This experimental study investigates the dynamic response of a slender compliant axisymmetric model when exposed to steady, freestream aerodynamic loads and when exposed to an SBLI-generated unsteady shock impingement in UT Austin’s Mach 5 blowdown wind tunnel. Z-type shadowgraph, pressure-sensitive paint (PSP), and edge-tracking measurements were implemented to measure the multiphysics nature of the FSI. The model was designed with a single flexure to only allow pitching motion, thus making it a single vibrational degree-of-freedom (DOF) system. Results from freestream FSI analysis quantify the aerodynamic stiffness term in the FSI governing equation, and measurements agree well with analytical formulas for estimating the stability derivatives of hypersonic pitching cones. Time-resolved analysis of the unsteady surface pressure field shows that higher standard deviation in pressure values occur when a stronger shock impinges on the model. Consequently, FSI analysis showed evidence of a stronger interaction between the shock foot motion and the structural response for strong shocks that impinge closer to the tip of the nose. For this particular FSI system, the shock foot motion and the structural response are measured to have a strong correlation.

This paper describes an experimental study of the mean flexural deflection induced by aerodynamic loads on a slender axisymmetric model in a Mach 5 flow. The experimental measurements used are pressure-sensitive paint (PSP), temperature-sensitive paint (TSP), and edge tracking, to obtain surface pressure, surface temperature, and mean deflection of the structure, respectively. Multiple generic vehicle models, based on the scaled outer-mold line of the IC3X vehicle developed by AFRL, were tested at varying angles of attack in the UT Austin Mach 5 wind tunnel. The models are 30 cm in length and have a maximum diameter of 3 cm. The models are 3D-printed and designed to have varying degrees of elasticity under the aerodynamic loads expected during testing. The PSP, TSP and edge tracking are performed at an image acquisition rate of 1 kHz. The data were used to evaluate the static pressure and temperature field of the model as well as its displacement when subjected to a 0- and 6- degree angle of attack in Mach 5 flow.

This chapter presents a comprehensive study that focuses on developing and rigorous assessment of a predictive model tailored for estimating bending loads within structural systems. The model leverages strain measurements as input parameters, processed through the pseudo-inverse matrix technique, resulting in highly accurate load predictions. The investigation explores the model's performance across various scenarios, with particular emphasis on its sensitivity to noise and its impact on prediction accuracy. This chapter highlights the model's sensitivity to point load placement (L-f), demonstrating that shifting the point load away from the boundary condition reduces load sensitivity, while positioning it closer heightens sensitivity, making it more susceptible to noise. Moreover, the research investigates scenarios involving sensor removal and malfunction, showing their substantial impact on load prediction. Additionally, the study extends the model's capabilities to predict temperature changes based on thermal strain inputs, achieving close alignment with actual values. In summary, this predictive model proves robust in estimating bending loads, but its sensitivity to noise, load placement, and the importance of sensor quality are emphasized, along with its versatile application in temperature change prediction.

A method is investigated to estimate the full-field deformation spectra of a vibrating clamped plate using a set of PVDF strain sensors. A thin, fully clamped brass panel is instrumented with five piezo film sensors and excited using broadband noise from a loudspeaker. In an initial training stage, the panel vibration is measured simultaneously using the PVDF sensors and Digital Image Correlation. A linear mixing matrix is then learned that relates the sensor voltages to the modal coordinates of the first three structural modes. The number of time steps used for training should exceed ten times the number of PVDF sensors. The mixing matrix is then used to estimate full-field deformation spectra of another test with different excitation. The estimated resonant peaks show good agreement when compared to the true vibration peaks obtained from Digital Image Correlation and exhibit a higher signal-to-noise ratio than the DIC data.

Three cases of ramp-induced shock/boundary-layer interactions (SBLIs) are investigated using 20 kHz fast-response pressure-sensitive paint (PSP). Various ramp angles (20 degrees, 26.5 degrees, and 28 degrees) in Mach 2 and Mach 5 flows resulted in different shock strength and separation length scales. The fast-response PSP effectively captured the unsteady dynamics of the interaction in the regions upstream of the compression ramp corner and the ramp face. In addition, the elongated structures on the compression ramp were observed in all interactions, which are likely to be Gortler vortices. The Gortler vortices were seen to be stronger and more stationary in Mach 5 interactions than in Mach 2 case where the structures were less noticeable. The shock foot location and the surrogate reattachment point were detected from the surface pressure field. To study how the shock motion and the pressure fluctuations are related, a cross-correlation analysis was conducted between the streamwise location of the shock foot and the entire surface pressure fields. A negative correlation was observed with the pressure in the intermittent region and a positive correlation was seen in the downstream separated flow and reattachment regions. Different interactions shared some similarities but the Mach 2 SBLI had higher correlations in general, especially in the upstream boundary layer region. Further coherence analysis revealed that all three cases exhibit dominant correlations between the shock foot and reattachment region in the lower frequency range which is consistent with the large-scale breathing motion of the separation bubble. In Mach 5 SBLIs, non-negligible coherence was observed downstream of the shock in the low- to mid-frequency. Only the weaker SBLI cases displayed significant coherence between the shock foot and the pressure fluctuations in the upstream boundary layer, which is not observed in the stronger interaction case. Even between two weaker interactions, the effect of upstream flow was more prominent in Mach 2 case, indicating the effect of Mach number on the unsteady dynamics.

Flight vehicles that operate in the supersonic regime can be subject to adverse fluid–structure interactions due to their lightweight design. The presence of geometric obstructions such as control surfaces or fins can induce shocks that can interact with the boundary layer, leading to flow separation. This work investigates experimentally the interaction between a compliant panel in a Mach 2 flow under a compression ramp-induced shock-wave/boundary-layer interaction (SBLI). Thin brass panels of different thickness are investigated in a wind tunnel. Tests are performed both with and without a 20° compression ramp installed. This direct comparison allows characterization of the effect of the SBLI on the system dynamics. High-speed stereoscopic digital image correlation (DIC) and fast-response pressure sensitive paint (PSP) are used to obtain simultaneous measurements of full field deformation and surface pressure of the panels. The panel vibration is dominated by the first bending mode. Despite the forcing of the separation shock foot, the presence of the SBLI does not significantly modify the operational deflection shape, frequency, and amplitude of the dominant vibration mode, beyond what is observed for the no-SBLI case. On the other hand, analysis of the shock foot motion shows that the shock primarily oscillates at the first natural frequency of the panel. This leads to the conclusion that the shock foot oscillation is driven by the panel vibration in a one-way coupling mechanism. The SBLI does modify the higher modes, which is likely due to localized forcing by the separation shock foot. Full-field surface pressure predictions are made using first order piston theory. Results show that the fluid–structure interaction is dominated by the large region of attached flow upstream of the shock foot.

Additive manufacturing methods have advanced a lot in the past year. Methods like Fused Deposition Modeling (FDM) have gained popularity due to their versatility in material and minimal limitation on the geometry. Structural modeling of additively manufactured parts can, however, be complicated. This is primarily due to the dependence of material stiffness on print settings such as layer height, infill density, and infill pattern. In addition, the material can exhibit anisotropic characteristics due to parameters like the adhesiveness of layers, the orientation of the raft, and the layer deposition speed. This study conducts an experimental modal analysis on a 40

The unsteadiness of a 28 degree compression ramp in a Mach 5 flow is investigated by using 100 kHz particle image velocimetry (PIV) and 20 kHz fast-response pressure sensitive paint. This work builds upon extensive measurements made in a Mach 2 compression ramp interaction using the same methods. The 28-degree ramp produces a large separated flow with a mean separation length scale that extends over about 3 boundary layer thicknesses. The fast-response PSP effectively monitored the unsteady dynamics of the interaction. The location of the shock foot was detected from the surface pressure field. To study how the shock motion and the pressure fluctuations are related, a cross-correlation analysis was conducted between the streamwise location of the shock foot and the entire surface pressure fields. A negative correlation was observed with the pressure in the intermittent region and a positive correlation was seen in the downstream separated flow region. Furthermore, the time-resolved PIV measurement in the x-y plane captured a significant scale of reverse flow near the compression ramp corner. From PIV data, the separation line (u = 0) has been tracked and compared to the extracted shock foot from PSP. In addition, the complex SBLI-present velocity field has been reconstructed using POD modes. In the reduced-order velocity field, velocity structures related to the separated flow and the associated shear layer were observed.

Optical measurement techniques such as digital image correlation (DIC) and laser Doppler vibrometry (LDV) are advantageous to measure structural vibrations due to their non-contact nature. While these techniques are immune to electromagnetic interference, they can suffer from optical distortions due to index-of-refraction gradients associated with boundary layers, shock, shock and expansion waves, and combustion. When the optical distortion is due to unsteady processes, such as those associated with turbulence or other time-dependent flow phenomena, these effects cannot be easily accounted for and may result in erroneous measurements of the vibrations. An exploratory test campaign was performed to characterize these errors in a flow-structure interaction experiment conducted in a Mach 5 low-enthalpy blowdown wind tunnel. The flow-induced vibration of a compliant brass panel (0.25 mm thick) was measured using 3D-DIC and LDV, by imaging the panel through the flow. Additional optical distortions were generated by a 27.5 ^∘ compression ramp that was installed on the floor of the tunnel and generated a shock-induced, turbulent separated flow. Results showed that the LDV data were not affected within the uncertainty of the measurement by flow-induced optical distortions. LDV and DIC results generally agreed well for frequencies between 250 Hz and 2000 Hz, which contained all dominant vibration modes. The shock unsteadiness was expected to generate dynamic distortions for all locations that were measured through the shock. No evidence of this was found, which indicates that such distortions were below the noise floor of the 3D-DIC setup used for this experiment. In one test, the local discrepancy between DIC and LDV differed more when imaged through the shock than for a case where both systems measured the vibration upstream of the shock.

The fluid-structure interaction of a compliant panel under a compression-ramp-induced shock/boundary layer interaction (SBLI) is investigated experimentally in a Mach 5 wind tunnel. A thin brass panel of dimensions L=121.9 mm (chord), W=63.5 mm (span) and h=0.254 mm (thickness) is installed flush with the floor of the tunnel test section. A 28◦compression ramp is installed downstream of the panel, creating a shock-induced turbulent separated flow with a separation length of approximately three boundary layer heights. Measurements of the panel vibration are performed using high-speed stereoscopic digital image correlation and the fluctuating surface pressure on the panel is measured using fast-response pressure sensitive paint. Clear evidence is found that the SBLI surface pressure fluctuations are significantly affected by the panel vibration. Importantly, the pressure standard deviation in the intermittent region increases by 50% due to surface compliance when compared to a rigid panel baseline case. Analysis also shows the shock foot motion is strongly correlated with the panel vibratory response. In addition, the panel vibration increased by several orders of magnitude in the presence of the SBLI as compared to the case with Mach 5 flow but without a ramp present. The importance of coupling between the SBLI and panel vibration is discussed and a possible mechanism of the coupling is suggested.

A thin compliant panel was tested in a Mach 2 wind tunnel. The panel was mounted flush with the tunnel floor and was of dimensions L=121.9 mm (chord), W=63.5 mm (span) and h=0.254 mm (thickness). A ����° compression ramp was placed 5 mm downstream of the model, which induced a shock/boundary layer interaction with fully separated flow over parts of the panel. Full-field deformation was measured using Digital Image Correlation and the surface pressure field was obtained from fast-response pressure-sensitive paint. Analysis of the shock foot motion was performed using a curve-fitting method. Comparison of the shock motion between a rigid and compliant panel case showed no difference in the size of the intermittent region but found that the shock motion over the compliant panel is affected by the panel vibration. Proper Orthogonal Decomposition revealed that the surface pressure is dominated by low-frequency unsteady shock motion, in both cases (rigid and compliant panel). The sixth POD mode clearly shows the streamwise shock foot motion oscillates at the first panel vibration frequency. The surface pressure field upstream of the shock foot is dominated by piston-theory aerodynamics and thus correlated to the slope of the compliant panel. The Sparse Identification of Nonlinear Dynamic Systems algorithm was employed to find low-order representations of the system dynamics. Linear stiffness matrices could be consistently recovered. The measurement noise however prevented extraction of additional relations, such as linear damping matrices or forcing terms from the surface pressure.

This work investigates surface pressure unsteadiness on a compliant panel under a shockwave/boundary-layer interaction (SBLI) induced by a 2D compression ramp with an angle of 20o in a Mach 2 wind tunnel. High-speed digital image correlation (DIC) and fast-response pressure-sensitive paint (PSP) measurements are used to measure the panel displacement and panel and ramp-face surface pressure fluctuations at 5kHz and 20kHz, respectively. The data reduction technique of POD (proper orthogonal decomposition) was employed both for pressure and displacement fields. POD mode distribution for the pressure fields reveals that the first six modes have 60% of the total energy and exhibit low-frequency content for both rigid and compliant panels. The vibration of the compliant panel was seen to alter the energy distribution of the high energy modes as compared to the rigid panel case. The cross-correlations between the displacement and pressure modes were made using the time coefficients. This analysis shows significant correlations were present among the lower modes. The highest correlation was between displacement mode 1 and the pressure mode 4, which stemmed from the upstream of the intermittent region. The analysis was also made for the surrogate shock foot and reattachment lines. The correlation shows that panel vibration lowers the correlation between the shock foot and reattachment line when compared with the rigid panel case.

Experiments are performed in a Mach 2 wind tunnel to investigate the vibration of a compliant panel under a ramp-induced shock wave/boundary layer interaction (SBLI). The panel is made from brass shim stock of length and width 122 mm × 63.5 mm. It is located just upstream of a 20° compression ramp that creates a shock-induced separated flow, where the mean separation length scale is about two boundary layer thicknesses. The region of the separation shock foot is characterized by large pressure fluctuations. These increase vibration amplitudes of the higher panel modes and especially the second mode, which has an antinode near the shock foot region. This work uses aeroelastic tailoring to reduce the panel vibration induced by the large pressure fluctuations of the shock foot. A thin rib is attached in the spanwise direction to the lee side of the panel at the location of the mean separation line of the SBLI. Stereoscopic digital image correlation is used to obtain time-resolved, full-field displacement fields during wind tunnel runs. Three different panel configurations are tested. First, a baseline case is established with a plain panel of thickness h = 0.254 mm. Then the rib is attached to the panel using double-sided, viscoelastic tape. Finally, the rib is attached directly to the panel using an epoxy adhesive. The results show that adding the rib in either configuration reduces the overall panel vibration by about 50% but especially reduces the vibration of the second mode. The configuration with the tape adds mass and damping to the system and is more effective at vibration reduction than the configuration with the epoxy, which increases mass and stiffness.

The fluid-structure interaction (FSI) of a compliant panel under a compression-ramp-induced shock-wave/boundary-layer interaction (SBLI) has been studied in Mach 2 flow. Simultaneous high-speed measurements of the velocity field and the panel displacement were conducted using 50 kHz particle image velocimetry (PIV) and 5 kHz stereoscopic digital image correlation (DIC). The mean effect of the panel displacement has been evaluated by monitoring the change in velocity profiles along the streamwise direction (x), upstream of the separated flow region. Streamwise (u) velocity near the panel surface has been shown to change its magnitude in response to the wall shape. Furthermore, the strong cross-correlation between fluctuations of the wall-normal panel displacement and the transverse (v) velocity can be explained by the flow remaining tangent to the wall surface as the panel deforms. This latter result is consistent with the panel motion being sufficiently low frequency compared to flow convective time scales that the flow is quasi-steady. In addition, assessment of the correlation between the separation shock position and panel displacement seems to suggest that when the panel is bulged down (concave up) at the downstream end of the panel, a larger separated flow is generated and the shock moves upstream. This observation remains speculative, but is consistent with the flow undergoing greater compression for the bulged down case.

This experimental study focuses on fluid-structure interaction (FSI) for a thin compliant panel under a shock/boundary layer interaction (SBLI) generated by a 2D compression ramp in a Mach 2 wind tunnel. In previous work, we have studied the FSI for this configuration using simultaneous fast-response pressure-sensitive paint (PSP) and digital image correlation (DIC). Simultaneous PSP/DIC allows for examination of the relationship between the dynamic panel displacement and surface pressure loading, respectively. Spectral analysis showed that pressure fluctuations within the interaction region and shock-foot unsteadiness tend to lock to the first mode resonant frequency of the compliant panel. The current study aims to utilize synchronous high-speed stereoscopic PIV (25 kHz) and DIC (5 kHz) techniques to better understand the coupling between the flow field and the panel displacement field. The PIV is obtained in a streamwise-spanwise plane located at 15% of the boundary layer height. Thin compliant polycarbonate panel with thicknesses of 1 mm is utilized, which has a first-mode vibrational frequency of 407 Hz. The 1 mm panel out-of-plane displacement amplitude was up to 15% of the boundary layer thickness. The analysis includes low-pass and band-pass filtering of the velocity data, including the surrogate separation line, and cross-correlation analysis between panel displacement and velocity. The results indicate a clear coupling of the panel motion and velocity field, but the spectral analysis suffers from limited time records associated with the pulse-burst laser used for PIV. Future work will focus on collecting more data to improve the statistical convergence of the results.

This experimental study aims to investigate and compare unsteady surface pressure fluctuations on rigid and compliant panels under a shock-wave/boundary-layer interaction (SBLI) generated by a 20o compression ramp in a Mach 2 wind tunnel. The compliant panel was made of 1mm thick polycarbonate, and had a first mode resonant frequency of 407 Hz. High-speed simultaneous pressure-sensitive paint (PSP) and digital image correlation (DIC) techniques allow for examination of the panel surface pressure and panel displacement, respectively, with acquisition frequencies of 20 kHz and 5 kHz respectively. The PSP measurements were also made on the face of the rigid compression ramp and so the effect of fluid-structure interaction on the reattachment dynamics could be explored. The rigid panel pressure measurements demonstrated the spectral content inherent to the SBLI. Spectral analysis of the surface pressure fields revealed that the SBLI shock foot and separation shear layer behave as low- and high-frequency filters, respectively. The results indicate the panel dynamics have a strong effect on separation- and reattachment-flow dynamics. Modes obtained by spectral proper orthogonal decomposition (SPOD) show good agreement with modes obtained from bandpass filtered displacement and pressure fields.

In this paper, broad-band phase-based motion magnification (BPMM) is used to improve the modal parameter estimation from high-speed video of a structure undergoing low amplitude vibration. The authors use a novel application of the phase-based motion magnification technique to obtain improved results in the presence of image noise. A numerical simulation is performed to demonstrate and quantify the effect of broad-band motion magnification. A clear correlation is found between the magnification factor and the error in the motion obtained from 2-dimensional point tracking (2DPT). In a laboratory experiment, operational modal analysis is performed on a metallic nozzle with a 5.3 in exit diameter and a constant wall thickness of 0.03 inches. Fluorescent markers are painted on the nozzle lip. The nozzle is attached to a test stand and excited by pressurized air. The induced vibrations are captured by a single high-speed camera, which takes images of the nozzle lip. Using a 2DPT algorithm, the displacement history of the markers in the nozzle exit plane is extracted. As is typical for small and stiff structures, the resonant frequencies are quite high and the resulting vibration amplitudes are fairly low. This leads to low signal-to-noise ratio in the higher frequencies, which makes the following operational modal analysis much harder. By using BPMM as a preprocessor, the authors demonstrate that the outcome of modal analysis is greatly improved. Comparison with Finite Element analysis shows that the mode shapes agree much better with the experimental results when motion magnification is used. The modal parameters of the first six modes are found in the frequency range 0-1400 Hz using the new methodology, whereas without motion magnification only the first five modes are found. (C) 2020 Elsevier Ltd. All rights reserved.

Flight vehicles that operate in the supersonic regime can be subject to adverse fluid-structure interactions due to their lightweight design. The presence of geometric obstructions such as control surfaces or fins can induce compression shocks that can interact with the boundary layer, leading to flow separation. The interaction of flow, compression shock and structural dynamics is very difficult to model and currently only poorly understood. This work investigates experimentally the interaction between a compliant panel in a Mach 2 flow under a ramp-induced shock wave boundary layer interaction (SWBLI). Brass panels of length 4.8" and width 2.5" and different thicknesses (h=0.020", 0.016", 0.012" and 0.010") are investigated. Tests are performed both with and without a compression ramp installed. This direct comparison allows characterization of the effect of the SWBLI on the system dynamics. High-speed stereoscopic digital image correlation (DIC) and fast-response pressure sensitive paint (PSP) are used to obtain simultaneous full field deformation and surface pressure of the panels. The results show that the shock induced by the 20-degree compression ramp leads to separation of the turbulent boundary layer close to the ramp starting at about 80\% of the panel length. This results in a region of large pressure fluctuations which primarily increase the vibration amplitude of the second panel mode. Analysis of the fundamental mode, which contains most of the vibration energy of the panel, shows that the SWBLI does not lead to changes of this mode, neither in frequency, amplitude or mode shape. On the other hand, analysis of the shock foot motion shows that the shock primarily oscillates at the fundamental frequency of the panel. This means that while the shock and panel oscillate at the same frequency, it is not two-way coupling. The panel vibration dictates the motion of the shock, but the shock (or rather the SWBLI) does not modify the fundamental panel vibration beyond the forcing provided by the turbulent boundary layer. Full field surface pressure predictions are made using linearized potential flow theory, which relates the local slope of the panel to the surface pressure. Results are found to be in good agreement in the region of attached flow.

This paper demonstrates the use of broad-band phase based motion magnification (PMM) to improve the modal parameter estimation from high-speed stereoscopic digital image correlation (DIC). PMM is used as a diagnostic technique to investigate the free vibration response of a panel. The compliant panel, consisting of a thin polycarbonate sheet, forms a test section wall in a supersonic blow-down wind tunnel, where it is used to investigate supersonic fluid-structure interaction in the presence of shock wave boundary layer interaction. The panel is excited by an impact hammer and the transient deformation is captured using high-speed cameras. The original and motion-magnified images are input to a digital image correlation algorithm to calculate the out-of-plane deformation of the panel. The measured deformation is used to extract the modal parameters of the compliant panel. By using PMM as a preprocessing tool in a broad frequency band containing multiple structural modes, the signal to noise ratio of the measured deformation is improved. The use of PMM improves the estimated mode shapes, increasing the MAC value of the first mode compared to FEM predictions from 0.29 to 0.99. Motion magnification also improves the coherence between measured input force and panel deformation by up to 13%if suitable parameters are chosen.