideas that have been around for a long time, and for good reason. It is clear that ultimately human exploration beyond low-Earth orbit will have to utilize the material resources available in space. Historically, the lack of sufficiently capable in-space transportation has been one of the key impediments to the harvesting of near-Earth asteroid resources. With the advent of high-power (or order 40 kW) solar electric propulsion systems, that impediment is being removed. High-power solar electric propulsion (SEP) would be enabling for the exploitation of asteroid resources. The design of a 40-kW end-of-life SEP system is presented that could rendezvous with, capture, and subsequently transport a 1,000-metric-ton near-Earth asteroid back to cislunar space. The conceptual spacecraft design was developed by the Collaborative Modeling for Parametric Assessment of Space Systems (COMPASS) team at the Glenn Research Center in collaboration with the Keck Institute for Space Studies (KISS) team assembled to investigate the feasibility of an asteroid retrieval mission. Returning such an object to cislunar space would enable astronaut crews to inspect, sample, dissect, and ultimately determine how to extract the desired materials from the asteroid. This process could jump-start the entire ISRU industry.

solar electric propulsion

Heat Capacity and Thermal Relaxation of Bulk Helium Very Near the Lambda Point

In October 1992 a low temperature experiment was flown on the Space Shuttle in low Earth orbit. The objective of the mission was to measure the heat capacity and thermal conductivity of helium very close to the lambda point with the smearing effect of gravity removed. We report preliminary results from the experiment, and compare them with related measurements performed on the ground. The sample was s sphere of helium 3.5 cm in diameter contained within a copper calorimeter of vey high thermal conductivity. The calorimeter was attached to a pair of high resolution paramagnetic salt thermometers with noise levels in the 10 -10 K range and suspended from a high stability thermal isolation system. During the mission we found that the resolution of the thermometers was degraded somewhat due to the impact of charged particles. This effect limited the useful resolution of the measurements to about two nanokelvins from the lambda point. The results reported here are limited to about ten nanokelvins from the transition.

John A Lipa

Sample Return Science by Hayabusa Near-Earth Asteroid Mission

Assigning the material species to each asteroid spectral type and finding out the corresponding meteorite category is crucial to make the global material map in the whole asteroid belt and to understand the evolution of the asteroid belt. Recent direct observations by spacecrafts are revealing new intriguing aspects of asteroids which cannot be obtained solely from ground-based observations or meteorite studies. However identification of the real material species constituting asteroids and their corresponding meteorite analogs are still ambiguous. Space weathering makes difficult to identify the true material, and there is still a great gap between the remote sensing data on the global surface and the local microscopic data from meteorites. Sample return from asteroids are inevitable to solve these problems. For this purpose sample return missions to asteroids belonging to various spectral classes are required. The HAYABUSA spacecraft (prelaunch name is MUSESC) launched last year is the first attempt on this concept. This report presents outline of the mission with special stress on its science.

A Fujiwara

Analysis of the Erosion of Cubic Centered and Face Centered Metallic Materials [Analyse de L'erosion de Matereaux Metalliques de Structures Cubiques Centree et Face Centree]

A generalized law of erosion, in nondimensional form, is proposed. The aforementioned explicitly gives an account of the nature and the microstructure of the material impacted, the angle of impact of the particles, and their hardness. The erosion behavior of various steels, pig iron, and cast iron is examined as well as the behavior of new ordered intermetallic materials, Fe-25% Al-(Zr, Cr, B). The concern of such alloys in an erosion-corrosion environment is shown. --- Une loi généralisée d'usure par érosion, sous forme non dimensionnelle, est proposée. Celle-ci rend compte explicitement de la nature et de la microstructure du matériau impacté, de l'angle d'impact des particules, de leur acuité at de leur durete. Le comportement à l'érosion de divers aciers et fontes est examiné ainsi que la tenue de nouveaux matériaux intermétalliques ordonnés Fe-25% Al - (Zr, Cr, B). L'interet de tels alliages dans des environnements agressifs du type érosion-corrosion est montré. Mots clés: usure, érosion, modèle, matériaux métalliques, intermétalliques Fe-Al.

A Magnée

A Study of the Aligned-Grid Retarding Potential Analyzer for Electric Propulsion Applications

During the development of energy analyzers for NASA’s Solar Electric Propulsion Plasma Diagnostics Package, detailed studies were performed to compare the benefits and drawbacks of different types of gridded potential analyzers. In particular, modeling and testing were performed on three types of retarding potential analyzer with aligned grids, and one type with unaligned grids. Additionally, a type of gridded energy analyzer was tested. Analyses of the model and test results showed that manufacturing an analyzer with aligned grids required greater precision and knowledge than other analyzers. A properly designed analyzer with aligned grids exhibited superior signal level, acceptance angle control, energy resolution, and compactness compared to an analyzer with unaligned grids. Additionally, the gridded energy analyzer was found to accept a broad range of incidence angles while having superior signal, energy resolution, and compactness compared to retarding potential analyzer with unaligned grid. This article describes the basic design principles deployed in the study, the associated modeling work, and the characterization tests that were performed. The article summarizes the benefits and drawbacks associated with each type of energy analyzer tested.

Electric Propulsion

Returning an Entire Near-Earth Asteroid in Support of Human Exploration Beyond Low-Earth Orbit

This paper describes the results of a study into the feasibility of identifying, robotically capturing, and returning an entire Near-Earth Asteroid (NEA) to the vicinity of the Earth by the middle of the next decade. The feasibility of such an asteroid retrieval mission hinges on finding an overlap between the smallest NEAs that could be reasonably discovered and characterized and the largest NEAs that could be captured and transported in a reasonable flight time. This overlap appears to be centered on NEAs roughly 7 m in diameter corresponding to masses in the range of 250,000 kg to 1,000,000 kg. The study concluded that it would be possible to return a approx.500,000-kg NEA to high lunar orbit by around 2025. The feasibility is enabled by three key developments: the ability to discover and characterize an adequate number of sufficiently small near-Earth asteroids for capture and return; the ability to implement sufficiently powerful solar electric propulsion systems to enable transportation of the captured NEA; and the proposed human presence in cislunar space in the 2020s enabling exploration and exploitation of the returned NEA. Placing a 500-t asteroid in high lunar orbit would provide a unique, meaningful, and affordable destination for astronaut crews in the next decade. This disruptive capability would have a positive impact on a wide range of the nation's human space exploration interests. It would provide a high-value target in cislunar space that would require a human presence to take full advantage of this new resource. It would offer an affordable path to providing operational experience with astronauts working around and with a NEA that could feed forward to much longer duration human missions to larger NEAs in deep space. It represents a new synergy between robotic and human missions in which robotic spacecraft would retrieve significant quantities of valuable resources for exploitation by astronaut crews to enable human exploration farther out into the solar system. The capture, transportation, examination, and dissection of an entire NEA would provide valuable information for planetary defense activities that may someday have to deflect a much larger near-Earth object. Transportation of the NEA to lunar orbit with a total flight time of 6 to 10 years would be enabled by a ~40-kW solar electric propulsion system with a specific impulse of 3,000 s. The flight system could be launched to low-Earth orbit (LEO) on a single Atlas V-class launch vehicle, and return to lunar orbit a NEA with at least 28 times the mass launched to LEO. Longer flight times, higher power SEP systems, or a target asteroid in a particularly favorable orbit could increase the mass amplification factor from 28-to-1 to 70-to-1 or greater. The NASA GRC COMPASS team estimated the full life-cycle cost of an asteroid capture and return mission at approx.$2.6B.

asteroid mining

PERSIANN-Unet: A Global Deep Learning Framework for Near-Real-Time Precipitation Estimation Using Infrared Data

Access to high-quality, high-resolution, near-real-time precipitation data is essential for hydrological and meteorological research and disaster mitigation. Traditional tools such as rain gauges and radar networks, though effective, have limitations, including sparse coverage in remote areas and high operational costs. Satellite data, with its global coverage and high spatial and temporal resolutions, mitigates limitations in coverage. Satellite precipitation products like Hydro Estimator (HE), Integrated Multi-satellitE Retrievals for Global Precipitation Measurement (IMERG), and Precipitation Estimation from Remotely Sensed Information using Artificial Neural Networks (PERSIANN) utilize both geosynchronous thermal infrared (IR) and passive microwave (PMW) data in their operation. PMW sensors offer detailed atmospheric profiles but suffer from higher latency, whereas IR sensors provide lower latency but only capture cloud-top information. Despite this constraint, IR data remains attractive for low-latency precipitation estimation. Recent advances in deep learning, particularly convolutional neural networks (CNNs), have further improved satellite precipitation retrievals. This study introduces PERSIANN-Unet (PUnet or PERSIANN V3), a quasi-global algorithm covering 60°N–60°S that combines IR data, monthly climatology, and the UNet architecture to produce half-hourly precipitation estimates at 0.04° resolution. The product is evaluated against HE, IMERG, and PDIR-Now for 2022–2023. Results show that PUnet closely matches its training target, IMERG V07 Final, at the global scale, and performance is further evaluated against Stage IV as a reference over CONUS. Training PUnet on IMERG (2016–2021) leverages a high-quality, integrated PMW IR-gauge precipitation product while developing an IR-based framework not reliant on PMW availability. By operating on a single global image, PUnet avoids tile partitioning and blending steps, reducing edge discontinuities, and produces more spatially consistent precipitation fields across hemispheres.

Phu Nguyen

Characterization of a New Phase and Its Effect on the Work Characteristics of a Near-Stoichiometric Ni30Pt20Ti50 High-Temperature Shape Memory Alloy (HTSMA)

A new phase observed in a nominal Ni 30 Pt 20 Ti 50 (at.%) high temperature shape memory alloy has been characterized using transmission electron microscopy and 3-D atom probe tomography. This phase forms homogenously in the B2 austenite matrix by a nucleation and growth mechanism and results in a concomitant increase in the martensitic transformation temperature of the base alloy. Although the structure of this phase typically contains a high density of faults making characterization difficult, it appears to be trigonal (-3m point group) with a o ~1.28 nm and c o ~1.4 nm. Precipitation of this phase increases the microhardness of the alloy substantially over that of the solution treated and quenched single-phase material. The effect of precipitation strengthening on the work characteristics of the alloy has been explored through load-biased strain-temperature testing in the solution-treated condition and after aging at 500 ºC for times ranging from 1 to 256 hours. Work output was found to increase in the aged alloy as a result of an increase in transformation strain, but was not very sensitive to aging time. The amount of permanent deformation that occurred during thermal cycling under load was small but increased with increasing aging time and stress. Nevertheless, the dimensional stability of the alloy at short aging times (1-4 hours) was still very good making it a potentially useful material for high-temperature actuator applications.

A Garg

Spike-Nosed Bodies and Forward Injected Jets in Supersonic Flow

The paper contains new numerical simulation and experimental test results of blunt body drag reduction using thin spikes mounted in front of a body and one- or two-phase jets injected against a supersonic flow. Numerical simulations utilizing the NASA CFL3D code were conducted at the Hampton University Fluid Mechanics and Acoustics Laboratory (FM&AL) and experimental tests were conducted using the facilities of the IM/MSU Aeromechanics and Gas Dynamics Laboratory. Previous results were presented at the 37 t h AIAA/ASME/SAE/ASEE Joint Propulsion Conference. Those results were based on some experimental and numerical simulation tests for supersonic flow around spike-nosed or shell-nosed bodies, and numerical simulations were conducted only for a single spike-nosed or shell-nosed body at zero attack angle, alpha=0 o . In this paper, experimental test results of gas, liquid and solid particle jet injection against a supersonic flow are presented. In addition, numerical simulation results for supersonic flow around a multiple spike-nosed body with non-zero attack angles and with a gas and solid particle forward jet injection are included. Aerodynamic coefficients: drag, C D , lift, C L , and longitudinal momentum, M z , obtained by numerical simulation and experimental tests are compared and show good agreement.

M Gilinsky

Spike-Nosed Bodies and Forward Injected Jets in Supersonic Flow

The paper contains new numerical simulation and experimental test results of blunt body drag reduction using thin spikes mounted in front of a body and one- or two-phase jets injected against a supersonic flow. Numerical simulations utilizing the NASA CFL3D code were conducted at the Hampton University Fluid Mechanics and Acoustics Laboratory (FM&AL) and experimental tests were conducted using the facilities of the IM/MSU Aeromechanics and Gas Dynamics Laboratory. Previous results were presented at the 37th AIAA/ASME/SAE/ASEE Joint Propulsion Conference. Those results were based on some experimental and numerical simulation tests for supersonic flow around spike-nosed or shell-nosed bodies, and numerical simulations were conducted only for a single spike-nosed or shell-nosed body at zero attack angle, alpha = 0 degrees. In this paper, experimental test results of gas, liquid and solid particle jet injection against a supersonic flow are presented. In addition, numerical simulation results for supersonic flow around a multiple spike-nosed body with non-zero attack angles and with a gas and solid particle forward jet injection are included. Aerodynamic coefficients: drag, C (sub D), lift, C(sub L), and longitudinal momentum, M(sub z), obtained by numerical simulation and experimental tests are compared and show good agreement.

M Gilinsky

Design, Build, and Testing of the Roman Space Telescope’s Wide Field Instrument Optical Stimulus System (SORC)

The Stimulus Of Ray Cones (SORC) is an optical stimulus system developed to verify, characterize, and calibrate the Roman Space Telescope’s (RST) Wide Field Instrument (WFI) under simulated operational conditions. SORC provides several critical test modes, the primary being point-source mode, which projects an image anywhere on the Focal Plane Assembly (FPA) detectors. This mode provides precise position knowledge of the FPA within WFI. Additional modes enable capturing WFI pupil alignment, evaluation of WFI’s selectable optical elements, and verification of focal plane fiber operation for higher-level system testing. The light source system incorporates a suite of narrowband and broadband fiber fed sources spanning the visible to near-infrared range, with options for pulsed or continuous wave illumination. SORC was designed and built at NASA’s Goddard Spaceflight Center (GSFC). Initial system-level testing occurred under ambient conditions in GSFC’s Spacecraft Systems Development and Integration Facility (SSDIF), followed by vacuum testing at operational temperatures (SORC at 214-222 K) in the Space Environment Simulator (SES). The system was then shipped to BAE Systems in Boulder, CO for post-shipment ambient and cryogenic testing before integration with WFI for two thermal vacuum test campaigns at cryogenic temperatures. This presentation will focus on design, development, and performance of SORC. Details of WFI verification and calibration using SORC, along with test results, have been published previously and will be referenced only as needed to describe SORC. The SORC ground test capability is critical to ensuring WFI meets stringent optical performance requirements, directly supporting the mission’s science objectives.

Stimulus of Ray Cones

Computation of Optimal Interplanetary Low-Thrust Trajectories With Bounded Thrust Magnitude By Means of the Generalized Newton-Raphson Method

The generalized Newton-Raphson method, an iterative procedure for solving nonlinear operator equations, has been extended in application to variational problems with bounded control variables. A minimum fuel interplanetary low thrust orbital transfer problem is worked out in detail to demonstrate the practical aspects of the algorithm as well as its computational effectiveness. The control variables are the thrust magnitude, limited from zero to some prescribed maximum value, and the thrust steering angle.

Computation

Ruled and holographic experiment (AO 138-5)

The AO 138-5 experiment has been designed, via the French Cooperative Payload (FRECOPA) experiment with the aim to study the optical behavior of different diffraction gratings submitted to space vacuum long exposure and solar radiation. Samples were rules and holographic gratings, masters or replica, and some additional control mirrors with various coatings. The experiment was located on the B3, trailing edge of the Long Duration Exposure Facility (LDEF) and has been protected against atomic oxygen flux. The experienced thermal cycling has been evaluated from -23 C to 66 C during the flight, 34,000 orbits. The analysis has been focused on the triple point characterization including light efficiency, wavefront flatness quality and stray light level. Tests were conducted on control mirrors and gratings loaded but not exposed to cosmic dust or solar irradiations. They did not show any significant variations. Solar exposure has damaged the coating reflectivity in the ultraviolet region, the degradation is higher with the gratings, in terms of efficiency. However, wavefront flatness quality and stray light level tests revealed no additional changes.

Francis Bonnemason

Battery Review Board

The topics covered are presented in viewgraph form: NASA Battery Review Board Charter; membership, board chronology; background; statement of problem; summary of problems with 50 AH standard Ni-Cd; activities for near term programs utilizing conventional Ni-Cd; present projects scheduled to use NASA standard Ni-Cd; other near-term NASA programs requiring secondary batteries; recommended direction for future programs; future cell/battery procurement strategy; and the NASA Battery Program.

Vaughn, Chester

Remote Guidance of a Mothership-Daughtership Formation for Asteroid Exploration

This work presents an application of Model Predictive Control to maintain long-term stability for a three-satellite formation around the asteroid Apophis via remote guidance. The mothership and two daughterships perform tomographic characterization with a bistatic radar. The mothership estimates the states of all three spacecraft and determines the necessary control to maintain the desired antipodal daughtership states. An Extended Kalman Filter estimates the mothership states. A Batch Least Squares algorithm estimates the daughtership states and performs maneuver reconstruction for the mothership-administered thrust commands under thruster and gravitational uncertainty. The formulation maintains the antipodal angle with growing instability amidst these uncertainties.

Guidance

Fluid-Thermal-Structural Interactions Induced by an Asymmetric Shock-Wave/Boundary-Layer Interaction in a Mach-6 Compression Corner

An experimental study is conducted of the fluid-thermal-structural interaction of a clamped compliant panel exposed to a three dimensional shock-wave/boundary-layer interaction (SWBLI) induced by a Mach-6 compression ramp with a spanwise nonuniform incoming boundary layer. The nonuniform boundary layer was produced by placing trips on one side of the upstream flat plate, resulting in largely turbulent flow on the tripped side and transitional flow on the untripped side. Measurements of the flowfield confirmed that the tripped boundary layer contained elevated levels of unsteadiness, and the SWBLI was observed to vary from attached to fully separated as the ramp angle was increased from 10◦ to 38◦; the separation region on the tripped side of the panel was noticeably smaller, showing the elevated turbulence levels of the tripped-side flow to remain relatively localized rather than diffusing across the whole model. Full-field, time-resolved panel deformations were measured using high-speed photogrammetry and the vibrational response at each compression angle was characterized. Although the measured modes conformed largely to those from classical clamped-plate theory, some skewing of the mode shapes was observed. IR thermography highlighted regions of the compliant region where elevated temperatures were likely to promote thermal softening effects to the transient panel response. The quasi-static deformation and stress field was used to characterize the internal stress factor of each mode and showed a meaningful relationship between transient panel response and stress contained within each mode: modes with antinodes lying in high-stress areas of the plate tended to exhibit increases in vibrational frequency and decreases in vibrational power, whereas the opposite was true for modes with antinodes in low-stress areas.

Spectral Proper Orthogonal Decomposition