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Trim analysis by shooting and finite elements and Floquet eigenanalysis by QR and subspace iterations in helicopter dynamics

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Date Issued:
1992
Summary:
The trim analysis for the initial state and control inputs that satisfy response periodicity and flight conditions, and the Floquet eigenanalysis for a few largest eigenvalues of the Floquet transition matrix (FTM) are investigated. In the trim analysis, the convergence of Newton iteration is investigated in computing the periodic initial state and control inputs sequentially and in parallel. The trim analysis uses the shooting method and two h-versions of temporal finite element methods, one based on displacement formulation and the other on mixed formulation of displacements and momenta. In each method, both the sequential and in-parallel schemes are used, and the resulting nonlinear equations are solved by damped Newton iteration with an optimally selected damping parameter. The reliability of damped Newton iteration, including earlier-observed divergence problems, is quantified by the maximum condition number of the Jacobian matrices of the iterative scheme. For illustrative purposes, rigid flap-lag and flap-lag-torsion models based on quasisteady aerodynamics are selected. Demanding trim analysis conditions are included by considering advance ratios or dimensionless flight speeds twice as high as those of current helicopters. Concerning the Floquet eigenanalysis, the feasibility of using the Arnoldi-Saad method, one of the emerging subspace iteration methods, is explored as an alternative to the currently used QR method, which is not economical for partial eigenanalysis. The reliability of the Arnoldi-Saad method is quantified by the eigenvalue condition numbers and the residual errors of the eigenpairs. In the three trim analysis methods, while the optimally selected damping parameter provides almost global convergence, the in-parallel scheme requires much less machine time than the conventional sequential scheme; both schemes have comparable reliability of the Newton iteration without and with damping. The Arnoldi-Saad method takes much less machine time than the QR method with comparable reliability.
Title: Trim analysis by shooting and finite elements and Floquet eigenanalysis by QR and subspace iterations in helicopter dynamics.
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Name(s): Achar, Nagari Shriranga.
Florida Atlantic University, Degree grantor
Gaonkar, Gopal H., Thesis advisor
College of Engineering and Computer Science
Department of Ocean and Mechanical Engineering
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Issuance: monographic
Date Issued: 1992
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 173 p.
Language(s): English
Summary: The trim analysis for the initial state and control inputs that satisfy response periodicity and flight conditions, and the Floquet eigenanalysis for a few largest eigenvalues of the Floquet transition matrix (FTM) are investigated. In the trim analysis, the convergence of Newton iteration is investigated in computing the periodic initial state and control inputs sequentially and in parallel. The trim analysis uses the shooting method and two h-versions of temporal finite element methods, one based on displacement formulation and the other on mixed formulation of displacements and momenta. In each method, both the sequential and in-parallel schemes are used, and the resulting nonlinear equations are solved by damped Newton iteration with an optimally selected damping parameter. The reliability of damped Newton iteration, including earlier-observed divergence problems, is quantified by the maximum condition number of the Jacobian matrices of the iterative scheme. For illustrative purposes, rigid flap-lag and flap-lag-torsion models based on quasisteady aerodynamics are selected. Demanding trim analysis conditions are included by considering advance ratios or dimensionless flight speeds twice as high as those of current helicopters. Concerning the Floquet eigenanalysis, the feasibility of using the Arnoldi-Saad method, one of the emerging subspace iteration methods, is explored as an alternative to the currently used QR method, which is not economical for partial eigenanalysis. The reliability of the Arnoldi-Saad method is quantified by the eigenvalue condition numbers and the residual errors of the eigenpairs. In the three trim analysis methods, while the optimally selected damping parameter provides almost global convergence, the in-parallel scheme requires much less machine time than the conventional sequential scheme; both schemes have comparable reliability of the Newton iteration without and with damping. The Arnoldi-Saad method takes much less machine time than the QR method with comparable reliability.
Identifier: 12297 (digitool), FADT12297 (IID), fau:9200 (fedora)
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): College of Engineering and Computer Science
Thesis (Ph.D.)--Florida Atlantic University, 1992.
Subject(s): Helicopters--Dynamics
Helicopters--Handling characteristics
Stability of helicopters--Mathematical models
Held by: Florida Atlantic University Libraries
Persistent Link to This Record: http://purl.flvc.org/fcla/dt/12297
Sublocation: Digital Library
Use and Reproduction: Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.