Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4975981 | Journal of the Franklin Institute | 2010 | 13 Pages |
Abstract
Recently [1] (Balakrishnan, 2000) it was shown that the linearized dynamics of the response of a flexible structure in inviscid incompressible airflow can be modeled as a convolution/evolution equation in a separable Hilbert space H(1)YË(t)=AY(t)+â«0tL(t-s)YË(s)dswhere Y(·) is the structure state, A is the infinitesimal generator of a c0 semigroup, with a compact resolvent, and L(t) is linear bounded and strongly continuous in tâ¥0. The convolution is characteristic of the aerodynamic force and moment but H is no longer an adequate state space, essential before we can consider controllability. Indeed currently there is no design theory for stability enhancement controllers. In this paper we develop a state space representation in the form(2)ZË(t)=AËZ(t)where the state space Z now a Banach space in which H is imbedded and AË is the infinitesimal generator of a c0 semigroup. A control term is readily added. The structure state is given by(3)Y(t)=PZ(t)where P is a projection operator onto H. The aeroelastic modes are now identified as eigenvalues (point spectrum) of AË.
Related Topics
Physical Sciences and Engineering
Computer Science
Signal Processing
Authors
A.V. Balakrishnan,