Aeroelastic and Aerothermoelastic Analysis in Hypersonic Flow: Past, Present, and Future
01 Jun 2011-AIAA Journal (American Institute of Aeronautics and Astronautics)-Vol. 49, Iss: 6, pp 1089-1122
TL;DR: In this article, it is shown that the body, surface panels, and aerodynamic control surfaces are flexible due to minimum-weight restrictions for hypersonic vehicle configurations, and that these flexible body designs will consist of long, slender lifting body designs.
Abstract: H YPERSONIC flight began in February 1949 when a WAC Corporal rocket was ignited from a U.S.-captured V-2 rocket [1]. In the six decades since this milestone, there have been significant investments in the development of hypersonic vehicle technologies. The NASA X-15 rocket plane in the early 1960s represents early research toward this goal [2,3]. After a lull in activity, the modern era of hypersonic research started in the mid-1980s with the National Aerospace Plane (NASP) program [4], aimed at developing a single-stage-to-orbit reusable launch vehicle (RLV) that used conventional runways. However, it was canceled due mainly to design requirements that exceeded the state of the art [1,5]. A more recent RLV project, the VentureStar program, failed during structural tests, again for lack of the required technology [5]. Despite these unsuccessful programs, the continued need for a low-cost RLV, as well as the desire of the U.S. Air Force (USAF) for unmanned hypersonic vehicles, has reinvigorated hypersonic flight research. An emergence of recent and current research programs [6] demonstrate this renewed interest. Consider, for example, the NASA Hyper-X experimental vehicle program [7], the University of Queensland HyShot program [8], the NASA Fundamental Aeronautics Hypersonics Project [9], the joint U.S. Defense Advanced Research Projects Administration (DARPA)/USAF Force Application andLaunch fromContinentalUnited States (FALCON) program [10], the X-51 Single Engine Demonstrator [11,12], the joint USAF Research Laboratory (AFRL)/Australian Defence Science and Technology Organisation Hypersonic International Flight Research Experimentation project [13], and ongoing basic hypersonic research at the AFRL (e.g., [14–20]). The conditions encountered in hypersonic flows, combined with the need to design hypersonic vehicles, have motivated research in the areas of hypersonic aeroelasticity and aerothermoelasticity. It is evident from Fig. 1 that hypersonic vehicle configurations will consist of long, slender lifting body designs. In general, the body, surface panels, and aerodynamic control surfaces are flexible due to minimum-weight restrictions. Furthermore, as shown in Fig. 2, these
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TL;DR: In this paper, the tradeoff between computational cost and accuracy is evaluated for aerothermoelastic analysis based on either quasi-static or time-averaged dynamic fluid-thermal-structural coupling, as well as computational fluid dynamics based reduced-order modeling of the aerodynamic heat flux.
Abstract: The field of aerothermoelasticity plays an important role in the analysis and optimization of airbreathing hypersonic vehicles, impacting the design of the aerodynamic, structural, control, and propulsion systems at both the component and multi-disciplinary levels. This study aims to expand the fundamental understanding of hypersonic aerothermoelasticity by performing systematic investigations into fluid-thermal-structural coupling, and also to develop frameworks, using innovative modeling strategies, for reducing the computational effort associated with aerothermoelastic analysis. Due to the fundamental nature of this work, the analysis is limited to cylindrical bending of a simply-supported, von K arm an panel. Multiple important effects are included in the analysis, namely: 1) arbitrary, nonuniform, in-plane and through-thickness temperature distributions, 2) material property degradation at elevated temperature, and 3) the effect of elastic deformation on aerodynamic heating. It is found that including elastic deformations in the aerodynamic heating computations results in non-uniform heat flux, which produces non-uniform temperature distributions and non-uniform material property degradations. This results in reduced flight time to the onset of flutter and localized regions in which the material temperature limits may be exceeded. Additionally, the trade-off between computational cost and accuracy is evaluated for aerothermoelastic analysis based on either quasi-static or time-averaged dynamic fluid-thermal-structural coupling, as well as computational fluid dynamics based reduced-order modeling of the aerodynamic heat flux. It is determined that these approaches offer the potential for significant improvements in aerothermoelastic modeling in terms of efficiency and/or accuracy.
224 citations
TL;DR: In this article, a reduced-order nonlinear unsteady aerodynamic modeling approach suitable for analyzing pitching/plunging airfoils subject to fixed or time-varying freestream Mach numbers is described.
Abstract: A reduced-order nonlinear unsteady aerodynamic modeling approach suitable for analyzing pitching/plunging airfoils subject to fixed or time-varying freestream Mach numbers is described. The reduced-order model uses kriging surrogates to account for flow nonlinearities and recurrence solutions to account for time-history effects associated with unsteadiness. The resulting surrogate-based recurrence framework generates time-domain predictionsofunsteadylift,moment,anddragthataccuratelyapproximate computational fluiddynamicssolutions, but at a fraction of the computational cost. Results corresponding to transonic conditions demonstrate that the surrogate-based recurrence framework can mimic computational fluid dynamics predictions of unsteady aerodynamic responses when flow nonlinearities are present. For an unsteady aerodynamic modeling problem considered in this study, an accurate reduced-order model was generated by the surrogate-based recurrence framework approach with significantly fewer computational fluid dynamics evaluations compared to results reported in the literature for a similar problem in which a proper-orthogonal-decomposition-based approach was applied. Furthermore, the results show that the surrogate-based approach can accurately model time-varying freestream Mach number effects and is therefore applicable to rotary-wing applications in addition to fixed-wing applications.
163 citations
TL;DR: In this paper, a quasi-static response of a carbon-carbon skin panel is investigated and the significance of this coupling depends largely on the in-plane boundary conditions, since increasing resistance to thermal expansion results in buckling and increasing deflections into the flow.
Abstract: DOI: 10.2514/1.J050617 The goal of the United States Air Force to field durable platforms capable of sustained hypersonic flight and responsive access to space depends on the ability to predict the response and the life of structures under combined aerothermal andaeropressure loading. However,current predictive capabilities are limitedfor these conditions due in part to the inability to seamlessly address fluid-thermal-structural interactions. This study aims to quantify the significance of a frequently neglected interaction, namely: the mutual coupling of structural deformation and aerodynamic heating, on response prediction. The quasi-static response of a carbon–carbon skin panel is investigated. It is found that the significance of this coupling depends largely on the in-plane boundary conditions, since increasing resistance to thermal expansion results in buckling and increasing deflections into the flow. Including these deformations in aerodynamic heating results in O10% increase in peak temperature and O100% increase in surface ply failure index for deflections O1% of panel length. In these cases, the locations of peaktemperaturesandstressesaresignificantlyaltered.Finally,neglectingdeformationsintheaeroheatinganalysis results in the prediction of snap-through for a gradual heating trajectory, whereas, inclusion leads to a higher mode dominated, dynamically stable response.
146 citations
Cites background or methods or result from "Aeroelastic and Aerothermoelastic A..."
...While piston theory represents a simplistic model for the inviscid aerodynamics, it has been observed in several studies [13] to provide reasonably accurate pressure predictions so long as the product of Mach number and surface inclination remains below unity....
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...Therefore, unlike other flow regimes where aeroelasticity is primarily dependent on instantaneous operating conditions, hypersonic aerothermoelasticity is dependent on the path between two points [13]....
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...A recent reviewpaper [13], in addition to several early studies [14– 22], provides insight into the salient aspects of aerothermoelasticity....
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...While less straightforward, a one-way coupled approach could be implemented using Navier– Stokes by performing a steady-state aerodynamic heating analysis of the trajectory first, using a reference configuration, followed by aeroelastic response tests at discrete points along the trajectory [13]....
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..., aerothermoelasticity) [11,13]....
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TL;DR: In this paper, various approximations to unsteady aerodynamics are examined for the aero-elastic analysis of a thin double-wedge airfoil in hypersonic flow.
Abstract: DOI: 10.2514/1.C000190 Various approximations to unsteady aerodynamics are examined for the aeroelastic analysis of a thin doublewedge airfoil in hypersonic flow. Flutter boundaries are obtained using classical hypersonic unsteady aerodynamic theories: piston theory, Van Dyke’s second-order theory, Newtonian impact theory, and unsteady shock-expansion theory. The theories are evaluated by comparing the flutter boundaries with those predicted using computational fluid dynamics solutions to the unsteady Navier–Stokes equations. Inaddition, several alternative approaches to the classical approximations are also evaluated: two different viscous approximations based on effective shapes and combined approximate computational approaches that use steady-state computational-fluid-dynamics-based surrogatemodelsinconjunction withpistontheory.Theresultsindicatethat,with theexceptionof first-order piston theory and Newtonian impact theory, the approximate theories yield predictions between 3 and 17% of normalized root-mean-square error and between 7 and 40% of normalized maximum error of the unsteady Navier–Stokes predictions. Furthermore, the demonstrated accuracy of the combined steady-state computational fluid dynamics and piston theory approaches suggest that important nonlinearities in hypersonic flow are primarily due to steadystate effects. This implies that steady-state flow analysis may be an alternative to time-accurate Navier–Stokes solutions for capturing complex flow effects.
111 citations
TL;DR: In this article, an aerothermoelastic framework with reduced-order aerothermal, heat transfer, and structural dynamic models for time-domain simulation of hypersonic vehicles is presented.
Abstract: Hypersonic vehicle control system design and simulation require models that contain a low number of states. Modeling of hypersonic vehicles is complicated due to complex interactions between aerodynamic heating, heat transfer, structural dynamics, and aerodynamics. Although there exist techniques for analyzing the effects of each of the various disciplines, thesemethods often require solution of large systems of equations, which is infeasible within a control design and evaluation environment. This work presents an aerothermoelastic framework with reducedorder aerothermal, heat transfer, and structural dynamicmodels for time-domain simulation of hypersonic vehicles. Details of the reduced-order models are given, and a representative hypersonic vehicle control surface used for the study is described. Themethodology is applied to a representative structure to provide insight into the importance of aerothermoelastic effects on vehicle performance. The effect of aerothermoelasticity on total lift and drag is found to result in up to an 8% change in lift and a 21% change in drag with respect to a rigid control surface for the four trajectories considered. An iterative routine is used to determine the angle of attack needed to match the lift of the deformed control surface to that of a rigid one at successive time instants.Application of the routine todifferent cruise trajectories shows a maximum departure from the initial angle of attack of 8%.
99 citations
References
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TL;DR: This paper presents a meta-modelling framework for estimating Output from Computer Experiments-Predicting Output from Training Data and Criteria Based Designs for computer Experiments.
Abstract: Many scientific phenomena are now investigated by complex computer models or codes A computer experiment is a number of runs of the code with various inputs A feature of many computer experiments is that the output is deterministic--rerunning the code with the same inputs gives identical observations Often, the codes are computationally expensive to run, and a common objective of an experiment is to fit a cheaper predictor of the output to the data Our approach is to model the deterministic output as the realization of a stochastic process, thereby providing a statistical basis for designing experiments (choosing the inputs) for efficient prediction With this model, estimates of uncertainty of predictions are also available Recent work in this area is reviewed, a number of applications are discussed, and we demonstrate our methodology with an example
6,583 citations
"Aeroelastic and Aerothermoelastic A..." refers methods in this paper
...Kriging is an interpolation method useful for replacing expensive computer models with computationally efficient approximations of nonlinear functions [93,96,97]....
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Book•
02 Sep 2008
TL;DR: This chapter discusses the design and exploration of a Surrogate-based kriging model, and some of the techniques used in that process, as well as some new approaches to designing models based on the data presented.
Abstract: Preface. About the Authors. Foreword. Prologue. Part I: Fundamentals. 1. Sampling Plans. 1.1 The 'Curse of Dimensionality' and How to Avoid It. 1.2 Physical versus Computational Experiments. 1.3 Designing Preliminary Experiments (Screening). 1.3.1 Estimating the Distribution of Elementary Effects. 1.4 Designing a Sampling Plan. 1.4.1 Stratification. 1.4.2 Latin Squares and Random Latin Hypercubes. 1.4.3 Space-filling Latin Hypercubes. 1.4.4 Space-filling Subsets. 1.5 A Note on Harmonic Responses. 1.6 Some Pointers for Further Reading. References. 2. Constructing a Surrogate. 2.1 The Modelling Process. 2.1.1 Stage One: Preparing the Data and Choosing a Modelling Approach. 2.1.2 Stage Two: Parameter Estimation and Training. 2.1.3 Stage Three: Model Testing. 2.2 Polynomial Models. 2.2.1 Example One: Aerofoil Drag. 2.2.2 Example Two: a Multimodal Testcase. 2.2.3 What About the k -variable Case? 2.3 Radial Basis Function Models. 2.3.1 Fitting Noise-Free Data. 2.3.2 Radial Basis Function Models of Noisy Data. 2.4 Kriging. 2.4.1 Building the Kriging Model. 2.4.2 Kriging Prediction. 2.5 Support Vector Regression. 2.5.1 The Support Vector Predictor. 2.5.2 The Kernel Trick. 2.5.3 Finding the Support Vectors. 2.5.4 Finding . 2.5.5 Choosing C and epsilon. 2.5.6 Computing epsilon : v -SVR 71. 2.6 The Big(ger) Picture. References. 3. Exploring and Exploiting a Surrogate. 3.1 Searching the Surrogate. 3.2 Infill Criteria. 3.2.1 Prediction Based Exploitation. 3.2.2 Error Based Exploration. 3.2.3 Balanced Exploitation and Exploration. 3.2.4 Conditional Likelihood Approaches. 3.2.5 Other Methods. 3.3 Managing a Surrogate Based Optimization Process. 3.3.1 Which Surrogate for What Use? 3.3.2 How Many Sample Plan and Infill Points? 3.3.3 Convergence Criteria. 3.3.4 Search of the Vibration Isolator Geometry Feasibility Using Kriging Goal Seeking. References. Part II: Advanced Concepts. 4. Visualization. 4.1 Matrices of Contour Plots. 4.2 Nested Dimensions. Reference. 5. Constraints. 5.1 Satisfaction of Constraints by Construction. 5.2 Penalty Functions. 5.3 Example Constrained Problem. 5.3.1 Using a Kriging Model of the Constraint Function. 5.3.2 Using a Kriging Model of the Objective Function. 5.4 Expected Improvement Based Approaches. 5.4.1 Expected Improvement With Simple Penalty Function. 5.4.2 Constrained Expected Improvement. 5.5 Missing Data. 5.5.1 Imputing Data for Infeasible Designs. 5.6 Design of a Helical Compression Spring Using Constrained Expected Improvement. 5.7 Summary. References. 6. Infill Criteria With Noisy Data. 6.1 Regressing Kriging. 6.2 Searching the Regression Model. 6.2.1 Re-Interpolation. 6.2.2 Re-Interpolation With Conditional Likelihood Approaches. 6.3 A Note on Matrix Ill-Conditioning. 6.4 Summary. References. 7. Exploiting Gradient Information. 7.1 Obtaining Gradients. 7.1.1 Finite Differencing. 7.1.2 Complex Step Approximation. 7.1.3 Adjoint Methods and Algorithmic Differentiation. 7.2 Gradient-enhanced Modelling. 7.3 Hessian-enhanced Modelling. 7.4 Summary. References. 8. Multi-fidelity Analysis. 8.1 Co-Kriging. 8.2 One-variable Demonstration. 8.3 Choosing X c and X e . 8.4 Summary. References. 9. Multiple Design Objectives. 9.1 Pareto Optimization. 9.2 Multi-objective Expected Improvement. 9.3 Design of the Nowacki Cantilever Beam Using Multi-objective, Constrained Expected Improvement. 9.4 Design of a Helical Compression Spring Using Multi-objective, Constrained Expected Improvement. 9.5 Summary. References. Appendix: Example Problems. A.1 One-Variable Test Function. A.2 Branin Test Function. A.3 Aerofoil Design. A.4 The Nowacki Beam. A.5 Multi-objective, Constrained Optimal Design of a Helical Compression Spring. A.6 Novel Passive Vibration Isolator Feasibility. References. Index.
2,335 citations
"Aeroelastic and Aerothermoelastic A..." refers background in this paper
..., surrogate function) from a discrete sampling of an unknown, nonlinear function over a bounded set of inputs [93,94]....
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TL;DR: The multi-objective optimal design of a liquid rocket injector is presented to highlight the state of the art and to help guide future efforts.
2,152 citations
"Aeroelastic and Aerothermoelastic A..." refers background or methods in this paper
...Methods for constructing the surrogate function include autoregressive moving average (ARMA) models, radial basis functions, neural networks, polynomial response surfaces, and kriging [86,91,93]....
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..., surrogate function) from a discrete sampling of an unknown, nonlinear function over a bounded set of inputs [93,94]....
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...Kriging is an interpolation method useful for replacing expensive computer models with computationally efficient approximations of nonlinear functions [93,96,97]....
[...]
Book•
01 Sep 2013
TL;DR: In this article, the authors discuss the properties of high-temperature gas dynamics, including the effects of high temperature on the dynamics of Viscous Flow and Vibrational Nonequilibrium Flows.
Abstract: Some Preliminary Thoughts * Part I: Inviscid Hypersonic Flow * Hypersonic Shock and Expansion-Wave Relations * Local Surface Inclination Methods * Hypersonic Inviscid Flowfields: Approximate Methods * Hypersonic Inviscid Flowfields: Exact Methods * Part II: Viscous Hypersonic Flow * Viscous Flow: Basic Aspects, Boundary Layer Results, and Aerodynamic Heating * Hypersonic Viscous Interactions * Computational Fluid Dynamic Solutions of Hypersonic Viscous Flows * Part III: High-Temperature Gas Dynamics * High-Temperature Gas Dynamics: Some Introductory Considerations * Some Aspects of the Thermodynamics of Chemically Reacting Gases (Classical Physical Chemistry) * Elements of Statistical Thermodynamics * Elements of Kinetic Theory * Chemical Vibrational Nonequilibrium * Inviscid High-Temperature Equilibrium Flows * Inviscid High-Temperature Nonequilibrium Flows * Kinetic Theory Revisited: Transport Properties in High-Temperature Gases * Viscous High-Temperature Flows * Introduction to Radiative Gas Dynamics.
1,960 citations
"Aeroelastic and Aerothermoelastic A..." refers background or methods in this paper
...Aside from these importantflow characteristics, another important aspect of hypersonic flight is the tight coupling of subsystems in hypersonic vehicles [1]....
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...Relatively simple and efficient approximations for the aerodynamic heating can be computed using the Eckert reference methods [1,72]....
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...Eckert reference methods have been used extensively to efficiently approximate viscous drag and convective heating of aerospace vehicles [1,73]....
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...Typically, a flow is characterized as hypersonic starting atMach numbers between three tofive [1,52]....
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...However, it was canceled due mainly to design requirements that exceeded the state of the art [1,5]....
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18 Jul 2008
TL;DR: In this article, the authors propose a sampling approach to estimate the distribution of elementary effects and then use this information to construct a kriging model of the data set, which is then used for regression.
Abstract: Preface. About the Authors. Foreword. Prologue. Part I: Fundamentals. 1. Sampling Plans. 1.1 The 'Curse of Dimensionality' and How to Avoid It. 1.2 Physical versus Computational Experiments. 1.3 Designing Preliminary Experiments (Screening). 1.3.1 Estimating the Distribution of Elementary Effects. 1.4 Designing a Sampling Plan. 1.4.1 Stratification. 1.4.2 Latin Squares and Random Latin Hypercubes. 1.4.3 Space-filling Latin Hypercubes. 1.4.4 Space-filling Subsets. 1.5 A Note on Harmonic Responses. 1.6 Some Pointers for Further Reading. References. 2. Constructing a Surrogate. 2.1 The Modelling Process. 2.1.1 Stage One: Preparing the Data and Choosing a Modelling Approach. 2.1.2 Stage Two: Parameter Estimation and Training. 2.1.3 Stage Three: Model Testing. 2.2 Polynomial Models. 2.2.1 Example One: Aerofoil Drag. 2.2.2 Example Two: a Multimodal Testcase. 2.2.3 What About the k -variable Case? 2.3 Radial Basis Function Models. 2.3.1 Fitting Noise-Free Data. 2.3.2 Radial Basis Function Models of Noisy Data. 2.4 Kriging. 2.4.1 Building the Kriging Model. 2.4.2 Kriging Prediction. 2.5 Support Vector Regression. 2.5.1 The Support Vector Predictor. 2.5.2 The Kernel Trick. 2.5.3 Finding the Support Vectors. 2.5.4 Finding . 2.5.5 Choosing C and epsilon. 2.5.6 Computing epsilon : v -SVR 71. 2.6 The Big(ger) Picture. References. 3. Exploring and Exploiting a Surrogate. 3.1 Searching the Surrogate. 3.2 Infill Criteria. 3.2.1 Prediction Based Exploitation. 3.2.2 Error Based Exploration. 3.2.3 Balanced Exploitation and Exploration. 3.2.4 Conditional Likelihood Approaches. 3.2.5 Other Methods. 3.3 Managing a Surrogate Based Optimization Process. 3.3.1 Which Surrogate for What Use? 3.3.2 How Many Sample Plan and Infill Points? 3.3.3 Convergence Criteria. 3.3.4 Search of the Vibration Isolator Geometry Feasibility Using Kriging Goal Seeking. References. Part II: Advanced Concepts. 4. Visualization. 4.1 Matrices of Contour Plots. 4.2 Nested Dimensions. Reference. 5. Constraints. 5.1 Satisfaction of Constraints by Construction. 5.2 Penalty Functions. 5.3 Example Constrained Problem. 5.3.1 Using a Kriging Model of the Constraint Function. 5.3.2 Using a Kriging Model of the Objective Function. 5.4 Expected Improvement Based Approaches. 5.4.1 Expected Improvement With Simple Penalty Function. 5.4.2 Constrained Expected Improvement. 5.5 Missing Data. 5.5.1 Imputing Data for Infeasible Designs. 5.6 Design of a Helical Compression Spring Using Constrained Expected Improvement. 5.7 Summary. References. 6. Infill Criteria With Noisy Data. 6.1 Regressing Kriging. 6.2 Searching the Regression Model. 6.2.1 Re-Interpolation. 6.2.2 Re-Interpolation With Conditional Likelihood Approaches. 6.3 A Note on Matrix Ill-Conditioning. 6.4 Summary. References. 7. Exploiting Gradient Information. 7.1 Obtaining Gradients. 7.1.1 Finite Differencing. 7.1.2 Complex Step Approximation. 7.1.3 Adjoint Methods and Algorithmic Differentiation. 7.2 Gradient-enhanced Modelling. 7.3 Hessian-enhanced Modelling. 7.4 Summary. References. 8. Multi-fidelity Analysis. 8.1 Co-Kriging. 8.2 One-variable Demonstration. 8.3 Choosing X c and X e . 8.4 Summary. References. 9. Multiple Design Objectives. 9.1 Pareto Optimization. 9.2 Multi-objective Expected Improvement. 9.3 Design of the Nowacki Cantilever Beam Using Multi-objective, Constrained Expected Improvement. 9.4 Design of a Helical Compression Spring Using Multi-objective, Constrained Expected Improvement. 9.5 Summary. References. Appendix: Example Problems. A.1 One-Variable Test Function. A.2 Branin Test Function. A.3 Aerofoil Design. A.4 The Nowacki Beam. A.5 Multi-objective, Constrained Optimal Design of a Helical Compression Spring. A.6 Novel Passive Vibration Isolator Feasibility. References. Index.
1,447 citations