PARALLEL COMPUTING CONCEPTS AND METHODS FOR FLOQUET ANALYSIS OF HELICOPTER TRIM AND STABILITY

Floquet analysis is widely used for small-order systems (say, order M < 100) to find trim results of control inputs and periodic responses, and stability results of damping levels and frequencies, Presently, ho wever, it is practical neither for design applications nor for compreh ensive analysis models that lead to large systems (M > 100); the run t ime on a sequential computer is simply prohibitive, Accordingly, a mas sively parallel Floquet analysis is developed with emphasis on large s ystems, and it is implemented on two SIMD or single-instruction, multi ple-data computers with 4096 and 8192 processors, The focus of this de velopment is a parallel shooting method with damped Newton iteration t o generate trim results; the Floquet transition matrix (FTM) comes out as a byproduct, The eigenvalues and eigenvectors of the FTM are compu ted by a parallel QR method, and thereby stability results are generat ed, For illustration, flap and flap-lag stability of isolated rotors a re treated by the parallel analysis and by a corresponding sequential analysis with the conventional shooting and QR methods; linear quasist eady airfoil aerodynamics and a finite-state three-dimensional wake mo del are used, Computational reliability is quantified by the condition numbers of the Jacobian matrices in Newton iteration, the condition n umbers of the eigenvalues and the residual errors of the eigenpairs, a nd reliability figures are comparable in both the parallel and sequent ial analyses, Compared to the sequential analysis, the parallel analys is reduces the run time of large systems dramatically, and the reducti on increases with increasing system order; this finding offers conside rable promise for design and comprehensive-analysis applications.