IFASD2024 Paper Submission & Registration
17 – 21 June 2024, The Hague, The Netherlands

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13:30   Nonlinear aeroelasticity
Chair: Julian Seeley
30 mins
Nonlinear Aeroelastic Response Analysis of Unmanned Multi-body Aircraft with Free Play
Chen Zhu, Ying Bi, Zijian Zhu, Zhuolin Ying, Xiaoping Ma
Abstract: The unmanned multi-body aircraft (MBA) proposed in this paper represents a novel aircraft configuration connecting multiple independent aircraft at their wingtips through hinges. This design has attracted considerable research interest due to its effective resolution of issues such as poor wind resistance, challenges in low-altitude flight, and limited mission agility, which is commonly associated with high aspect ratio aircraft. The nonlinearity of the free play at flexible hinges between adjacent flight units is common existed, which can result in deviations in the aeroelastic stability boundaries of the aircraft. It is essential to conduct research that takes into account the free-play nonlinearity in the context of aeroelastic response analysis. In this study, the free play between the wing tips of the lead aircraft (mother aircraft) and the trailing aircraft (daughter aircraft) within an unmanned multi-body aircraft system is taken as the research object. To address the challenges posed by these free play, the fictitious mass method is used to linearize modal vibration patterns, establishing a modal array capable of expressing deformations across the entire response field. Additionally, the minimum state method is utilized to fit non-constant aeroelastic rational functions, in that case, how different design parameters for the gaps between aircraft wings affect the corresponding response characteristics of limit cycles is analysed. The results show that when there is a free play between the wings of an unmanned multi-body aircraft, nonlinear limit cycle oscillations occur within a specific region below the linear flutter threshold. Moreover, the parameters of free play will affect the amplitude of these limit cycle oscillations and the divergence critical dynamic pressure. The critical velocity of the limit cycle oscillation decreases with the increase of the gap and increases with the increase of the initial deviation of the gap; Besides, the free-play nonlinearity increases the amplitude of the system's limit cycle oscillation; as the flow rate increases, the system shows a complex response, with periodic and chaotic motions occurring intermittently. This study contributes valuable insights into the behaviour of unmanned multi-body aircraft, shedding light on the complex interplay of free play and their nonlinear effects on aeroelastic performance.
30 mins
An Incremental Modal Shape Sensing Method for Geometrically Non-Linear Deformed Wings
Janto Gundlach, Marc Böswald, Jurij Sodja
Abstract: Shape sensing techniques enable the real-time reconstruction of wing displacements based on measured strain. As wing designs become more flexible, they may at some point exhibit geometric non-linear deformation. This eventually leads to erroneous displacement estimates if applied methods rely on the assumption of linear deformation. In this research, the Incremental Modal Method (IMM) is presented which accounts for the change of the employed mode shapes due to structural deformation. The method is applied on the finite element model of a high aspect ratio wing undergoing geometric non-linear deflections in flap-wise bending. In the process, a setup of virtual strain sensors is presumed which is representative as instrumentation in experiments. Along a reference line of the wing, the displacement estimates of IMM are compared to results obtained using the Modal Rotation Method (MRM), another shape sensing scheme recently developed for the non-linear regime. For the chosen segmentation and virtual instrumentation of the investigated wing, IMM proves to be a promising candidate for realtime displacement reconstruction in experiments, provided that mode shapes in intermediate deflected states can be determined.
30 mins
Nonlinear analysis of a flexible half-wing model tested in a subsonic wind tunnel with control-surface freeplay and preloading
Breno Moura Castro, Wellington Luziano Paulo Junior, Douglas Domingues Bueno, Cleber Spode
Abstract: Wind tunnel tests were conducted using a flexible, half-wing model provided with a control surface. The main purpose of these tests was to evaluate the methodology developed at Embraer to accomplish nonlinear aeroelastic analyses. To introduce nonlinear effects in the system, the flexible connection between the control surface and the main surface of the wing was fitted with a freeplay mechanism. Another important feature of the experimental setup was the position of the model inside the test section. For various reasons, the model was installed in the horizontal position and, therefore, the control surface was subjected to preloading due to the moment around the hinge line generated by its own weight. Limit cycle oscillations (LCO) were observed in the subsonic wind tunnel tests but only when the equilibrium position of the control surface, which depended on the tunnel flow velocity, was within the freeplay deadspace. The treatment of preloading found in the literature (see Laurenson and Trn [1]), however, was not developed for such a condition. The condition in which the preloading formulation was developed in Ref. [1] assumed that the equilibrium may only occur outside the freeplay deadspace. Therefore, a special treatment for a preload equilibrium inside the freeplay deadspace was developed for frequency-domain aeroelastic analyses. The special treatment was based on Ref. [1] and new equations were developed, based on the same assumptions, for the present conditions. The new approach needed a method for determining the equilibrium position of the control surface for a given wind tunnel flow condition (preload parameter). The determination of the control surface equilibrium position demanded some specific aerodynamic coefficients along with mass and inertia properties of the aeroelastic system. The aerodynamic characteristics were evaluated both by vortex lattice and CFD methods. The results of such equilibrium position predictions, and then the preloading parameter, agreed well with the measurements in the wind tunnel tests. The predictions of the adapted methodology for the aeroelastic analysis of a nonlinear system with preload were consistent with the experimental LCO frequencies and amplitudes evaluated in the wind tunnel tests. References: [1] Robert M. Laurenson and Robert M. Trn. Flutter of Control Surfaces with Structural Nonlinearities. Technical Report Report MDC E1734, McDonnell Douglas Astronautics Company, East. St Louis, Missouri, 1977.
30 mins
Nonlinear dynamic response of a pazy wing variant using Koiter-Newton model reduction
Kautuk Sinha, Farbod Alijani, Wolf Krüger, Roeland De Breuker
Abstract: 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.

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