This paper presents a general state-space realization of the unsteady vortex-lattice method together with a bespoke model-order reduction strategy. The aim is to provide a computationally-efficient aerodynamic description suitable for integration in aeroelasticity with arbitrary kinematics. The state-space realization is obtained from linearization, around arbitrary geometries and static loading conditions, of lifting surfaces and their free wakes. All components of the forces are evaluated in time domain using Joukowski's the
A method for frequency-limited balancing of the unsteady vortex-lattice equations is introduced that results in compact models suitable for computational-intensive applications in load analysis, aeroelastic optimisation, and control synthesis. The balancing algorithm relies on a frequency-domain solution of the vortex-lattice equations that effectively eliminates the cost associated to the wake states. It is obtained from a Z-transform of the underlying discrete-time equations, and requires no additional geometrical or kinematic assumptions for the lifting surfaces. Parametric reduced-order modelling is demonstrated through interpolation over (a) projection matrices, (b) state-space realisations and (c) transfer functions, which trade accuracy, robustness and cost. Methods are finally exemplified in the dynamic stability of a T-tail configuration with varying incidence. Numerical studies show that a very small number of balanced realisations is sufficient to accurately capture the unconventional aeroelastic response of this system, which includes in-plane kinematics and steady loads, over a wide range of operation conditions. Nomenclature γ i interpolation weight for design parameter p i Γ vector of circulation strengths κ i integration weight at frequency k i K number of integration points, k i
The single-shooting method is used to identify optimal manoeuvres in the lateral dynamics of partially-supported flexible wings. Efficient actuation strategies are sought when large wing deflections substantially modify the geometry of the vehicle during the manoeuvre. For that purpose, geometrical nonlinear models are first built using composite beams and an unsteady vortex lattice, and the optimal control problem is then solved via a gradient-based algorithm. A flight-dynamics model based on elastified stability derivatives is shown to capture the relevant dynamics either under slow actuation or for stiff wings and it is used as a reference. Embedding the full aeroelastic description into the optimisation framework expands the space of achievable manoeuvres, such as quick wing response with low structural vibrations or large lateral forces with minimal lift losses.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.