Timothy J. Beberniss

High-Speed Digital Image Correlation Measurements of Random Nonlinear Dynamic Response

Future United States Air Force (USAF) high-speed vehicles will require innovative, non-contacting full-field measurement techniques to validate analysis and design practices. In this experimental investigation, the authors explore the feasibility of using high-speed 3D digital image correlation (DIC) to measure the geometrically nonlinear and stochastic response of a compliant panel representing thin-gauge aircraft-like structure. Existing measurement techniques typically employed for this application include laser vibrometry, accelerometers, and discrete strain gages. However, these approaches are limited to a few points or direct contact resulting in altered structural response. The possibility of full-field noncontact displacement and strain measurement is an attractive alternative for this type of dynamic response testing, particularly as one is not limited to predetermined sensor location. The technical challenges of using DIC for this application include extending the technique from quasi-static or extremely short duration transient dynamic measurement technique to steady-state, long-duration (seconds of data) random response. Multiple, long-time sample records are desired for ensemble averaging, and correspondingly high sample rates generate appreciable volumes of digital images never before attempted with this type of analysis. DIC displacement and strain results are compared to the more traditional measurement methods to establish accuracy. Results demonstrate the feasibility of using DIC for nonlinear dynamic displacement and strain response measurements. The ability to obtain full-field displacement data was beneficial towards identification and differentiation of the dynamic panel response from the inherent dynamic response of the experimental facility.

Mode Shape Comparison Using Continuous-Scan Laser Doppler Vibrometry and High Speed 3D Digital Image Correlation

Experimental structural dynamic measurements are traditionally obtained using discrete sensors such as accelerometers, strain gauges, displacement transducers, etc. These techniques are known for providing measurements at discrete points. Also, a majority of these sensors require contact with the structure under test which may modify the dynamic response. In contrast, a few recently developed techniques are capable of measuring the response over a wide measurement field without contacting the structure. Two techniques are considered here: continuous-scan laser Doppler vibrometry (CSLDV) and high speed three dimensional digital image correlation (3D-DIC). The large amount of measured velocities and displacements provide an unprecedented measurement resolution; however, they both require post processing to obtain measurements. In this investigation, the frequency response function of a clamped-clamped flat beam will be determined using a modal hammer test, CSLDV, and high speed 3D-DIC. The mode shapes of the beam determined by each of these experimental methods will then be compared to assess the relative merits of each measurement approach.

Experimental Investigation of Dynamic out of Plane Displacement Error in 3D Digital Image Correlation

With the development and implementation of digital image correlation (DIC) in static and dynamic experimentation, a deeper understanding of the variation of measurement error due to the experimental setup is sought. In this investigation, dynamic rigid body motion is measured using two high speed digital CMOS cameras paired with 3D digital image correlation (3D-DIC), a single point laser vibrometer, and a single axis accelerometer. To determine measurement error, a comparison is made between the measured displacement, velocity, and acceleration in the frequency domain. Prior to dynamic testing, characterization experiments with no motion were performed to determine potential sources of noise in a static environment. It was shown that the camera cooling fans and source of lighting can contribute to measurement noise. Dynamic experiments were designed to investigate the potential effect camera angle, sampling rate, and shutter speed have on measurement error. In addition to the 3D-DIC setup, speckle patterns with varying size, distribution, and randomness were investigated. Results show that the 3D-DIC setup and speckle pattern characteristics can affect the measurement error and measurement quality

Measurement of Nonlinear Normal Modes Using Mono-harmonic Force Appropriation: Experimental Investigation

A structure undergoing large amplitude deformations can exhibit nonlinear behavior which is not predicted by traditional linear theories. Structures with some initial curvature offer an additional complication due to buckling and snap through phenomena, and can exhibit softening, hardening and, internal resonance. As a structure transitions into a region of nonlinear response, a structure’s nonlinear normal modes (NNMs) can provide insight into the forced responses of the nonlinear system. Mono-harmonic excitations can often be used to experimentally isolate a dynamic response in the neighborhood of a single NNM. This is accomplished with an extension of the modal indicator function and force appropriation to ensure the dynamic response of the structure is on the desired NNM. This work explores these methods using two structures: a nominally-flat beam and a curved axi-symmetric plate. Single-point force appropriation is used by manually tuning the excitation frequency and amplitude until the mode indicator function is satisfied for the fundamental harmonic. The results show a reasonable estimate of the NNM backbone, the occurrence of internal resonance, and couplings between the underlying linear modes along the backbone.

The Measurement of a Nonlinear Resonant Decay Using Continuous-Scan Laser Doppler Vibrometry

The nonlinear resonant decay of a structure offers much insight into the frequency-amplitude behavior of a structure’s dynamic response. The spatial deformation during this decay is especially important since nonlinear responses can cause unexpected stress concentrations necessitating full-field measurements for comparison with a model. In this context, full-field measurement techniques, such as continuous scan laser Doppler vibrometry (CSLDV) and high speed three dimensional digital image correlation (3D-DIC) provide tools to obtain the full-field dynamic response experimentally. While CSLDV has been used to measure the steady state response of linear and nonlinear structures as well as transient responses of linear structures, it is unclear whether the approach can be successful for transient nonlinear measurements where the frequency of the dynamic response is amplitude dependent. In this investigation, the capabilities of CSLDV will be utilized to measure the nonlinear resonant decay of a clamped-clamped flat beam. The response measured using CSLDV will then be compared with the decay response measured with 3D-DIC to validate the CSLDV method and to understand the advantages and disadvantages of each.

Nonlinear Dynamic Response Prediction of a Thin Panel in a Multi-Discipline Environment: Part II—Numerical Predictions

Hypersonic aircraft structures must operate in a complex loading environment, where the coupling of the aircraft structural response with the aerodynamics will lead to conditions involving rich nonlinear dynamics. The modeling of these fluid-thermal-structural interactions is complex and prohibitively expensive when high fidelity models are used (i.e., CFD and FEA). This aspect, and the lack of relevant flight-test and experimental data, have resulted in knowledge gaps, which have led to the design of overly-conservative structures in the past. Work at the Structural Sciences Center (SSC) of the USAF Research Laboratory has focused on addressing these knowledge gaps from a structures perspective. As discussed in Part I of this paper, 3 years ago the SSC began a series of wind-tunnel experiments to provide full-field experimental data for a clamped nominally flat panel exposed to supersonic flow. The present work will focus on numerical predictions of the panel dynamic response using a reduced order model (ROM) for the structural response and full-field measurement data to represent the loads on the panel.

Nonlinear Response of a Thin Panel in a Multi-Discipline Environment: Part I—Experimental Results

High-speed aircraft structures are susceptible to the extreme and transient effects of the associated aerodynamic environment. These structures can experience a myriad of limit states—yield, fatigue, creep, buckling, and the response is very often path-dependent. Hypersonics, defined as flight speeds greater than Mach 5 (Heppenheimer, NASA Technical Report, NASA SP-2007-4232, September 2007) where aerodynamic heating drives the analysis and design, often causing appreciable structural concerns, is a flight regime with very little practical experience. While the NASA Space Shuttle Orbiter and other space-access vehicles routinely transit the Mach 5 barrier, long-duration air-breathing flights represent but a scant portion of past flight-test programs. As a result, the aerospace industry accounts for the associated uncertainties in the structural response through overly-conservative, and often program-deleterious, design assumptions. The USAF Research Laboratory, Structural Sciences Center (SSC), is investigating and developing analysis methods to predict the changing, nonlinear response of hypersonic hot-structures; however, there is a lack of relevant flight-test and experimental data useful for validating these developing structures-centric methods. The SSC recently began a series of thorough wind-tunnel experiments to provide quality, full-field experimental data for a simple, clamped nominally flat panel exposed to supersonic flow, shock boundary-layer interactions (SBLI) and heated flow. External heating sufficient to buckle the test article during supersonic wind tunnel experiments is being explored. Early results are presented in the present study. Additionally, wind tunnel conditions will be sought that lead to panel snap-through dynamics. The present study documents the evolution of the experiments, emphasizing the nonlinear response of the panel in preparation for upcoming wind-tunnel experiments. Also discussed are the characteristics of the experimental conditions leading to the nonlinear structural response, and the full-field displacement, pressure and thermal results necessary for model validation. Part II of this study will present the results of a numerical study of the same structure in the supersonic environment.

Linear and Nonlinear Response of a Rectangular Plate Measured with Continuous-Scan Laser Doppler Vibrometry and 3D-Digital Image Correlation

Dynamic measurement of real structures, such as panels, can be difficult due to their low mass and complicated deformations under large amplitude loading conditions. These conditions bring to light shortcomings of traditional sensors such as accelerometers, strain gauges, displacement transducers, etc. A majority of these sensors require contact with the structure under test which tends to modify the dynamic response of these light structures. In contrast, a few recently developed techniques are capable of measuring the response over a wide measurement field without contacting the structure, which is ideal for these structures. Two techniques are considered here: continuous-scan laser Doppler vibrometry (CSLDV) and high speed three dimensional digital image correlation (3D-DIC). Both techniques can be used to return real-time deformation shapes under certain conditions; however, measurements will be obtained using post processing here. The linear and nonlinear deformations of a clamped flat plate under steady state sinusoidal loading will be measured using both techniques and compared with a finite element model to assess the relative merits of each measurement approach.

Temporal Aliasing in High-Speed 3-Dimensional Digital Image Correlation Vibration Measurement

High-speed 3-dimmensional digital image correlation is rapidly becoming a feasible and practical method for vibration measurement. Despite the growing popularity in dynamic DIC, no known studies focusing on temporal aliasing of a DIC measured vibration response exist. Therefore a study on the potential for and methods to deal with aliasing in vibration measurement utilizing high-speed 3D digital image correlation is conducted. In this study both spatial and temporal aliasing in image processing is addressed. To date it was found that despite there being a wealth of spatial anti-aliasing solutions, they have limited to no impact on aliasing of the DIC displacement time signal used for vibration measurement. No known temporal anti-aliasing technique currently exists for digitized high-speed images for the purposes of motion tracking. Temporal aliasing is therefore likely a pitfall that needs to be systematically avoided during DIC vibration measurement.

Prediction of Dynamic Response for Ti/TiB Functionally Graded Beams

Functionally graded ceramic‐metal materials are candidates for use in aerospace structures that are exposed to high temperatures. These structures will experience other demands such as significant pressure fluctuations that will cause panels to vibrate at high frequencies. These materials must be engineered for specific applications. Standard engineering methods were used to predict the response of Ti/TiB cantilever beams to quasi‐static and dynamic loadings. Experiments were performed and compared to the predictions. The predictions and experiments did not agree due to significant uncertainty about the elastic modulus of TiB.