Serial and Parallel Fast-Floquet Analyses in Rotorcraft Aeroelasticity

Abstract

Rotorcraft stability investigation involves a nonlinear trim analysis for the control inputs and periodic responses, and, as a follow-up, a linearized stability analysis for the Floquet transition matrix (FTM), and its eigenvalues and eigenvectors. The trim analysis is based on a shooting method with damped Newton iteration, which gives the FTM as a byproduct, and the eigenanalysis on the QR method; the corresponding trim and stability analyses are collectively referred to as the Floquet analysis. A rotor with Q blades that are identical and equally spaced has Q planes of symmetry. Exploiting this symmetry, the fast-Floquet analysis, in principle, reduces the run time and frequency indeterminacy of the conventional Floquet analysis by a factor of Q. It is implemented on serial computers and on all three types of mainstream parallel-computing hardware: SIMD and MIMD computers, and a distributed computing system of networked workstations; large models with hundreds of states are treated. A comprehensive database is presented on computational reliability such as the eigenvalue condition number and on parallel performance such as the speedup and efficiency, which show, respectively, how fast a job can be completed with a set of processors and how well their idle times are minimized. Despite the Q-fold reduction, the serial run time is excessive and grows between quadratically and cubically with the number of states. By contrast, the parallel run time can be reduced dramatically and its growth can be controlled by a judicious combination of speedup and efficiency. Moreover, the parallel implementation on a distributed computing system is as routine as the serial implementation.