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Experimental and Numerical Analysis of Structural Acousticcontrol Interior Noise Reduction

The research results contained in this technical report were performed under the NASA grant entitled "Experimental and Numerical Structural Acoustic Control for Interior Noise Reduction". The report is based essentially on partial progress of the Ph.D. dissertation prepared by Jeffrey S. Bevan under direct guidance of Dr. Chuh Mei. The document presents a finite element formulation and control of sound radiated from cylindrical panels embedded with piezoceramic actuators. The extended MIN6 shallow shell element is fully electrical-structural coupled. A piezoelectric modal actuator participation (PMAP) is defined which indicates the actuator performance to each of the offending modes. Genetic algorithm is also employed to validate the sensor and actuator locations determined by the PMAP criteria. The work was conducted at the Department of Aerospace Engineering, Old Dominion University. Mr. Travis L. Turner, Structural Acoustics Branch, NASA Langley Research Center is the technical monitor.

Mei, Chuh↗

Sensitivity Analysis for Coupled Aero-structural Systems

A novel method has been developed for calculating gradients of aerodynamic force and moment coefficients for an aeroelastic aircraft model. This method uses the Global Sensitivity Equations (GSE) to account for the aero-structural coupling, and a reduced-order modal analysis approach to condense the coupling bandwidth between the aerodynamic and structural models. Parallel computing is applied to reduce the computational expense of the numerous high fidelity aerodynamic analyses needed for the coupled aero-structural system. Good agreement is obtained between aerodynamic force and moment gradients computed with the GSE/modal analysis approach and the same quantities computed using brute-force, computationally expensive, finite difference approximations. A comparison between the computational expense of the GSE/modal analysis method and a pure finite difference approach is presented. These results show that the GSE/modal analysis approach is the more computationally efficient technique if sensitivity analysis is to be performed for two or more aircraft design parameters.

Giunta, Anthony A.↗

Progress in Integrated Fluid/Structure/Controls Computations Using High Fidelity Equations

Aeroelasticity that involves strong coupling of fluids, structures and controls is an important element in designing an aircraft. Computational aeroelasticity using low fidelity methods such as the linear aerodynamic flow equations coupled with the modal structural equations are well advanced. Though these low fidelity approaches are computationally less intensive, they are not adequate for the analysis of aircraft which can experience complex flow/structure interactions. Supersonic transports can experience vortex induced aeroelastic oscillations whereas subsonic transports can experience transonic buffet associated structural oscillations. Both aircraft may experience a dip in the flutter speed at the transonic regime. For accurate aeroelastic computations at these complex fluid/structure interaction situations, high fidelity equations such as the Navier-Stokes for fluids and the finite-elements for structures are needed. Using these high fidelity methods, design quantities such as structural stresses can be directly computed. Computations using these high fidelity equations require state-of-the-art large computational resources. This paper will describe the transition from potential equations to Euler/Navier-Stokes equations for fluids and from modal equations to finite element equations for structures. Complexities associated with grids for moving control surfaces will be discussed. All contents of the paper will be limited to those already presented at domestic conferences within U.S. such as those sponsored by AIAA. It will not include any materials related to HPCCP computational work.

Guruswamy, Guru P.↗

Statistical of a Characterization and the Simulation of a Reverberation Chamber Using Finite-Element Techniques

The statistical characterization of a simulation reverberation chamber is performed by considering a two-dimensional finite element model. This model includes a source to study the particular modal fields that couple into either a transverse electric or transverse magnetic configuration. The analysis includes a characterization of the basic field statistics, max-to-average ratio, normalized standard deviation, stirring ratio, and field uniformity. The shielding effectiveness of an aperture will be studied that will provide some insight into the nature of the fields coupled from a complex to a noncomplex environment.

Bunting, Charles F.↗

Quiet Spike(TradeMark) Build-up Ground Vibration Testing Approach

Flight tests of the Gulfstream Aerospace Corporation s Quiet Spike(TradeMark) hardware were recently completed on the National Aeronautics and Space Administration Dryden Flight Research Center F-15B airplane. NASA Dryden uses a modified F-15B (836) airplane as a testbed aircraft to cost-effectively fly flight research experiments that are typically mounted underneath the airplane, along the fuselage centerline. For the Quiet Spike(TradeMark) experiment, instead of a centerline mounting, a forward-pointing boom was attached to the radar bulkhead of the airplane. The Quiet Spike(TradeMark) experiment is a stepping-stone to airframe structural morphing technologies designed to mitigate the sonic-boom strength of business jets flying over land. Prior to flying the Quiet Spike(TradeMark) experiment on the F-15B airplane several ground vibration tests were required to understand the Quiet Spike(TradeMark) modal characteristics and coupling effects with the F-15B airplane. Because of flight hardware availability and compressed schedule requirements, a "traditional" ground vibration test of the mated F-15B Quiet Spike(TradeMark) ready-for-flight configuration did not leave sufficient time available for the finite element model update and flutter analyses before flight-testing. Therefore, a "nontraditional" ground vibration testing approach was taken. This report provides an overview of each phase of the "nontraditional" ground vibration testing completed for the Quiet Spike(TradeMark) project.

Spivey, Natalie D.↗

Electrical Resistance of SiC/SiC Ceramic Matrix Composites for Damage Detection and Life-Prediction

Ceramic matrix composites (CMC) are suitable for high temperature structural applications such as turbine airfoils and hypersonic thermal protection systems due to their low density high thermal conductivity. The employment of these materials in such applications is limited by the ability to accurately monitor and predict damage evolution. Current nondestructive methods such as ultrasound, x-ray, and thermal imaging are limited in their ability to quantify small scale, transverse, in-plane, matrix cracks developed over long-time creep and fatigue conditions. CMC is a multifunctional material in which the damage is coupled with the material s electrical resistance, providing the possibility of real-time information about the damage state through monitoring of resistance. Here, resistance measurement of SiC/SiC composites under mechanical load at both room temperature monotonic and high temperature creep conditions, coupled with a modal acoustic emission technique, can relate the effects of temperature, strain, matrix cracks, fiber breaks, and oxidation to the change in electrical resistance. A multiscale model can in turn be developed for life prediction of in-service composites, based on electrical resistance methods. Results of tensile mechanical testing of SiC/SiC composites at room and high temperatures will be discussed. Data relating electrical resistivity to composite constituent content, fiber architecture, temperature, matrix crack formation, and oxidation will be explained, along with progress in modeling such properties.

Smith, Craig↗

Multiscale Mesh Adaptation for Transonic Aeroelastic Flutter Problems

This work applies multiscale mesh adaptation with refine to reduce spatial discretization error of aeroelastic computational fluid dynamics (CFD) simulations. Benchmark flutter models, such as the pitch and plunge NACA64A-010 airfoil and the benchmark supercritical wing, are studied with both a linearized frequency-domain solver and time-marching CFD coupled to a modal structural solver in FUN3D. The undeformed NASA Common Research Model (CRM), an aeroelastic jig shape variant of the CRM, is also studied with the linearized frequency-domain approach. For these cases, the adaptation process converges to comparable flutter predictions to hand-generated meshes but with smaller node counts. However the additional disciplines of the linearized frequency-domain analysis, the mesh deformation, and the unsteady finite-volume solver create robustness challenges that need to be addressed before it can be applied as a fully automated process for complex transonic aeroelastic problems. In particular, negative volumes are observed to be an issue for FUN3D’s linear elasticity mesh deformation solver when moving the adapted meshes.

Aeroelasticity↗

Estimation of Sonic Fatigue by Reduced-Order Finite Element Based Analyses

A computationally efficient, reduced-order method is presented for prediction of sonic fatigue of structures exhibiting geometrically nonlinear response. A procedure to determine the nonlinear modal stiffness using commercial finite element codes allows the coupled nonlinear equations of motion in physical degrees of freedom to be transformed to a smaller coupled system of equations in modal coordinates. The nonlinear modal system is first solved using a computationally light equivalent linearization solution to determine if the structure responds to the applied loading in a nonlinear fashion. If so, a higher fidelity numerical simulation in modal coordinates is undertaken to more accurately determine the nonlinear response. Comparisons of displacement and stress response obtained from the reduced-order analyses are made with results obtained from numerical simulation in physical degrees-of-freedom. Fatigue life predictions from nonlinear modal and physical simulations are made using the rainflow cycle counting method in a linear cumulative damage analysis. Results computed for a simple beam structure under a random acoustic loading demonstrate the effectiveness of the approach and compare favorably with results obtained from the solution in physical degrees-of-freedom.

Rizzi, Stephen A.↗

A Coupled Fluid-Structure Interaction Analysis of Solid Rocket Motor with Flexible Inhibitors

A capability to couple NASA production CFD code, Loci/CHEM, with CFDRC's structural finite element code, CoBi, has been developed. This paper summarizes the efforts in applying the installed coupling software to demonstrate/investigate fluid-structure interaction (FSI) between pressure wave and flexible inhibitor inside reusable solid rocket motor (RSRM). First a unified governing equation for both fluid and structure is presented, then an Eulerian-Lagrangian framework is described to satisfy the interfacial continuity requirements. The features of fluid solver, Loci/CHEM and structural solver, CoBi, are discussed before the coupling methodology of the solvers is described. The simulation uses production level CFD LES turbulence model with a grid resolution of 80 million cells. The flexible inhibitor is modeled with full 3D shell elements. Verifications against analytical solutions of structural model under steady uniform pressure condition and under dynamic condition of modal analysis show excellent agreements in terms of displacement distribution and eigen modal frequencies. The preliminary coupled result shows that due to acoustic coupling, the dynamics of one of the more flexible inhibitors shift from its first modal frequency to the first acoustic frequency of the solid rocket motor.

Yang, H. Q.↗

Modeling and numerical simulation of microwave pulse propagation in air breakdown environment

It is shown that ionization occurs wherever the field intensity of the pulse exceeds the local breakdown threshold field of the background air. The produced plasma then attenuates the pulse and gives rise to a tail erosion phenomenon that plays the primary role in limiting the energy transfer of the pulse from source to destination. A theoretical model describing the propagation of an intense microwave pulse in an air breakdown environment is developed that includes the possible focusing effect introduced by either using phase array antennas or the other arrangements. The self-consistent description of the propagation process is provided by a set of two modal equations. These include a continuity equation (Poynting's equation) for the energy density of the pulse and a rate equation of the electron density. A forward wave approximation is used to simplify Poynting's equation, and a semiempirical formula is used for the ionization frequency, nu(sub i). This frequency provides the coupling between the two modal equations, and is used to express the electron rate equation explicitly. In terms of the relevant parameters of the atmosphere, these two equations are normalized for numerical analysis of pulse propagation in the atmosphere. The dependencies of the propagation characteristics of the pulse on intensity, frequency, width, and shape of the pulse are determined. The numerical simulations lead to a useful empirical relation p(exp 3)w = alpha = constant, where p and w are the incident power and width of the pulse and alpha depends on the percentage of pulse energy transferred from the source point to a destined position. The density distribution of the pulse's self-generated plasma is also evaluated. The results also show that for ionization caused by a single unfocused microwave pulse transmitted upwards from the ground, the maximum electron density produced at, for example, 50 km altitude is limited by the tail erosion effect to below 10(exp 6) cm(exp -3). Repetitive pulse and focused beam approaches are also examined. Both approaches can increase the maximum electron density by no more than an order of magnitude. A scheme using two obliquely propagating pulses intersecting at the destined height, e.g. 50 km, is considered. It is shown that the electron density generated at the lowest intersecting position can easily reach a value of 6.6 x 10(exp 8) cm(exp -3), which is considered to be high enough for artificial ionospheric mirror (AIM) application.

Kim, J.↗

Damping in coupled bending and torsion - An experiment

Traditional experimental modal testing methods are used to determine the damping properties of a Euler-Bernoulli beam with offset inertial tip mass. Both viscous and strain rate damping models are considered in bending and in torsion. A partial differential equation model of the coupled system is used. Eigenfunctions are derived for the coupled system by using a Green's function approach to derive the approximate uncoupled eigenfunctions. These eigenfunctions are used in a decoupled fashion with experimental modal data to estimate the damping parameters of the coupled system. The experimental modal data were obtained from both free and impulse responses using a combined translational and rotational accelerometer.

Umland, Jeffrey W.↗

Adaptive control of a flexible beam using least square lattice filters

This paper presents an indirect adaptive control scheme for the control of flexible structures using recursive least square lattice filters. The identification scheme uses lattice filters which provide an on-line estimate of the number of modes, mode shapes and modal amplitudes. These modes are coupled and a transformation to decouple them in order to obtain the natural modes is presented. The decoupled modal amplitude time series are then used in an equation error identification scheme to identify the model parameters in an autoregressive moving average (ARMA) form. The control is based on modal pole placement scheme with the objective of vibration suppression. The control gains are calculated based on the identified ARMA parameters. Before using the identified parameters for control, detailed testing and validation procedures are carried out on the identified parameters. The full adaptive control scheme is demonstrated using the simulation for the 12 foot free-free beam apparatus at NASA Langley Research Center.

Sundararajan, N.↗

Statistical analysis of static shape control in space structures

The article addresses the problem of efficient analysis of the statistics of initial and corrected shape distortions in space structures. Two approaches for improving efficiency are considered. One is an adjoint technique for calculating distortion shapes: the second is a modal expansion of distortion shapes in terms of pseudo-vibration modes. The two techniques are applied to the problem of optimizing actuator locations on a 55 m radiometer antenna. The adjoint analysis technique is used with a discrete-variable optimization method. The modal approximation technique is coupled with a standard conjugate-gradient continuous optimization method. The agreement between the two sets of results is good, validating both the approximate analysis and optimality of the results.

Burdisso, Ricardo A.↗

Nonlinear Response of Composite Panels Under Combined Acoustic Excitation and Aerodynamic Pressure

A finite element formulation is presented for the analysis of large deflection response of composite panels subjected to aerodynamic pressure- at supersonic flow and high acoustic excitation. The first-order shear deformation theory is considered for laminated composite plates, and the von Karman nonlinear strain-displacement relations are employed for the analysis of large deflection panel response. The first-order piston theory aerodynamics and the simulated Gaussian white noise are employed for the aerodynamic and acoustic loads, respectively. The nonlinear equations of motion for an arbitrarily laminated composite panel subjected to a combined aerodynamic and acoustic pressures are formulated first in structure node degrees-of-freedom. The system equations are then transformed and reduced to a set of coupled nonlinear equations in modal coordinates. Modal participation is defined and the in-vacuo modes to be retained in the analysis are based on the modal participation values. Numerical results include root mean square values of maximum deflections, deflection and strain response time histories, probability distributions, and power spectrum densities. Results showed that combined acoustic and aerodynamic loads have to be considered for panel analysis and design at high dynamic pressure values.

Abdel-Motagaly, K.↗

Aeroelastic Indicial Response Reduced-Order Modeling for Flexible Flight Vehicles

A reduced-order modeling method capable of providing computationally efficient predictions of the nonlinear, unsteady aerodynamics encountered by flexible flight vehicles under- going forced oscillations is presented. Models are developed using indicial response theory, which characterizes a vehicle’s dynamics through identification of time-accurate aerodynamic responses due to step changes in the vehicle-state parameters, e.g., angle-of-attack, pitch rate. A coupled computational fluid dynamics aeroelastic analysis is proposed for identifying step (indicial) responses of flexible vehicles. In this approach, aeroelastic indicial responses are simulated via prescribed rigid body motions, while fluid-structure interactions are captured at the subiterative level through coupling to a linear modal structural solver. A nonlinear extension of indicial response theory is applied through time-dependent linear interpolation of a database of locally linear aeroelastic step responses. Reduced-order models are then created using the mathematical principle of convolution applied to the interpolated aeroelastic indicial responses to predict the time-dependent aerodynamic response of a flexible vehicle to any arbitrary prescribed flight maneuver. The NASA FUN3D computational fluid dynamics solver is utilized for simulating full-order trajectories and indicial response functions. Aerodynamic predictions were generated for the X-56A aircraft undergoing a series of harmonic forced oscillations. The s are shown to provide a practical option for evaluating the unsteady aerodynamics of flexible vehicles using high-fidelity simulations.

Hiller, Brett↗

On the convergence of the coupled-wave approach for lamellar diffraction gratings

Among the many existing rigorous methods for analyzing diffraction of electromagnetic waves by diffraction gratings, the coupled-wave approach stands out because of its versatility and simplicity. It can be applied to volume gratings and surface relief gratings, and its numerical implementation is much simpler than others. In addition, its predictions were experimentally validated in several cases. These facts explain the popularity of the coupled-wave approach among many optical engineers in the field of diffractive optics. However, a comprehensive analysis of the convergence of the model predictions has never been presented, although several authors have recently reported convergence difficulties with the model when it is used for metallic gratings in TM polarization. Herein, three points are made: (1) in the TM case, the coupled-wave approach converges much slower than the modal approach of Botten et al; (2) the slow convergence is caused by the use of Fourier expansions for the permittivity and the fields in the grating region; and (3) is manifested by the slow convergence of the eigenvalues and the associated modal fields. The reader is assumed to be familiar with the mathematical formulations of the coupled-wave approach and the modal approach.

Li, Lifeng↗

Modal interaction in linear dynamic systems near degenerate modes

In various problems in structural dynamics, the eigenvalues of a linear system depend on a characteristic parameter of the system. Under certain conditions, two eigenvalues of the system approach each other as the characteristic parameter is varied, leading to modal interaction. In a system with conservative coupling, the two eigenvalues eventually repel each other, leading to the curve veering effect. In a system with nonconservative coupling, the eigenvalues continue to attract each other, eventually colliding, leading to eigenvalue degeneracy. Modal interaction is studied in linear systems with conservative and nonconservative coupling using singularity theory, sometimes known as catastrophe theory. The main result is this: eigenvalue degeneracy is a cause of instability; in systems with conservative coupling, it induces only geometric instability, whereas in systems with nonconservative coupling, eigenvalue degeneracy induces both geometric and elastic instability. Illustrative examples of mechanical systems are given.

Afolabi, D.↗

Performing a Large-Scale Modal Test on the B2 Stand Crane at NASA's Stennis Space Center

A modal test of NASA's Space Launch System (SLS) Core Stage is scheduled to occur at the Stennis Space Center B2 test stand. A derrick crane with a 150-ft long boom, located at the top of the stand, will be used to suspend the Core Stage in order to achieve defined boundary conditions. During this suspended modal test, it is expected that dynamic coupling will occur between the crane and the Core Stage. Therefore, a separate modal test was performed on the B2 crane itself, in order to evaluate the varying dynamic characteristics and correlate math models of the crane. Performing a modal test on such a massive structure was challenging and required creative test setup and procedures, including implementing both AC and DC accelerometers, and performing both classical hammer and operational modal analysis. This paper describes the logistics required to perform this large-scale test, as well as details of the test setup, the modal test methods used, and an overview and application of the results.

Stasiunas, Eric C.↗