Author Type

Graduate Student

Date of Award

1994

Document Type

Thesis

Publication Status

Version of Record

Submission Date

October 2026

Thesis/Dissertation Advisor [Chair]

Gaonkar, Gopal H.

Abstract

The rotorcraft trim solution involves a search for control inputs for required flight conditions as well as for corresponding initial conditions for periodic response or orbit. The control inputs are specified indirectly to satisfy flight conditions of prescribed thrust levels, rolling and pitching moments etc. In addition to the nonlinearity of the equations of motion and control inputs, the control inputs appear not only in damping and stiffness matrices but also in the forcing-function or input matrix; they must be found concomitantly with the periodic response from external constraints on the flight conditions. The Floquet Transition Matrix (FTM) is generated for perturbations about that periodic response; usually, a byproduct of the trim analysis. The damping levels or stability margins are computed from an eigenanalysis of the FTM. The Floquet analysis comprises the trim analysis and eigenanalysis and is routinely used for small order systems (order N < 100). However, it is practical for neither design applications nor comprehensive analysis models that lead to large systems (N > 100); the execution time on a sequential computer is prohibitive. The trim analysis takes the bulk of this execution time. Accordingly, this thesis develops concepts and methods of parallelism toward Floquet analysis of large systems with computational reliability comparable to that of sequential computations. A parallel shooting scheme with damped Newton iteration is developed for the trim analysis. The scheme uses parallel algorithms of Runge-Kutta integration and linear equations solution. A parallel QR algorithm is used for the eigenanalysis of the FTM. Additional parallelism in each iteration cycle is achieved by concurrent operations such as perturbations of initial conditions and control inputs, follow-up integrations and formations of the columns of the Jacobian matrix. These parallel shooting and eigenanalysis schemes are applied to the nonlinear flap-lag stability with a three-dimensional dynamic wake (N ~ 150). The stability also is investigated by widely used sequential schemes of shooting with damped Newton iteration and QR eigenanalysis. The computational reliability is quantified by the maximum condition number of the Jacobian matrices in the Newton iteration, the eigenvalue condition numbers and the residual errors of the eigenpairs. The saving in computer time is quantified by the speedup, which is the ratio of the execution times of Floquet analysis by sequential and parallel schemes. The work is carried out on massively parallel MasPar MP-1, a distributed-memory, single-instruction multiple-data or SIMD computer. A major finding is that with increasing system order, while the parallel execution time remains nearly constant, the sequential execution time increases nearly cubically with N. Thus, parallelism promises to make large-scale Floquet analysis practical.

Extent

90 p.

Comments

College of Engineering and Computer Science|FAU Electronic Theses and Dissertations Collection|Thesis (M.S.E.)--Florida Atlantic University, 1994.|College of Engineering and Computer Science

Identifier

FADT15085

Format

pdf

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