Some developments of expansion methods for solving the flutter equations

Abstract

SummaryIn a theoretical flutter analysis, the real zeros x˂0,y˃0, of a stability determinant Δ(√x, y) which is a polynomial in y are required, and can readily be evaluated once the polynomial expansions are known for assigned values of x. When the air loads are estimated on the basis of classical derivative theory, Δ becomes a bivariate polynomial in √x and y of a special type. Direct expansion of the stability determinant becomes too involved when the number of degrees of freedom is large and indirect methods of expansion are needed.A method of bivariate expansion which uses a framework of lines subject to certain restrictions is examined in Part I, and is applied to a quaternary wing-flutter problem. The analysis shows that frameworks previously proposed, having all intersections outside the flutter quadrant (x˂0, y˃0), demand very high computational accuracy. A new framework is suggested having all intersections inside the flutter quadrant. The improvement in computational accuracy is considerable.