M. Nowak

Two different techniques for root calculation in the Laplace domain will be presented. It will be assumed, that the used method for computing of aerodynamic forces permits not only calculation of the Laplace transforms of the generalized forces, but also its first and second derivatives (with respect to the non-dimensional transform variable). The flutter equation will be stated as an generalized eigenvalue problem in which the the eigenvalues are related to the Laplace variable. In the iteration processes described in this paper, each step contains the calculation of all eigenvalues and left and right eigenvectors. Next the Newton-Raphson technique is applied to the used relation between the eigenvalues and the Laplace variable. The first procedure described in the paper, enables the calculation of a single root at a given velocity U when the corresponding mode is selected from a known root found at another velocity. The initial roots are calculated at the velocity U=O. All roots which correspond to the natural modes with non-zero frequency can be calculated simultaneously from one eigenvalue problem. In the compressible case, aerodynamic forces may be calculated using the piston theory. The iteration process for the roots which corresponds to the rigid modes must include the elimination of already computed roots, as they form an unordered set. The second procedure is a generalization of known automated procedures for determining the flutter velocity, enabling the calculation of the roots for a given decrement of motion. This problem is reduced to a determination of the roots of a multivalued, real function. The crossings with root loci are determined in a descending order of the modulus of the non-dimensional Laplace variable.

International Forum on Aeroelasticity and Structural Dynamics 1991, Aachen

Conference Paper

englisch

21,0 x 29,7 cm, 10 Seiten

DGLR-Bericht, 1991, 1991-06, International Forum on Aeroelasticity and Structural Dynamics 1991 Proceedings; S.319-328; 1991; Deutsche Gesellschaft für Luft- und Raumfahrt - Lilienthal-Oberth e.V., Bonn

NA

aeroelasticity

Bestellbar

1991