Paolo Tiso

Morphing Wing Flight Control Via Postbuckled Precompressed Piezoelectric Actuators

The design, modeling, and testing of a morphing wing for flight control of an uninhabited aerial vehicle is detailed. The design employed a new type of piezoelectric flight control mechanism which relied on axial precompression to magnify control deflections and forces simultaneously. This postbuckled precompressed bending actuator was oriented in the plane of the 12% thick wing and mounted between the end of a tapered D-spar at the 40% chord and a trailing-edge stiffener at the 98% chord. Axial precompression was generated in the piezoelectric elements by an elastic skin which covered the outside of the wing and served as the aerodynamic surface over the aft 70 % of the wing chord. A two-dimensional semi-analytical model based on the Rayleigh-Ritz method of assumed modes was used to predict the static and dynamic trailing-edge deflections as a function of the applied voltage and aerodynamic loading. It was shown that static trailing-edge deflections of ±3.1 deg could be attained statically and dynamically through 34 Hz, with excellent correlation between theory and experiment. Wind tunnel and flight tests showed that the postbuckled precompressed morphing wing increased roll control authority on a 1.4 meter span uninhabited aerial vehicle while reducing weight, slop, part-count, and power consumption.

Post-buckled precompressed elements: a new class of control actuators for morphing wing UAVs

This paper describes how post-buckled precompressed (PBP) piezoelectric bender actuators are employed in a deformable wing structure to manipulate its camber distribution and thereby induce roll control on a subscale UAV. By applying axial compression to piezoelectric bimorph bender actuators, significantly higher deflections can be achieved than for conventional piezoelectric bender actuators. Classical laminated plate theory is shown to capture the behavior of the unloaded elements. A Newtonian deflection model employing nonlinear structural relations is demonstrated to predict the behavior of the PBP elements accurately. A proof of concept 100 mm (3.94 �� ) span wing employing two outboard PBP actuator sets and a highly compliant latex skin was fabricated. Bench tests showed that, with a wing chord of 145 mm (5.8 �� ) and an axial compression of 70.7 gmf mm −1 , deflection levels increased by more than a factor of 2 to 15.25 ◦ peak-to-peak, with a corner frequency of 34 Hz (an order of magnitude higher than conventional subscale servoactuators). A 1.4 m span subscale UAV was equipped with two PBP morphing panels at the outboard stations, each measuring 230 mm

Dynamic Nonlinear Aeroelastic Model of a Kite for Power Generation

chord length, camber, and thickness per section, and it is derived by fitting precomputed data from computational fluiddynamicanalysis.Toreducecomputationtimes,localdynamicdeformationphenomenaareneglected.Foreach integration time step, the steady aerodynamic loading is determined first and then used to update the static equilibriumshape ofthewing.Thisstaticaeroelastic modelis embedded inadynamicsystemmodelthatincludesthe tether, bridle lines, and kite control unit. The iterative approach can accurately describe bending and torsion of the wing,whichcontributeto theaerodynamic steeringmoments.Thepresentedapproach iscomplementedwithaflight controller and used to simulate figure-eight flight maneuvers of a leading-edge inflatable tube kite used for traction power generation.

Optimal second order reduction basis selection for nonlinear transient analysis

Effective Model Order Reduction (MOR) for geometrically nonlinear structural dynamics problems can be achieved by projecting the Finite Element (FE) equations on a basis constituted by a set of vibration modes and associated second order modal derivatives. However, the number of modal derivatives gener- ated by such approach is quadratic with respect to the number of chosen vibration modes, thus quickly making the dimension of the reduction basis large. We show that the selection of the most important second order modes can be based on the convergence of the underlying linear modal truncation approximation. Given a cer- tain time dependency of the load, this method allows to select the most significant modal derivatives set before computing it.

Reduction methods for MEMS nonlinear dynamic analysis

Practical MEMS applications feature non-linear effects that are important to be realistically simulated. Thistypically involves large dynamic non-linear finite element (FE) models, and therefore efficient model reduction techniques are of great need. Proper Orthogonal Decomposition (POD) is a well-known technique for the effective orderreduction of large dynamic (non-linear) systems. POD does not require any knowledge of the system at hand but features the disadvantage of the need of running a full simulation to extract the reduction basis. On the other hand, a basis constituted by few vibration modes enriched with modal derivatives (MD) can describe the main effect of nonlinearity without the need of a full model solution. We present a comparison of the two described reduction methods (POD and MD) applied to a geometircally non-linear micro-beam subjected to electrostatic forces.

A Substructuring Method for Geometrically Nonlinear Structures

We present an extension of the well established Craig–Bampton and Rubin methods for component mode synthesis for the case of geometric nonlinearities. The internal modal basis of a substructure is enriched with modal derivatives to capture the nonlinear behavior. We show that the Rubin method outperforms the Craig–Bampton method in cases characterized by large rigid motions of the substructures.

Discrete Empirical Interpolation Method for Finite Element Structural Dynamics

Model Order Reduction (MOR) in nonlinear structural analysis problems in usually carried out by a Galerkin projection of the primary variables on a sensibly smaller space. However, the cost of computing the nonlinear terms is still of the order of the full system. The Discrete Empirical Interpolation Method is an effective algorithm to reduce the computational of the nonlinear term. However, its efficiency is diminished when applied to a Finite Element (FE) framework. We present here an alternative formulation of the DEIM that suits an FE formulation and preserves the efficiency of the method.

A Computational Method for Structurally Nonlinear Joined Wings Based on Modal Derivatives

Past studies showed that the overconstrained nature of Joined Wings and the strong structural geometric nonlinearities make difficult the use of standard packages of aeroelastic solvers (usually modally reduced and frequency domain based) which have been effectively adopted by the industry for decades. We present here a study on the reduction of the computational cost in presence structural nonlinear effects that cannot be neglected in Joined Wings, even at small angles of attack and attached flow. In particular, a reduced order model is achieved with a basis constituted by vibration modes augmented with the corresponding modal derivatives. The results can be considered excellent when compared to the full order reference solution. However, a convergence test showed that the required number of vectors is relatively high and the basis needs to be often updated to achieve the best performance. More investigations will be necessary for an effective use in the industry and complicate dynamic problems involving the unsteadiness of the aerodynamics.

A quadratic manifold for model order reduction of nonlinear structural dynamics

Abstract This paper describes the use of a quadratic manifold for the model order reduction of structural dynamics problems featuring geometric nonlinearities. The manifold is tangent to a subspace spanned by the most relevant vibration modes, and its curvature is provided by modal derivatives obtained by sensitivity analysis of the eigenvalue problem, or its static approximation, along the vibration modes. The construction of the quadratic manifold requires minimal computational effort once the vibration modes are known. The reduced-order model is then obtained by Galerkin projection, where the configuration-dependent tangent space of the manifold is used to project the discretized equations of motion.

Nonlinear Aeroelasticity, Flight Dynamics and Control of a Flexible Membrane Traction Kite

This chapter presents a computational method to describe the flight dynamics and deformation of inflatable flexible wings for traction power generation. A nonlinear Finite Element approach is used to discretize the pressurized tubular support structure and canopy of the wing. The quasi-steady aerodynamic loading of the wing sections is determined by empirical correlations accounting for the effect of local angle of attack and shape deformation. The forces in the bridle lines resulting from the aerodynamic loading are imposed as external forces on a dynamic system model to describe the flight dynamics of the kite. Considering the complexity of the coupled aeroelastic flight dynamics problem and the Matlab® implementation, simulation times are generally low. Spanwise bending and torsion of the wing are important deformation modes as clearly indicated by the simulation results. Asymmetric actuation of the steering lines induces the torsional deformation mode that is essential for the mechanism of steering. It can be concluded that the proposed method is a promising tool for detailed engineering analysis. The aerodynamic wing loading model is currently the limiting factor and should be replaced to achieve future accuracy improvements.