Multiparameter Spectral Analysis for Aeroelastic Instability Problems

Abstract

This paper presents a novel application of multiparameter spectral theory to the study of structural stability, with particular emphasis on aeroelastic flutter. Methods of multiparameter analysis allow the development of significant new solution and analysis algorithms for aeroelastic flutter problems; including direct solvers for polynomial problems of arbitrary order and size, and a pseudospectral method for characterizing the nature of the flutter point and its local modal damping gradient. Two variants of the flutter point direct solver are presented, their computational characteristics are compared, and an efficient hybrid method of direct spectral solution and iterative pseudospectral solution is developed. This method is well suited to the analysis of problems arising in reduced-order modeling and preliminary design optimization and has the advantage of computing all the system flutter points and their characteristics with minimal user oversight. The aeroelastic inverse problem, with applications in parameter identification and system optimization, is also shown to be solvable via multiparameter analysis. Extensions and improvements to this new conceptual framework and associated solvers are discussed.