S.M. Spottswood

Nonlinear Sonic Fatigue Response Prediction from Finite Element Modal Models: A Comparison with Experiments

Aircraft skins can fatigue when exposed to high acoustic levels. Accurate prediction of sonic fatigue response is important in designing aircraft structures for long life. The dynamic response of these stiffened skins is both nonlinear and stochastic. Early prediction methods were based on single-mode, linear models which were not accurate for complex structures or large amplitude response levels. Direct time integration of full, nonlinear, finite element models can provide accurate results but requires a significant computational expense. Recent methods reduce the finite element model to a low order system of nonlinear modal equations. The modal equations can then be integrated in the time domain. The computational burden is greatly reduced and an accurate response prediction can be accomplished. Unfortunately, there have been no thorough comparisons of these new methods to experimental data. In this paper, experimental results from a clamped-clamped beam are compared to response predictions from two nonlinear modal methods. Measured strain and displacement spectra agree well with predictions from nonlinear modal models obtained via the finite element method.

On the Use of Reduced-Order Models for a Shallow Curved Beam Under Combined Loading

Future USAF vehicles require structures that can withstand extreme combined environments. Examples include vehicles exposed to launch, sustained hypersonic velocities, re-entry, and stealth aircraft with buried engines and ducted exhaust. Two of the many conditions that a structure in these environments will experience are elevated temperatures and high acoustic loading. Computational methods are needed to rapidly explore the design space for extreme environment structures. There has been a significant amount of work in the area of reduced-order modeling to address the issue of sonic fatigue. These methods have been demonstrated useful for predicting the geometric nonlinear response of aircraft structures to random, fluctuating pressure loadings. Recent work shows that these methods are sufficient for predicting the response of planar structures in combined thermal-acoustic environments. The present study demonstrates that a reduced-order model can also be extended to curved structures experiencing combined thermal-acoustic loading. Successful displacement and strain comparisons for a curved beam structure are made between results from a commercial finite element package and reduced-order models, using a single random pressure load (162 dB) and varying temperature cases.

Characterizing Dynamic Transitions Associated With Snap-Through: A Discrete System

Geometrically nonlinear structures often possess multiple equilibrium configurations. Under extreme conditions of excitation it is possible for these structures to exhibit oscillations about and between these co-existing configurations. This behavior may have serious implications for fatigue in the context of aircraft surface panels. Snap-through is a name often given to sudden changes in dynamic behavior associated with mechanical instability (buckling). This is an often encountered problem in hypersonic vehicles in which severe thermal loading and acoustic excitation conspire to create an especially hostile environment for structural elements. In this paper, a simple link model is used, experimentally and numerically, to investigate the mechanisms of snap-through buckling from a phenomenological standpoint.

NONLINEAR STRUCTURAL REDUCED ORDER MODELING METHODS FOR HYPERSONIC STRUCTURES

This paper focuses on the extension and continued validation of coupled thermal-structural reduced order models for the prediction of the nonlinear geometric response of heated panels of hypersonic aircraft. The large spatial and temporal variations of temperature expected in such structures imply similar variations of the material properties, most notably elastic properties and coefficient of thermal expansion, which must be captured for an accurate response prediction. Accordingly, earlier reduced order models are first extended to include linear variations with local temperature of the elasticity tensor and coefficients of thermal expansion. The validation of these concepts is achieved on a beam structural model. A representative 3-D hypersonic panel is considered next in isothermal conditions to extend the validation of nonlinear reduced order modeling methods to complex structural models. Key in the reduced order model construction is the basis selection and the combination of linear and dual modes introduced and validated in prior efforts is once again found to capture well the structural response, although an additional set of functions, referred to as the tangent duals is introduced to complete the structural response modeling. The corresponding predictions of the forced static and dynamic responses are found to match full Nastran results very well.

Reduced-Order Models for a Shallow Curved Beam Under Combined Loading

Future U.S. Air Force vehicles require structures that can withstand extreme combined environments. Examples include vehicles exposed to launch, sustained hypersonic velocities, reentry, and stealthy aircraft with buried engines and ducted exhaust. Two of the many conditions that a structure in these environments will experience are elevated temperatures and high acoustic loading. Computational methods are needed to rapidly explore the design space for extreme environment structures. There has been a significant amount of work toward developing reduced-order modeling to address the issue of sonic fatigue. These methods have been demonstrated to be useful for predicting the geometric nonlinear response of aircraft structures to stochastic loading. Recent work also demonstrates that these methods are able to predict the response of planar structures in these combined environments. The present study demonstrates that the implicit condensation reduced-order modeling method can also be extended to curved structures experiencing combined thermal-acoustic loading with changing thermal conditions. Successful displacement and strain comparisons for a curved beam structure are made between results from a commercial finite element code and reduced-order models, using a single random pressure load (162 dB) and varying temperature cases.

On Snap-Through Buckling

Snap-through buckling can reduce the life-span of structural systems such as aircraft surface paneling. This is envisioned to be a specific problem in hypersonic vehicles in which severe thermal loading and acoustic excitation conspire to create an especially hostile environment for structural elements. A shallow arch, and two simplified link models are used to investigate the mechanisms of snap-through buckling from a fundamental, or phenomenological, standpoint. The complexities introduced by modal interactions are introduced and a method for identifying snap-through buckling is developed.

Thermoacoustic effects in high-speed compressible transitional and turbulent boundary layers

A numerical investigation of the thermal and acoustic effects in high-speed compressible flows is presented. Two case studies are considered: i) transition to turbulence in supersonic flows over a flat plate, and ii) supersonic shock wave turbulent boundary layer interaction (SWTBLI) over a compression ramp. Implicit Large Eddy Simulations (iLES) are performed using the second and fifth order Monotone-Upstream Central Scheme for Conservation Laws (MUSCL) and the ninth order Weighted Essentially Non-Oscillatory (WENO) schemes. The aim of this study is twofold: i) to examine the acoustic and thermal effects associated with transitional and turbulent boundary layers, particularly in the near wall region; ii) to investigate the effects of numerical accuracy on acoustic and thermal loading. The results are compared with theoretical models, Direct Numerical Simulations (DNS) and experiments.

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.

Inferring unstable equilibrium configurations from experimental data

This research considers the structural behavior of slender, mechanically buckled beams and panels of the type commonly found in aerospace structures. The specimens were deflected and then clamped in a rigid frame in order to exhibit snap-through. That is, the initial equilibrium and the buckled (snapped-through) equilibrium configurations both co-existed for the given clamped conditions. In order to transit between these two stable equilibrium configurations (for example, under the action of an externally applied load), it is necessary for the structural component to pass through an intermediate unstable equilibrium configuration. A sequence of sudden impacts was imparted to the system, of various strengths and at various locations. The goal of this impact force was to induce relatively intermediate-sized transients that effectively slowed-down in the vicinity of the unstable equilibrium configuration. Thus, monitoring the velocity of the motion, and specifically its slowing down, should give an indication of the presence of an equilibrium configuration, even though it is unstable and not amenable to direct experimental observation. A digital image correlation (DIC) system was used in conjunction with an instrumented impact hammer to track trajectories and statistical methods used to infer the presence of unstable equilibria in both a beam and a panel.