Backbone curves can offer valuable insight into the behaviour of nonlinear systems along with significant information about any coupling between the underlying linear modes in their response. This paper presents a technique for the extraction of backbone curves of lightly damped nonlinear systems that is well suited for the experimental investigation of structures exhibiting nonlinear behaviour. The approach is based on estimations of the instantaneous frequency and the envelope amplitude of a decaying response following a tuned steady-state oscillation of the system. Results obtained from simulations and experiments demonstrate that the proposed procedure is capable of achieving an accurate estimation of the backbone curves and damping ratios of the system provided that the premise of damping having low impact on its oscillation frequency is met

In collaboration with Airbus-UK, the dimensional growth of aircraft panels while being riveted with stiffeners is investigated. Small panels are used in this investigation. The stiffeners have been fastened to the panels with rivets and it has been observed that during this operation the panels expand in the longitudinal and transverse directions. It has been observed that the growth is variable and the challenge is to control the riveting process to minimize this variability. In this investigation, the assembly of the small panels and longitudinal stiffeners has been simulated using static stress and nonlinear explicit finite element models. The models have been validated against a limited set of experimental measurements; it was found that more accurate predictions of the riveting process are achieved using explicit finite element models. Yet, the static stress finite element model is more time efficient, and more practical to simulate hundreds of rivets and the stochastic nature of the process. Furthermore, through a series of numerical simulations and probabilistic analyses, the manufacturing process control parameters that influence panel growth have been identified. Alternative fastening approaches were examined and it was found that dimensional growth can be controlled by changing the design of the dies used for forming the rivets.

Reliability-based design is concerned with ensuring that constraints are enforced with acceptable probability under inherent variability in properties. In aircraft design, such a constraint may be that aeroelastic instability does not occur at velocities encountered by the aircraft. This approach can be complicated, as the aeroelastic instability speed is a discontinuous function of material properties, on account of particular modes only becoming unstable for some parameter values. In reliability analysis, it is common to use surrogate models due to the computational expense associated with Monte Carlo Simulation, however, such methods can be inaccurate when emulating discontinuous functions such as the aeroelastic instability speed. In this paper, an alternative approach is proposed in which Gaussian process surrogate models are fitted directly to each of the modal eigenvalues at the design air-speed, and used to emulate a stability margin based upon the most critical eigenvalue. Using this approach, it is shown that the reliability may be estimated for the aeroelastic stability using smooth emulators, thereby overcoming the problems associated with discontinuities. The method is demonstrated for layup optimisation of composite plate wings with uncertain ply angles, in which the probability of aeroelastic instability occurring is minimised for a prescribed air-speed. In uncertainty quantification, a good agreement is found with Monte Carlo Simulation with an order of two magnitudes reduction in model runs. Through reliability-based design, reductions in the probability of failure of up to 99.8% are achieved by increasing the stability margin at the design speed.

This paper applies numerical continuation techniques to a nonlinear aeroelastic model of a highly flexible, high-aspect-ratio wing. Using continuation, it is shown that subcritical limit cycle oscillations, which are highly undesirable phenomena previously observed in numerical and experimental studies, can exist due to geometric nonlinearity alone, without need for nonlinear or even unsteady aerodynamics. A fully nonlinear, reduced-order beam model is combined with strip theory and one-parameter continuation is used to directly obtain equilibria and periodic solutions for varying airspeeds. The two-parameter continuation of specific bifurcations (i.e., Hopf points and periodic folds) reveals the sensitivity of these complex dynamics to variations in out-of-plane, in-plane and torsional stiffness and a ‘wash out’ stiffness coupling parameter. Overall, this paper demonstrates the applicability of continuation to nonlinear aeroelastic analysis and shows that complex dynamical phenomena, which cannot be obtained by linear methods or numerical integration, readily exist in this type of system due to geometric nonlinearity.

In this paper, the effect of distributed electric propulsion on the aeroelastic stability of an electric aircraft wing was investigated. All the electric propulsors, which are of different properties, are attached to the wing of the aircraft in different positions. The wing structural dynamics was modelled by using geometrically exact beam equations, while the aerodynamic loads were simulated by using an unsteady aerodynamic theory. The electric propulsors were modelled by using a concentrated mass attached to the wing, and the motor’s thrust and angular momentum were taken into account. The thrust of each propulsor was modelled as a follower force acting exactly at the centre of gravity of the propulsor. The nonlinear aeroelastic governing equations were discretised using a time–space scheme, and the obtained results were verified against available results and very good agreement was observed. Two case studies were considered throughout the paper, resembling two flight conditions of the electric aircraft. The numerical results show that the tip propulsor thrust, mass, and angular momentum had the most impact on the aeroelastic stability of the wing. In addition, it was observed that the high-lift motors had a minimal effect on the aeroelastic stability of the wing.

Recent studies have considered the use of flared folding wingtips (FFWTs) to enable higher aspect ratios—reducing overall induced drag—while reducing gust loading and meeting airport operational requirements. The majority of these analyses have employed linear assumptions despite the presence of large wingtip deformations. In this paper the effect of geometric nonlinearities introduced by an FFWT on the static and dynamic aeroelastic response of a wing is assessed. A geometrically exact expression was formulated to describe the change in the local angle of attack in the chordwise direction across all fold angles. This expression highlighted that the aerodynamic stiffness of an FFWT and, therefore, quantities such as the linear flutter speed are a function of the fold angle and, hence, the attitude of the wing. This effect was verified using both a wind tunnel model of a flexible semispan wing and a numerical model utilizing MSC Nastran, which linearized the model about the equilibrium position of the wingtip. These experiments showed that the geometric nonlinearities introduced due to the large deformations of FFWTs can significantly affect the dynamics of the system, with flutter speeds varying by over 28%, simply by changing the angle of attack of the model.