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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

An Exploratory Study of a Subspace Iteration Method as an Alternative to the QR Method for Floquet Eigenanalysis

Floquet eigenanalysis requires a few dominant eigenvalues of the Floquet transition matrix (FTM). Although the QR method is used almost exclusively, it is expensive for such partial eigenanalysis; the operation counts and, thereby, the approximate machine-time grow cubically with the matrix order. Accordingly, for Floquet eigenanalysis, the Arnold-Saad method, a subspace iteration method, is investigated as an alternative to the QR method. The two methods are compared for machine-time efficiency and the residual errors of the corresponding eigenpairs. The Arnolds-Saad method takes much less machine-time than the QR method with comparable computational reliability and offers promise fpr large-scale Floquet eigenanalysis.

Achar, N. S.↗
NASA NTRS1993

Floquet operator as integral of motion

Nonstationary quantum systems have no energy levels. However, for time-dependent periodical quantum systems, the notion of quasi-energy levels has been introduced. The main point of the quasi-energy concept is to relate quasi-energies to eigenvalues of the Floquet operator or monodromy operators which is equal to the evolution operator of a quantum system taken at the moment coinciding with the period of the system. The purpose of this article is to relate the Floquet operator to integrals of the motion and to introduce a new operator which is the integral of motion and has the same quasi-energy spectrum that the Floquet operator has. We wish to discuss an explicit formula for this new integral of motion.

Manko, V. I.↗
NASA NTRS1974

An application of Floquet theory to prediction of mechanical instability

The problem of helicopter mechanical instability is considered for the case where one blade damper is inoperative, and it is shown that if the hub is considered to be nonisotropic, the equations of motion have periodic coefficients which cannot be eliminated. The Floquet transition matrix method is shown to be an effective way of dealing with the nonisotropic hub and nonisotropic rotor situation. Time history calculations are examined and shown to be inferior to the Floquet technique for determining system stability. It is shown that instabilities which occur when one blade damper is inoperative may consist of nearly pure blade motion or they may be similar to the classical mechanical instability.

Hammond, C. E.↗
NASA NTRS1974

An application of Floquet theory to prediction of mechanical instability

The problem of helicopter mechanical instability is considered for the case where one blade damper is inoperative. It is shown that, if the hub is considered to be nonisotropic, the equations of motion have periodic coefficients which cannot be eliminated. However, if the hub is isotropic, the equations can be transformed to a rotating frame of reference and the periodic coefficients eliminated. The Floquet transition matrix method is shown to be an effective way of dealing with the nonisotropic hub and nonisotropic rotor situation. Time history calculations are examined and shown to be inferior to the Floquet technique for determining system stability.

Hammond, C. E.↗
NASA NTRSDate not supplied

Floquet Codes on Non-Trivalent Lattices

Floquet codes are a novel form of quantum error correcting codes, where the logical degrees of freedom appear in a dynamical form. The first example of such a code was constructed by Hastings and Haah on a honeycomb lattice. Specifically, they showed how to Floquetify the Kitaev honeycomb model, which when viewed as a subsystem code, encodes no logical qubits. However, by choosing a particular measurement schedule of the check operators, this model leads to dynamically encoded logical qubits. Since this initial work, several examples of Floquet codes have been constructed, mainly on trivalent lattices. Here, we report progress on understanding when such codes can be implemented on lattices of different connectivities.

Muhammad Sohaib Alam↗
NASA NTRS1976

Floquet and coupled-waves analysis of higher-order Bragg coupling in a periodic medium

The paper considers wave propagation in longitudinally periodic media near the first- and higher-order Bragg resonances. An extended coupled-waves (ECW) approach is applied to media with single or multiharmonic periodicities and is numerically compared with the Floquet theory. The ECW approach predicts coupling coefficients that vary as the magnitude of the perturbation raised to the power of the Bragg order. Explicit expressions are also given for the band-gap width and band-gap shift for all Bragg orders. A number of applications are discussed.

Jaggard, D. L.↗
NASA NTRS1992

Computational aspects of helicopter trim analysis and damping levels from Floquet theory

Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.

Gaonkar, Gopal H.↗
NASA NTRS2022

Geometrical Analysis of Station-Keeping Strategies About Libration Point Orbits

Throughout the years, different strategies have been proposed for the station-keeping around the libration point orbits. In this paper, a geometrical comparative analysis is performed between different approaches making use of the Floquet modes reference frame. Two particular station-keeping procedures are considered: the commonly used velocity constraint at the plane crossing, and the Floquet mode approach. The first method finds the Δv that ensures that the x component of the velocity vector is zero at a plane crossing, whereas the Floquet mode approach finds the Δv that cancels the unstable mode in the Floquet reference frame. It will be seen that both approaches have some basic common geometrical features, even when they are compared using high-order techniques.

station keeping↗
NASA NTRS1986

Flap-lag-torsional dynamics of helicopter rotor blades in forward flight

A perturbation/numerical methodology to analyze the flap-lead/lag motion of a centrally hinged spring restrained rotor blade that is valid for both hover and for forward flight was developed. The derivation of the nonlinear differential equations of motion and the analysis of the stability of the steady state response of the blade were conducted entirely in a Symbolics 3670 Machine using MACSYMA to perform all the lengthy symbolic manipulations. It also includes generation of the fortran codes and plots of the results. The Floquet theory was also applied to the differential equations of motion in order to compare results with those obtained from the perturbation analysis. The results obtained from the perturbation methodology and from Floquet theory were found to be very close to each other, which demonstrates the usefullness of the perturbation methodology. Another problem under study consisted in the analysis of the influence of higher order terms in the response and stability of a flexible rotor blade in forward flight using Computerized Symbolic Manipulation and a perturbation technique to bypass the Floquet theory. The derivation of the partial differential equations of motion is presented.

Crespodasilva, M. R. M.↗
NASA NTRS1993

Asymptotic behavior of modulated Taylor-Couette flows with a crystalline inner cylinder

The linear stability of a modulated Taylor-Couette system when the inner cylindrical boundary consists of a crystalline solid-liquid interface is considered. Both experimentally and in numerical calculations it is found that the two-phase system is significantly less stable than the analogous rigid-walled system for materials with moderately large Prandtl numbers. A numerical treatment based on Floquet theory is described, which gives results that are in good agreement with preliminary experimental findings. In addition, this instability is further examined by carrying out a formal asymptotic expansion of the solution in the limit of large Prandtl number. In this limit the Floquet analysis is considerably simplified, and the linear stability of the modulated system can be determined to leading order through a conventional stability analysis, without recourse to Floquet theory. The resulting simplified problem is then studied for both the narrow gap geometry and for the case of a finite gap. It is surprising that the determination of the linear stability of the two-phase system is considerably simpler than that of the rigid-walled system, despite the complications introduced by the presence of the crystal-melt interface.

Braun, R. J.↗
NASA NTRS1976

An investigation of flap-lag stability of wind turbine rotors in the presence of velocity gradients and helicopter rotors in forward flight

The flap-lag equations of motion of a torsionally rigid and centrally hinged spring-restrained rigid blade are developed using quasi-steady blade-element aerodynamic theory. These equations have periodic coefficients and are applicable to both wind-turbine rotors with velocity gradients and helicopter rotors in forward flight. By solving these equations both by the Floquet-Liapunov method and by an approximate method, the range of applicability of the latter method is established. Flap-lag and pure flapping stability boundaries illustrating the effects of flow and rotor parameters are presented. Finally, some discussion on the techniques for generating the Floquet transition matrix and on the relative merits of the coordinate axes system is presented.

Kaza, K. R. V.↗
NASA NTRS1978

Plans for wind energy system simulation

A digital computer code and a special purpose hybrid computer, were introduced. The digital computer program, the Root Perturbation Method or RPM, is an implementation of the classic floquet procedure which circumvents numerical problems associated with the extraction of Floquet roots. The hybrid computer, the Wind Energy System Time domain simulator (WEST), yields real time loads and deformation information essential to design and system stability investigations.

Dreier, M. E.↗
NASA NTRS1985

Flap-Lag-Torsion Stability in Forward Flight

An aeroelastic stability of three-degree flap-lag-torsion blade in forward flight is examined. Quasisteady aerodynamics with a dynamic inflow model is used. The nonlinear time dependent periodic blade response is calculated using an iterative procedure based on Floquet theory. The periodic perturbation equations are solved for stability using Floquet transition matrix theory as well as constant coefficient approximation in the fixed reference frame. Results are presented for both stiff-inplane and soft-inplane blade configurations. The effects of several parameters on blade stability are examined, including structural coupling, pitch-flap and pitch-lag coupling, torsion stiffness, steady inflow distribution, dynamic inflow, blade response solution and constant coefficient approximation.

Panda, B.↗
NASA NTRS1987

Flap-lag-torsion aeroelastic stability of a circulation control rotor in forward flight

The aeroelastic stability of a circulation control rotor blade undergoing three degrees of motion (flap, lag, and torsion) is investigated in forward flight. Quasi-steady strip theory is used to evaluate the aerodynamics forces; and the airfoil characteristics are from data tables. The propulsive and the auxiliary power trims are calculated from vehicle and rotor equilibrium equations through the numerical integration of element forces in azimuth as well as in radial directions. The nonlinear time dependent periodic blade response is calculated using an iterative procedure based on Floquet theory. The periodic perturbation equations are solved for stability using Floquet transition matrix theory. The effects of several parameters on blade stability are examined, including advance ratio, collective pitch, thrust level, shaft tilt, structural stiffnesses variation, and propulsive and auxiliary power trims.

Chopra, Inderjit↗