Results for “eigenvalue analysis” — Page 12

NASA NTRS1999

Aerodynamic and Aeroelastic Insights using Eigenanalysis

This paper presents novel analytical results for eigenvalues and eigenvectors produced using discrete time aerodynamic and aeroelastic models. An unsteady, incompressible vortex lattice aerodynamic model is formulated in discrete time; the importance of several modeling parameters is examined. A detailed study is made of the behavior of the aerodynamic eigenvalues both in discrete and continuous time. The aerodynamic model is then incorporated into aeroelastic equations of motion. Eigenanalyses of the coupled equations produce stability results and modal characteristics which are valid for critical and non-critical velocities. Insight into the modeling and physics associated with aeroelastic system behavior is gained by examining both the eigenvalues and the eigenvectors. Potential pitfalls in discrete time model construction and analysis are examined.

Heeg, Jennifer↗

NASA NTRS2004

Aerodynamic and Aeroelastic Insights using Eigenanalysis

This paper presents novel analytical results for eigenvalues and eigenvectors produced using discrete time aerodynamic and aeroelastic models. An unsteady, incompressible vortex lattice aerodynamic model is formulated in discrete time; the importance of several modeling parameters is examined. A detailed study is made of the behavior of the aerodynamic eigenvalues both in discrete and continuous time. The aerodynamic model is then incorporated into aeroelastic equations of motion. Eigenanalyses of the coupled equations produce stability results and modal characteristics which are valid for critical and non-critical velocities. Insight into the modeling and physics associated with aeroelastic system behavior is gained by examining both the eigenvalues and the eigenvectors. Potential pitfalls in discrete time model construction and analysis are examined.

Heeg, Jennifer↗

NASA NTRS1983

A modal analysis of flexible aircraft dynamics with handling qualities implications

A multivariable modal analysis technique is presented for evaluating flexible aircraft dynamics, focusing on meaningful vehicle responses to pilot inputs and atmospheric turbulence. Although modal analysis is the tool, vehicle time response is emphasized, and the analysis is performed on the linear, time-domain vehicle model. In evaluating previously obtained experimental pitch tracking data for a family of vehicle dynamic models, it is shown that flexible aeroelastic effects can significantly affect pitch attitude handling qualities. Consideration of the eigenvalues alone, of both rigid-body and aeroelastic modes, does not explain the simulation results. Modal analysis revealed, however, that although the lowest aeroelastic mode frequency was still three times greater than the short-period frequency, the rigid-body attitude response was dominated by this aeroelastic mode. This dominance was defined in terms of the relative magnitudes of the modal residues in selected vehicle responses.

Schmidt, D. K.↗

NASA NTRS1995

On the nonlinear stability of the unsteady, viscous flow of an incompressible fluid in a curved pipe

The stability of the flow of an incompressible, viscous fluid through a pipe of circular cross-section curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is obtained by identifying the saddle point of the Taylor number in the complex plane of the cross-sectional angle co-ordinate. The equation governing the nonlinear evolution of the leading order vortex amplitude is thus determined. The stability analysis of this flow to periodic disturbances leads to a partial differential system dependent on three variables, and since the differential operators in this system are periodic in time, Floquet theory may be applied to reduce this system to a coupled infinite system of ordinary differential equations, together with homogeneous uncoupled boundary conditions. The eigenvalues of this system are calculated numerically to predict a critical Taylor number consistent with the analysis of Papageorgiou. A discussion of how nonlinear effects alter the linear stability analysis is also given, and the nature of the instability determined.

Shortis, Trudi A.↗

NASA NTRS1989

The application of TSIM software to act design and analysis on flexible aircraft

The TSIM software is described. This is a package which uses an interactive FORTRAN-like simulation language for the simulation on nonlinear dynamic systems and offers facilities which include: mixed continuous and discrete time systems, time response calculations, numerical optimization, automatic trimming of nonlinear aircraft systems, and linearization of nonlinear equations for eigenvalues, frequency responses and power spectral response evaluation. Details are given of the application of TSIM to the analysis of aeroelastic systems under the RAE Farborough extension FLEX-SIM. The aerodynamic and structural data for the equations of motion of a flexible aircraft are prepared by a preprocessor program for incorporation in TSIM simulations. Within the simulation, the flexible aircraft model may then be selected interactively for different flight conditions and modal reduction techniques applied. The use of FLEX-SIM is demonstrated by an example of the flutter prediction for a simple aeroelastic model. By utilizing the numerical optimization facility of TSIM, it is possible to undertake identification of required parameters in the TSIM model within the simulation.

Kaynes, Ian W.↗

NASA NTRS1976

Nonlinear periodic waves

Systematic perturbation procedures for the analysis of nonlinear problems are reviewed. The cases when the multiplicity of an eigenvalue is finite or infinite are treated for self-sustained and forced oscillations. The possibility of the formation of shock waves is discussed. Applications to acoustic problems are presented.

Ting, L.↗

NASA NTRS1979

Analysis of integral controls in linear quadratic regulator design

The application of linear optimal control to the design of systems with integral control action on specified outputs is considered. Using integral terms in a quadratic performance index, an asymptotic analysis is used to determine the effect of variable quadratic weights on the eigenvalues and eigenvectors of the closed loop system. It is shown that for small integral terms the placement of integrator poles and gain calculation can be effectively decoupled from placement of the primary system eigenvalues. This technique is applied to the design of integral controls for a STOL aircraft outer loop guidance system.

Slater, G. L.↗

NASA NTRS1984

Enthalpy damping for the steady Euler equations

For inviscid steady flow problems where the enthalpy is constant at steady state, it was previously proposed to use the difference between the local enthalpy and the steady state enthalpy as a driving term to accelerate convergence of iterative schemes. This idea is analyzed, both on the level of the partial differential equation and on the level of a particular finite difference scheme. It is shown that for the two-dimensional unsteady Euler equations, a hyperbolic system with eigenvalues on the imaginary axis, there is no enthalpy damping strategy which moves all the eigenvalues into the open left half plane. For the numerical scheme, however, the analysis shows and examples verify that enthalpy damping is potentially effective in accelerating convergence to steady state.

Jespersen, D. C.↗

NASA NTRS1984

Perturbation analysis of optimal integral controls

The application of linear optimal control to the design of systems with integral control action on specified outputs is considered. Using integral terms in a quadratic performance index, an asymptotic analysis is used to determine the effect of variable quadratic weights on the eigenvalues and eigenvectors of the closed loop system. It is shown that for small integral terms the placement of integrator poles and gain calculation can be effectively decoupled from placement of the primary system eigenvalues. This technique is applied to the design of integral controls for a STOL aircraft outer loop guidance system.

Slater, G. L.↗

NASA NTRS1985

Enthalpy damping for the steady Euler equations

For inviscid steady flow problems where the enthalpy is constant at steady state, it was previously proposed to use the difference between the local enthalpy and the steady state enthalpy as a driving term to accelerate convergence of iterative schemes. This idea is analyzed, both on the level of the partial differential equation and on the level of a particular finite difference scheme. It is shown that for the two-dimensional unsteady Euler equations, a hyperbolic system with eigenvalues on the imaginary axis, there is no enthalpy damping strategy which moves all the eigenvalues into the open left half plane. For the numerical scheme, however, the analysis shows and examples verify that enthalpy damping is potentially effective in accelerating convergence to steady state.

Jespersen, D. C.↗

NASA NTRS1992

Negative-energy states in the Dirac-Hartree-Fock problem - The effect of omission of two-electron integrals involving the small component

The effect of omission of two-electron integrals involving basis functions for the small component of the wavefunction on the eigenvalue spectrum in the Dirac-Hartree-Fock problem is studied. From an analysis of the Fock matrix it is shown that omission of these integrals moves the negative-energy states down, not up. Their complete omission does not give rise to intruder states. The appearance of intruder states occurs when only some of the core integrals are omitted, due to the nature of particular contraction schemes used for the core basis functions. Use of radially localized functions rather than atomic functions alleviates the intruder state problem.

Dyall, Kenneth G.↗

NASA NTRS1993

Sensitivity of discrete systems

Sensitivity techniques are examined for structures discretized by finite element analysis. The discussion covers finite difference sensitivities, sensitivity of static response, sensitivity of eigenvalues and eigenvectors, sensitivity of linear transient response, and an example of use of transient sensitivity.

Haftka, Raphael T.↗

NASA NTRS1993

Viscous analysis of three-dimensional rotor flows using a multigrid method

A three-dimensional code for rotating blade-row flow analysis was developed. The space discretization uses a cell-centered scheme with eigenvalues scaling for the artificial dissipation. The computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. An application is presented for the NASA rotor 67 transonic fan. Due to the blade stagger and twist, a zonal, non-periodic H-type grid is used to minimize the mesh skewness. The calculation is validated by comparing it with experiments in the range from the maximum flow rate to a near-stall condition. A detailed study of the flow structure near peak efficiency and near stall is presented by means of pressure distribution and particle traces inside boundary layers.

Arnone, A.↗

NASA NTRS2005

Sunspot Pattern Classification using PCA and Neural Networks (Poster)

The sunspot classification scheme presented in this paper is considered as a 2-D classification problem on archived datasets, and is not a real-time system. As a first step, it mirrors the Zuerich/McIntosh historical classification system and reproduces classification of sunspot patterns based on preprocessing and neural net training datasets. Ultimately, the project intends to move from more rudimentary schemes, to develop spatial-temporal-spectral classes derived by correlating spatial and temporal variations in various wavelengths to the brightness fluctuation spectrum of the sun in those wavelengths. Once the approach is generalized, then the focus will naturally move from a 2-D to an n-D classification, where "n" includes time and frequency. Here, the 2-D perspective refers both to the actual SOH0 Michelson Doppler Imager (MDI) images that are processed, but also refers to the fact that a 2-D matrix is created from each image during preprocessing. The 2-D matrix is the result of running Principal Component Analysis (PCA) over the selected dataset images, and the resulting matrices and their eigenvalues are the objects that are stored in a database, classified, and compared. These matrices are indexed according to the standard McIntosh classification scheme.

Rajkumar, T.↗

NASA NTRS1984

Sensitivity analysis of discrete structural systems: A survey

Methods for calculating sensitivity derivatives for discrete structural systems are surveyed, primarily covering literature published during the past two decades. Methods are described for calculating derivatives of static displacements and stresses, eigenvalues and eigenvectors, transient structural response, and derivatives of optimum structural designs with respect to problem parameters. The survey is focused on publications addressed to structural analysis, but also includes a number of methods developed in nonstructural fields such as electronics, controls, and physical chemistry which are directly applicable to structural problems. Most notable among the nonstructural-based methods are the adjoint variable technique from control theory, and the Green's function and FAST methods from physical chemistry.

Adelman, H. M.↗

NASA NTRS1990

Aeroelastic stability analysis of a high-energy turbine blade

The dynamic analysis for the SSME HPOTP first stage turbine blade is presented wherein the rotor aeroelastic stability is assessed. The method employs normal modes analysis to simulate the coupled blade/fluid system. A three-dimensional finite element model of the blade is used in conjunction with a two-dimensional linearized unsteady aerodynamic theory which accounts for steady aerodynamic loading effects. This unsteady aerodynamic model is applied in stacked axisymmetric strips along the airfoil span. The blade dynamic and aerodynamic behaviors are coupled within modal space by expressing the unsteady aerodynamic forces in the frequency domain. A complex eigenvalue problem is solved to determine the stability of the rotor assuming tuned blades. The present analysis indicates that the HPOTP rotor experiences very low aerodynamic damping in the first four vibrational modes. The edgewise mode was found to be dynamically unstable. This mode of the blade became stable when the effect of mechanical damping was considered.

Smith, Todd E.↗

NASA NTRS2009

Subspace Iteration Method for Complex Eigenvalue Problems with Nonsymmetric Matrices in Aeroelastic System

Modern airplane design is a multidisciplinary task which combines several disciplines such as structures, aerodynamics, flight controls, and sometimes heat transfer. Historically, analytical and experimental investigations concerning the interaction of the elastic airframe with aerodynamic and in retia loads have been conducted during the design phase to determine the existence of aeroelastic instabilities, so called flutter .With the advent and increased usage of flight control systems, there is also a likelihood of instabilities caused by the interaction of the flight control system and the aeroelastic response of the airplane, known as aeroservoelastic instabilities. An in -house code MPASES (Ref. 1), modified from PASES (Ref. 2), is a general purpose digital computer program for the analysis of the closed-loop stability problem. This program used subroutines given in the International Mathematical and Statistical Library (IMSL) (Ref. 3) to compute all of the real and/or complex conjugate pairs of eigenvalues of the Hessenberg matrix. For high fidelity configuration, these aeroelastic system matrices are large and compute all eigenvalues will be time consuming. A subspace iteration method (Ref. 4) for complex eigenvalues problems with nonsymmetric matrices has been formulated and incorporated into the modified program for aeroservoelastic stability (MPASES code). Subspace iteration method only solve for the lowest p eigenvalues and corresponding eigenvectors for aeroelastic and aeroservoelastic analysis. In general, the selection of p is ranging from 10 for wing flutter analysis to 50 for an entire aircraft flutter analysis. The application of this newly incorporated code is an experiment known as the Aerostructures Test Wing (ATW) which was designed by the National Aeronautic and Space Administration (NASA) Dryden Flight Research Center, Edwards, California to research aeroelastic instabilities. Specifically, this experiment was used to study an instability known as flutter. ATW was a small-scale airplane wing comprised of an airfoil and wing tip boom. This wing was formulated based on a NACA-65A004 airfoil shape with a 3.28 aspect ratio. The wing had a span of 18 inch with root chord length of 13.2 inch and tip chord length of 8.7 inch. The total area of this wing was 197 square inch. The wing tip boom was a 1 inch diameter hollow tube of length 21.5 inch. The total weight of the wing was 2.66 lbs.

Pak, Chan-gi↗

NASA NTRS1973

Matrix Perturbation Techniques in Structural Dynamics

Matrix perturbation are developed techniques which can be used in the dynamical analysis of structures where the range of numerical values in the matrices extreme or where the nature of the damping matrix requires that complex valued eigenvalues and eigenvectors be used. The techniques can be advantageously used in a variety of fields such as earthquake engineering, ocean engineering, aerospace engineering and other fields concerned with the dynamical analysis of large complex structures or systems of second order differential equations. A number of simple examples are included to illustrate the techniques.

Caughey, T. K.↗