Cantilevers find a wide range of applications in the design of scientific equipment and large-scale engineering structures such as aircraft wings. Analysis techniques based on linearization approximations are unable to capture the large amplitude oscillation behaviour of such structures and thus, necessitates development of dedicated nonlinear methods. In this work, the recent developments in the Koiter-Newton model reduction method are utilized to obtain nonlinear reduced order models (ROMs) from full finite element structural models in order to simulate large amplitude dynamics of cantilevers. The method describes a nonlinear system of governing equations comprising quadratic and cubic terms which are obtained as higher order derivatives of the in-plane strain energy. To ensure that the large rotations in cantilevers and the resultant foreshortening effect is also accounted for, a ROM updating algorithm is adopted where the ROM parameters are varied with the structural deflections. Linear eigenmodes of the structure are utilized to form the reduction subspace. To validate the methodology, the ROM solution is compared against experimental results and a convergence study is conducted to identify the number of modes needed to replicate the nonlinear response. Finally, a composite wingbox structure is considered for which time domain simulations are conducted and frequency response curves, obtained through a frequency sweep, are presented.

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This research takes a further step towards the development of an autonomous aeroservoelastic wing concept with distributed flaps. The wing demonstrator, developed within the TU Delft SmartX project, aims to demonstrate in-flight performance optimization and multi-objective control using an over-actuated wing design. To address the challenges posed by the aeroelastic system’s nonlinearities and uncertainties, this paper employs an optimal control method relying on solving the State-Dependent Riccati Equation (SDRE). Geometrical nonlinearities, introduced in the form of plunge and torsion stiffness, make the system state-dependent and unsuitable for linear control methods. Additionally, a backlash model is incorporated to represent the uncertainty of the actuation system. The control strategy is implemented in a multi-objective manner to perform maneuver and gust load alleviation while accounting for the nonlinearities and uncertainties using the SDRE control. Firstly, a numerical sample case is investigated involving a state-dependent and highly non-linear canard aircraft configuration, to assess the ability of the SDRE control method. Then, in a numerical experiment, the effectiveness of the control strategy is evaluated through the nonlinear aeroelastic model. Evaluations are made on the practicality of the control approach, laying a foundation for future static and dynamic wind tunnel experiments with the SmartX-Neo demonstrator.

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This paper presents an experimental investigation into the aeroelastic behavior of an innovative wind turbine design featuring a downwind two-blade rotor with a teetering hub mounted on a tower with adjustable tilt. The rotor model incorporates two sets of elastic blades—stiff and flexible—for scaling purposes, each instrumented with strain gauges and accelerometers. Ground and wind tunnel tests were conducted to analyze the aeroelastic response. Static tests exhibited discrepancies between measured and numerically predicted displacements, with maximum displacements near the tip exceeding numerical predictions by 14% and 31% for flexible and stiff blades respectively. Frequency differences between measured and numerically simulated elastic modes ranged from 0.5% to 18% for both blade sets, as determined by ground vibration tests. Wind tunnel tests revealed the dominance of rotational speed harmonics, particularly the second harmonic, in the blades’ periodic response. A sensitivity analysis was also carried out with respect to tower tilt angle, rotational speed and blade pitch angle, for both blade sets at a range of tip-speed ratio values. The static response of the system, as captured by the generated power and thrust, was primarily sensitive to tower tilt angle variation and to a lesser extent blade pitch angle. Conversely, the tip-speed ratio in conjunction with rotational speed were found to dictate the dynamic response, influencing the azimuthal position and magnitude of the maximum bending moment at the blade root. Finally, no dynamic aeroelastic instability was observed during wind tunnel tests.

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This paper contributes towards the development of a reduced-order modelling methodology for nonlinear, unsteady aerodynamic loads for the active control of transonic aeroelastic flutter. To this end, a 1-DOF torsional NACA0012 airfoil is chosen as the test configuration. The aim is to develop the reduced-order model in nonlinear state-space form to be used in active control scenarios. Hence, a nonlinear coupled differential equation that captures the shock dynamics. The underlying hypothesis of this work is that, once these aerodynamic effects are included in the low-order model, the nonlinear trend in the flutter stability boundary, specifically in the transonic regime, will be predicted purely based on first principles, without the need for numerical or experimental corrections. In this work, we observe that the aeroelastic system could become prematurely unstable as soon as the aerodynamic flow field undergoes a Hopf bifurcation. For low amplitude airfoil pitching below a certain threshold, the aerostructural system is seen to exhibit a coupled oscillator behaviour that has an exact linear analytical formulation. The analytical formulation thus produces an accurate prediction whilst being orders of magnitude faster than the numerical simulation. @en

In line with recent advancements in aviation, which lead to more fuel-efficient aircraft, this paper presents a novel continuous movable parameterisation methodology. The methodology takes advantage of the ability of the doublet lattice method (DLM) to describe aerodynamic forces using downwash. The movables are described in the continuous space using a downwash distribution generated using a B-spline surface. To demonstrate and assess the movable modelling methodology, the U-HARWARD aircraft model has been used, with the performance of the continuous parameterisation compared to a reference movable parameterisation for roll control, manoeuvre load alleviation and cruise performance. The results show that the continuous parameterisation can determine a downwash distribution that is at least equal in performance – during roll – or has better performance – for manoeuvre load alleviation and cruise performance – than the reference parameterisation. The continuous parameterisation showed a 3 percentage points improvement with respect to the reference parameterisation for manoeuvre load alleviation and a 2.4 percentage points improvement for the induced drag coefficient. The results in the paper demonstrated the successful application of a movable parameterisation methodology, which can be applied to an aircraft for which only the planform and initial structural parameters are known.@en

Design optimisation potentially leads to lightweight aircraft structures with lower environmental impact. Due to the high number of design variables and constraints, these problems are ordinarily solved using gradient-based optimisation methods, leading to a local solution in the design space while the global space is neglected. Bayesian Optimisation is a promising path towards sample-efficient, global optimisation based on probabilistic surrogate models. While for problems with a low number of design variables, Bayesian Optimisation methods have demonstrated their strength, the scalability to high-dimensional problems while incorporating large-scale constraints is still lacking. Especially in aeroelastic tailoring where directional stiffness properties are embodied into the structural design of aircraft, to control aeroelastic deformations and to increase the aerodynamic and structural performance, the safe operation of the system needs to be ensured by involving constraints resulting from different analysis disciplines. Hence, a global design space search becomes even more challenging. The present study attempts to tackle the problem by using high-dimensional Bayesian Optimisation in combination with a dimensionality reduction approach to solve the optimisation problem occurring in aeroelastic tailoring, presenting a novel approach for high-dimensional problems with large-scale constraints. Experiments on well-known benchmark cases with black-box constraints show that the proposed approach can incorporate large-scale constraints.@en

This research investigates the application of aeroelastic tailoring to enhance the post-control surface reversal regime on a mid-range aircraft. Conventionally, active Maneuver Load Alleviation (MLA) is achieved through control surface actuation, while passive MLA utilizes structural modifications at the material or layout level to exploit wing wash-out deformation. Previous studies have demonstrated the significance of high control effectiveness in active MLA and the limitations of composite tailoring in passive MLA due to roll control authority constraints which typically result in stiffer wings with moderate mass savings. The aeroelastic optimization framework PROTEUS, developed at TU Delft, is employed to enhance operation in the post-control surface reversal regime. This is done to capitalize on increased control authority and thus promote load alleviation. The approach taken in this study is to identify critical constraints and assess the advantages of this strategy while acknowledging the technology’s immaturity, particularly its challenges in maintaining roll control effectiveness in certain flight envelope sectors. The results demonstrate significant mass savings in active MLA within the post-control surface reversal regime compared to conventional active MLA and highlight the substantial impact of the cruise-twist constraint on enhancing this regime. @en

Hybrid-electric aircraft represent a promising solution for the urgent need to decarbonize short-haul flights and bolster aviation sustainability. Nevertheless, the realization of hybrid-electric aircraft demands rigorous environmental impact analysis, given the substantial investments, time, and research required for technology development. This study offers a comprehensive life cycle inventory spanning the years 2030, 2040, and 2050 for both conventional and hybrid-electric aircraft configurations. Our inventory datasets are meticulously constructed through a systematic approach, ensuring data harmonization by drawing upon scientific literature, industry expertise, and primary data sources. This extensive dataset encompasses all pertinent systems necessary to model the environmental footprint of flights covering distances ranging from 200 to 600 nautical miles, utilizing a 50-passenger aircraft with the ATR42 as a reference model. Additionally, we furnish supplemental data for end-of-life considerations and uncertainty analysis. The systems under examination include the airframe, powertrain, power electronics and drives, batteries, fuel cells, hydrogen onboard storage, airport infrastructure, and battery charging stations. Notably, the carbon footprint of conventional aircraft aligns with data from the ecoinvent v3.8 database; however, our provided datasets are more than tenfold more detailed and incorporate a forward-looking perspective. These meticulously curated life cycle inventories can be amalgamated to simulate the potential environmental ramifications of conventional aircraft powered by kerosene or alternative aviation fuels, hybrid-electric aircraft utilizing battery technology, and hybrid-electric aircraft employing hydrogen as a fuel in conjunction with batteries. In this context, our findings play a pivotal role in nurturing the development of technology roadmaps that prioritize environmental sustainability within the realm of regional aviation.

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This paper presents a method for identifying flight dynamics models for aircraft that includes effects from the flexible structure and the effects from unsteady aerodynamics. In the time domain, the unsteady aerodynamic effects are often modelled using aerodynamic lag states. The proposed method involves first determining the poles that govern the dynamics for these lag states from flight data. This is followed by reconstructing the time signal histories for these lag states so that they can then be used as part of the model fitting procedure. Flight tests were conducted using a scaled Diana2 glider unmanned aerial vehicle (UAV) in order to collect experimental data for modelling. To be able to measure the response of the aircraft and its structure, the glider was instrumented with a wide range of sensors including accelerometers, gyroscopes and strain gauges placed across the aircraft structure. During the flight, various excitation manoeuvres were conducted by the pilot while the aircraft responses were collected. From these measurements, a full flight dynamics model consisting of both lateral and longitudinal dynamics was then identified. Additionally, a model predicting the tail and wing root loads was also identified. First, a rigid aircraft model was fitted that was then extended with states corresponding to the flexible modes and aerodynamic lags. Comparison between the rigid and extended model showed that the addition of structural modes and aerodynamic lag states to the identified models can lead up to 30% improvement in predicting aircraft responses. In conclusion, the method developed and presented in this paper is able to identify flight dynamics models from flight data that more accurately capture the dynamics of flexible aircraft by including effects from the flexible structure and unsteady aerodynamics. @en

Recent investigations pertaining to high aspect ratio wings have demonstrated the influence of geometric nonlinearities on structural and aeroelastic response when large deflections occur [1,2]. While utilization of nonlinear analyses techniques is beneficial for more realistic predictions of large deflection behaviour, it is accompanied with the drawback of high computational costs since finite element (FE) solvers are based on iterative predictor-corrector models. Nonlinear reduced order modelling can be an effective tool for conducting efficient analyses in such cases. In the proposed study we aim to exploit the recent developments in the Koiter-Newton (K-N) model reduction technique [3] for nonlinear dynamic response analysis of a high aspect ratio wing and thus, demonstrate the achievable reduction in computational costs in comparison to full FE simulations. The K-N reduction is a FE-based formulation which describes a system of nonlinear governing equations comprising quadratic and cubic stiffness terms. The higher order stiffness terms are evaluated as derivatives of the in-plane strain energy. To ensure that the effect of large rotations is accounted for, the reduced order model (ROM) is updated at fixed load intervals. Linear eigenmodes of the deformed structure are used to formulate the reduction subspace at the different load steps. The test structure chosen in this work is a variant of the Pazy wing [4] which is an experimental benchmark wing designed for nonlinear aeroelastic studies. The Pazy wing variant is based on the dimensions of the original design with minor modifications in the inner geometry. The FE model is constructed entirely using shell elements with 21,712 grid points and 130,272 degrees of freedom. For the initial validation, we conduct a nonlinear static analysis with a concentrated follower force, and compare it to FE solution from MSC Nastran. It is seen that by using just a single degree of freedom ROM, the nonlinear static solution is reproducible within a 2 % error margin for up to 40 % tip deflections. Subsequently, a nonlinear dynamic response analysis is conducted where the wing is subjected to large amplitude transient loads. The preliminary studies show a reduction in simulation time of over 95 % without significant loss in solution accuracy. References [1] Riso, Cristina, and Carlos E. Cesnik. "Low-Order Geometrically Nonlinear Aeroelastic Modeling and Analysis of the Pazy Wing Experiment." AIAA SciTech 2022 Forum. 2022. [2] Hilger, Jonathan, and Markus Raimund Ritter. "Nonlinear aeroelastic simulations and stability analysis of the Pazy wing aeroelastic benchmark." Aerospace 8.10 (2021): 308. [3] Sinha, Kautuk, et al. "Koiter–Newton Based Model Reduction for Large Deflection Analysis of Wing Structures." AIAA Journal (2023): 1-10. [4] Avin, Or, et al. "Experimental aeroelastic benchmark of a very flexible wing." AIAA Journal 60.3 (2022): 1745-1768. @en

This study explores the implementation of aeroelastic tailoring in the design of a regional aircraft featuring a strut-braced wing (SBW). Making use of the aeroelastic optimisation framework from Delft University of Technology, PROTEUS, the research addresses two distinct cases. The first case involves a simplified SBW geometry to validate the modifications of PROTEUS, which were conducted to include the strut in the aeroelastic analysis. Static and dynamic load cases are compared with a NX Nastran aeroelastic model, showing good agreement in displacements, strains, and gust response. In the second case, the study investigates the weight-saving potential of aeroelastic tailoring in an SBW aircraft based on the ATR-72. Three optimisation scenarios, allowing various laminate types, are examined: unbalanced symmetric laminates, balanced symmetric laminates, and a thickness optimisation with a prescribed balanced symmetric stacking sequence. The results reveal that the prescribed stacking sequence limits stiffness tailoring, thereby also reducing potential weight savings. Moreover, the study shows how the presence of a strut reduces wing deflections, limiting the effectiveness of aeroelastic tailoring.@en

The ram air inlets flaps are used in some aircraft to modulate the amount of ram air cooling the Environmental Control System. The current flap design features two metallic plates connected with a hinge. The present work studies an alternative design that replaces the metallic plates with a single composite laminate with morphing capabilities. An optimization framework is proposed to define the thickness distribution of the laminate taking into account the desired operational shapes, manufacturing guidelines and maximum allowable strains. This framework combines linear and nonlinear simulations to account for the large deflections while limiting the computational cost of the optimization. The results of the optimization framework are discussed at the end of the paper and next steps are formulated.@en

This paper proposes an extension to the traditional flight path reconstruction filter to simultaneously reconstruct the aircraft rigid body states together with modal amplitudes and velocities of the structure. To achieve this, the filter makes use of additional accelerometers, gyroscopes and strain gauges placed across the aircraft structure. These measurements are used in a Kalman filter together with kinematic equations of a flexible aircraft and structural mode shapes. First a simulation model is used to evaluate the filter performance on reference signals where the true state is known. Finally, flight test measurements obtained using an instrumented Diana 2 scaled glider are used to validate the filter.@en

In this paper, an innovative design methodology is proposed to simultaneously optimize the size, layout, and number of stiffeners of a stiffened panel using a gradient-based optimizer. In the proposed method, CAD-based parameterization is used to parameterize the layout of the stiffeners. The location and orientation of each stiffener are controlled with only two layout variables. The geometric constraints to avoid overlapping and crossing of stiffeners are implicitly applied through the layout parameterization scheme, therefore no additional constraints on the grid point coordinates are required. Moreover, the CAD model is maintained throughout the optimization process, therefore the additional step of converting the optimal design back to CAD is eliminated. The layout changes are accommodated in the finite element mesh through the re-meshing technique. The number of stiffeners is controlled by allowing an optimizer to transform an existing stiffener into a ghost stiffener. Every stiffener is assigned a topology variable that can be optimized to a value of either 0 or 1 using a penalization constraint. In case the optimal value is 0 then the contribution of that stiffener in determining the mass and the stiffness of the panel is lost, and it is considered an inactive or ghost stiffener. The stiffener is considered fully active when the optimal value is 1. The sensitivities of grid point coordinates relative to layout variables are calculated analytically. The sensitivities of the structural responses relative to size, layout, and topology variables are achieved through Nastran. The effectiveness of the proposed methodology is evident from the obtained results.@en

This paper aims to explore the advantages offered by machine learning (ML) for dimensionality reduction of nonlinear transonic aerodynamics. Three ML techniques are evaluated in terms of their ability to generate interpretable low-dimensional manifolds of the transient pressure distributions over a NACA4412 airfoil equipped with a flap. These ML techniques are Kernel Principle Component Analysis (kPCA), Locally Linear Embedding (LLE), and t-distributed Stochastic Neighbourhood Embedding (t-SNE). Initial investigations are also carried out to evaluate the performance of Artificial Neural Networks (ANNs). Three transient aerodynamic test cases are evaluated. First, a static aerodynamic transient analysis. Second, pitching and heaving airfoils in terms of prescribed sinusoidal displacements. Lastly, the airfoil geometry is adapted to include a flap under sinusoidal actuation. The snapshots forming the ground truth are obtained from unsteady CFD simulations. The preliminary results of this study reveal that patterns exist in low-dimensional nonlinear manifolds. Furthermore, unsupervised learning techniques are seen to outperform supervised neural networks in terms of both training cost and reconstruction accuracy. Promising reconstruction capabilities are observed with unsupervised learning.@en

This study presents an aeroelastic wind-tunnel experiment to identify the influence of the wing stiffness and hinge release threshold on the gust load alleviation performance of a folding wingtip design. Five models with different stiffness and tailoring properties are tested, and the wing root bending moment at different conditions is compared to the response with the locked-hinge condition to assess the impact on the gust load alleviation capabilities of the folding wingtip. The results show that the structural properties do not have an important impact on the peak load alleviation but the hinge release threshold and timing do. Releasing with the correct timing can reduce significantly the peak loads. However, the dynamics of the system are affected by this release; the flutter speed is decreased, and, although the performance can improve, load oscillations increase, which can be considered detrimental for reasons such as fatigue or passenger comfort.@en

The present study regards a novel wind turbine design featuring a two-bladed rotor on ate etering hub and a yawed tower. A reduced order modelling methodology is proposed for the equation of motion, using a lumped parameter approximation to derive expressions for the structural, rotor dynamic and geometric stiffness terms. The analytical expressions are validated numerically. In addition, a methodology is developed for aero elastic scaling of the rotor for use in wind tunnel tests. This results in two blade design templates, a "stiff" and a "flexible" design focusing on the vibration behaviour and deflected shapes respectively. The templates are designed to be 3D-printable as a single part. Design optimisation was performed in MSCN as tran, yielding two rotor designs, each aiming to match the non-dimensional parameters of interest. The stiff rotor matches the flap wise and torsional natural frequencies within 2.7%error, but has a mismatch in the edgewise mode, as well as the mode shapes and anti-symmetric modes. The flexible rotor is capable of capturing the target normalised displacement profile, at reduced structural mass, partially alleviating the mismatch in Lock number.

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Wing structures subjected to large deflections are prone to nonlinear load-deflection behavior. Geometric nonlinearities can arise due to the accompanying large rotations and in-plane deflections that manifest in the form of stiffening effects in the nonlinear static response. To account for these nonlinearities, reduced-order modeling techniques in combination with nonlinear finite element formulations have been previously proposed. However, these methods often have a limited range of validity due to linear eigenmode-based formulations with assumptions of small rotations. In this paper, a large deflection analysis framework based on the Koiter–Newton model reduction technique is presented. It is demonstrated that the reduced model in its basic form is ineffective for large deflection analysis. To resolve this, an incremental updating procedure is used for the reduced-order model that incorporates the necessary nonlinear effects. The model updating enables the computation of nonlinear response for a large range of deflections.

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This paper proposes an incremental nonlinear control method for an aeroelastic system’s gust load alleviation and active flutter suppression. These two control objectives can be achieved without modifying the control architecture or the control parameters. The proposed method has guaranteed stability in the Lyapunov sense and also has robustness against external disturbances and model mismatches. The effectiveness of this control method is validated by wind tunnel tests of an active aeroelastic parametric wing apparatus, which is a typical wing section containing heave, pitch, flap, and spoiler degrees of freedom. Wind tunnel experiment results show that the proposed nonlinear incremental control can reduce the maximum gust loads by up to 46.7% and the root mean square of gust loads by up to 72.9%, while expanding the flutter margin by up to 15.9%.

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