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Numerous powerful methods exist for developing Reduced-order Models (ROMs) using Finite Element (FE) models. Ensuring the accuracy of these ROMs is essential; however, the validation using dynamic responses is expensive. In this work, we propose a method to ensure the accuracy of ROMs without extra dynamic FE simulations. It has been shown that the well-established Implicit Condensation and Expansion (ICE) method can produce an accurate ROM when the FE model's static behaviours are captured accurately. However, this is achieved via a fitting procedure, which may be sensitive to the selection of load cases and ROM's order, especially in the multi-mode case. To alleviate this difficulty, we define an error metric that can evaluate the ROM's fitting error efficiently within the displacement range, specified by a given energy level. Based on the fitting result, the proposed method provides a strategy to enrich the static dataset, i.e. additional load cases are found until the ROM's accuracy reaches the required level. Extending this to the higher-order and multi-mode cases, some extra constraints are incorporated into the standard fitting procedure to make the proposed method more robust. A clamped-clamped beam is utilised to validate the proposed method, and the results show that the method can robustly ensure the accuracy of the static fitting of ROMs.

Predicting the forced responses of nonlinear systems is a topic that attracts extensive studies. The energy balancing method considers the net energy transfer in and out of the system over one period, and establishes connections between forced responses and nonlinear normal modes (NNMs). In this paper, we consider the energy balancing across multiple harmonics of NNMs for predicting forced resonances. This technique is constructed by combining the energy balancing mechanism with restrictions (established via excitation scenarios) on external forcing and harmonic phase-shifts; a semi-analytical framework is derived to achieve both accurate/robust results and efficient computations. With known inputs from NNM solutions, the required forcing amplitudes to reach NNMs at resonances, along with their discrepancy, i.e. the harmonic phase-shifts, are computed via a one-step scheme. Several examples are presented for different excitation scenarios to demonstrate the applicability of this method, and to show its capability in accurately predicting the existence of an isola where multiple harmonics play a significant part in the response.

Wind tunnel oscillatory testing is a technique conventionally used for the measurement of dynamic aerodynamic loads on subscale aircraft models. Oscillatory testing is commonly used for identificat...

Spoilers are secondary control surfaces mainly used for roll control, load alleviation and as airbrakes. However, when considering very flexible wings, spoilers could also play a primary role in controlling the aircraft’s attitude as an ideal alternative or complement to ailerons since they are distributed over the wingspan and, therefore, potentially less affected by the wing deformation. However, due to its nonlinear nature, spoilers aerodynamics can only beaccurately simulated through high-fidelity software, such as CFD. The work presented in this paper aims to provide a novel method to model spoiler aerodynamics in a low-fidelity Unsteady Vortex Lattice framework by proposing an approach able to predict the impact of multiple spoilers on the wing lift distribution. The approach is verified through data acquired in a series of wind tunnel tests on a rigid wing equipped with servo-controlled spoilers carried out in the University of Bristol Low Turbulence Wind Tunnel. Load cell measurements and PIV data are shown for comparison. Numerical predictions show good agreement with the experimental data proving the low-fidelity UVLM aerodynamic solver’s ability to successfully model the nonlinear flow field behind the extended spoiler.

Non-intrusive or indirect reduced-order modelling strategies, such as the implicit condensation and expansion method, are applicable to geometrically nonlinear structures modelled using commercial finite-element (FE) software. Traditionally, the non-conservative forces acting on the structure are reduced via a linear projection onto the space spanned by the reduced modeshapes. As such, only the forces acting directly on these reduced modes can be captured, while any energy gained or dissipated by the statically condensed modes is neglected. This can lead to significant inaccuracies in the reduced-order model (ROM) predictions, which is demonstrated here using a 2-degrees-of-freedom (DOF) oscillator, and an FE model of a cantilever beam. It is shown that the non-conservative forces acting on the statically condensed modes can be captured using a nonlinear mapping of the physical DOFs into the reduced coordinates. This introduces additional terms in the reduced equations of motion, which we describe as force compensation . Excellent agreement is observed between the forced response curves of the full-order models and those of our proposed ROMs, both for the oscillator as well as the cantilever beam under different external excitation conditions (i.e. a constant-direction force and a follower force).

[No Abstract]

It is common practice within multi-body dynamic (MBD) modeling to assume that individual bodies are rigid however this can be an oversimplification especially when slender bodies are present resulting in inaccurate estimations of the system's natural frequencies and overall behavior. To address this shortfall, we extend the Udwadia–Kalaba (U–K) MBD formulation in this paper to model flexible multibody systems for purposes of exploring system natural frequencies. To model the flexibility, a lumped parameter approach is proposed, which in this work idealizes a flexible beam as a series of discrete rigid elements connected by torsional springs. In the U–K formulation, a mechanical system can also be discretized into rigid elements and adapted. This is viewed as a benefit for incorporating a lumped parameter approach within the U–K formulation to model flexible multibody systems. A flexible crank-slider mechanism is introduced and modeled within the Udwadia–Kalaba formulation to capture the dynamics of flexibility through linkage compliance. The model is validated against an alternatively formulated MBD model and system natural frequencies and mode shapes numerically predicted. Results of the study show the effectiveness and potential of extending the application of the Udwadia–Kalaba formulation by using a lumped parameter approach to dynamically model flexible multibody systems.

The performance benefits of passive vibration suppression with network configurations consisting of stiffness, damping and inertance elements have been demonstrated for a wide range of mechanical systems. Considering physical implementations of these beneficial network configurations, hydraulic realisations have the advantages of durability and simplicity for integration with existing hydraulic dampers. Such designs are exemplified by fluid inerters and fluid-inerter-damper devices. However, in contrast to the convenience of realising inertance and damping elements, realising ‘embedded’ stiffness is very challenging. We use ‘embedded’ to refer to a network element, which is not purely in series or in parallel with the remainder of the network but instead lies within the network layout. In this work, a setup using a rubber membrane to realise such embedded stiffness is proposed, together with a procedure for hydraulic implementations of any stiffness-damping-inertance configurations. The nonlinear properties of the embedded stiffness due to rubber membrane properties are then investigated both theoretically and experimentally. In addition, the effectiveness of both the membrane setup and the design procedure are demonstrated via a case study of suspension design for passenger vehicle ride comfort enhancement.

In the field of structural dynamics, system identification usually refers to building mathematical models from an experimentally-obtained data set. To build reliable models using the measurement data, the mathematical model must be representative of the structure. In this work, attention is given to robust identification of nonlinear structures. We draw inspiration from reduced order modelling to determine a suitable model for the system identification. There are large similarities between reduced order modelling and system identification fields, i.e. both are used to replicate the dynamics of a system using a mathematical model with low complexity. Reduced Order Models (ROMs) can accurately capture the physics of a system with a low number of degrees of freedom; thus, in system identification, a model based on the form of a ROM is potentially more robust. Nonlinear system identification of a structure is presented, where inspiration is taken from a novel ROM to form the model. A finite-element model of the structure is built to simulate an experiment and the identification is performed. It is shown how the ROM-inspired model in the system identification improves the accuracy of the predicted response, in comparison to a standard nonlinear model. As the data is gathered from simulations, system identification is first demonstrated on the high fidelity data, then the fidelity of data is reduced to represent a more realistic experiment. A good response agreement is achieved when using the ROM-inspired model, which accounts for the kinetic energy of unmodelled modes. The estimated parameters of this model are also demonstrated to be more robust and rely on the underlying physics of the system.

In this study, we consider the experimentally obtained, periodically forced response of a nonlinear structure in the presence of process noise. Control-based continuation is used to measure both the stable and unstable periodic solutions, while different levels of noise are injected into the system. Using these data, the robustness of the control-based continuation algorithm and its ability to capture the noise-free system response are assessed by identifying the parameters of an associated Duffing-like model. We demonstrate that control-based continuation extracts system information more robustly, in the presence of a high level of noise, than open-loop parameter sweeps and so is a valuable tool for investigating nonlinear structures.

Internal resonances can be widely observed in nonlinear systems; even a simple nonlinear system can exhibit intricate internal resonances when vibrating at large amplitudes. In this study, the existence and locations of internal resonances of a general two-mode system with an arbitrary eigenfrequency ratio are considered. This is achieved by first considering the symmetric case, where the internal resonances are found to be approximately captured by the Mathieu equation. It is shown that the bifurcations can exist in pairs; and, for each pair, the bifurcated solution branches capture modal interactions with the same commensurate frequency relationship but different phase relationships. To determine the existence and locations of internal resonances, the divergence and convergence for correlated bifurcation pairs are then considered. Lastly, the internal resonances in asymmetric cases are analytically derived, where the asymmetry induced bifurcation splitting is captured by a non-homogeneous extended Mathieu equation. This work explores the mechanism underpinning internal resonances, and explains their topological features, such as which internal resonances are observed as amplitude increases. A graphical method is also proposed for efficient determination of the existence and locations of internal resonances.

Real-Time Hybrid Simulation (RTHS) is an experimental framework that allows the testing of components or substructures under realistic, dynamic boundary conditions, by imposing the reactions calculated from a model of the rest of the assembly through one or more actuators. In the context of rapid prototyping of mechanical components, RTHS could be used to explore the design space of a device while at the same time physically validating its interaction with other components of the final assembly from the early stages of the design-to-production cycle. In this work, RTHS was applied for the first time to the investigation of aerodynamic gust loading alleviation devices in a highly flexible strut-braced wing. The model wing was taken as the physical substructure and tested in a low-speed wind tunnel equipped with gust generators. The load alleviation device was simulated through a real-time feedforward-feedback controller, and its response imposed via an electro-mechanical linear actuator, in contrast with the hydraulic actuators more commonly used in standard RTHS. The controller-actuator subsystem was studied in detail to assess and minimise errors at the physical interface with the wing. The behaviour of the electromechanical subsystem showed a strong dependence on the characteristics of the numerical substructure and the frequency of excitation, and resulted in a significant discrepancy between the simulated and real displacements at the interface between the actuator and the wing. A narrow-band feedforward displacement control scheme based on a model of this subsystem alone was therefore developed and shown to significantly reduce synchronisation errors at the interface.

Oshore wind turbines have the potential to capture the high-quality wind resource. However the signicant wind and wave excitations may result in excessive vibrations and decreased reliability. To reduce vibrations, passive structural control devices, such as the tuned mass damper (TMD), have been used. To further enhance the vibration suppression capability, inerter-based absorbers (IBAs) have been studied using the structure-based approach, i.e. proposing specic stiness-damping-inertance elements layouts for investigation. Such an approach has a critical limitation of being only able to cover specic IBA layouts, leaving numerous benecial congurations not identied. This paper adopts the newly introduced structure-immittance approach, which is able to cover all network lay out possibilities with a predetermined number of elements. Linear monopile and spar-buoy turbine models are rst established for optimisation. Results show that the performance improvements can be up to 6.5% and 7.3% with 4 and 6 elements, respectively, compared to the TMD. Moreover, a complete set of benecial IBA layouts with explicit element types and numbers have been obtained, which is essential for next step real-life applications. In order to verify the eectiveness of the identied absorbers with OpenFAST, an approach has been established to integrate any IBA transfer functions. It has been shown that the performance benets preserve under both the Fatigue Limit State (FLS) and the Ultimate Limit State (ULS). Furthermore, results show that the mass component of the optimum IBAs can be reduced by up to 25.1% (7486kg) to achieve the same performance as the TMD.

This paper considers the effect of geometric nonlinearty on gust load analyses of high aspect ratio commercial aircraft. Three variants of a conceptual aircraft,featuring wing aspect ratios of 10,18 and 26,are sized using an industrially-inspired procedure to obtain realistic structures of existing and future designs. These aircraft are modelled in a nonlinear aeroelastic framework, featuring a geometrically-exact beam formulation coupled with unsteady aerodynamics, and subjected to a gust loads process adapted for nonlinear systems. The gust analysis is also carried out using a linear approach (linearising the equations of motion about an undeformed or trimmed geometry) to understand how nonlinearities influence the loads and dynamic behaviour of aircraft as the aspect ratio increases. Load envelopes show that vertical shear and bending moments are predicted well by the linear analyses, even for the aspect ratio 26 case, providing that the linearisation is performed about the trimmed geometry. In contrast, the in-plane and axial loads are significantly underestimated using linear analyses. Torque behaviour is problem specific,and therefore difficult to generalise. Even on the aspect ratio 10 case,which would traditionally be considered as a linear problem, it can shown that the torque loads are considerably affected by nonlinearity

View Video Presentation: https://doi.org/10.2514/6.2022-1932.vidAlthough quasi-steady aerodynamic modelling is a widely used technique, its shortcomings in representing the stall and post-stall dynamics have been noted in the literature. Various methods to model the unsteady aerodynamics effects have been proposed as a result, but their direct implications on the aircraft’s flight dynamics characteristics have not been widely studied. In this paper, we combine the state-space method for unsteady aerodynamic modelling with bifurcation analysis to examine the sensitivity of stall and post-stall behaviour to the choice of aerodynamic modelling method: quasi-steady or unsteady. It is found that quasi-steady modelling is adequate for the chosen example of a T-tailed transport aircraft that does not undergo rapid manoeuvring. The study is then expanded to investigate a hypothetical situation with highly unsteady aerodynamic characteristics resembling a delta wing configuration – achieved by increasing the time delay constants in the unsteady model. This results in an aircraft with significantly lower flying qualities as indicated by bifurcation analysis. These findings highlight the need to implement unsteady aerodynamic modelling techniques in high-performance aircraft with significant vortex-related unsteady aerodynamics in order to sufficiently capture their stall and post-stall dynamics.

High aspect ratio wings have been the focus of several recent studies for efficiency improvements in modern aircraft. Many numerical studies can be found in literature with some experimental validations. The work presented here describes the design, manufacture, and the ground testing of three wings with a half-span of 0.85 m and full-span aspect ratio of 19 aimed for the future wind tunnel studies of nonlinear geometric effects on static and dynamic behaviour. Comparisons with a numerical model featuring geometric nonlinearity is made. The wing design approach used here is unique in the sense that the wings are designed simultaneously such that each will have a different level of flexibility, with other parameters such as mass distribution remaining constant. These wings will be used in future experiments aimed at investigating the effects of geometric nonlinearity and flexibility on the overall flight dynamics of an aircraft model on a multi-degree-of-freedom manoeuvre rig. The design considerations and interdependent constraints are discussed. The designed wings were manufactured and assembled to identical mass distributions and in good agreement with numerical models in terms of stiffness and frequency response. The design process, challenges, and learned lessons are presented.

The inerter completes the force-current analogy between mechanical and electrical components, providing the mechanical equivalent to the capacitor. As such, it is a two-terminal passive element that, when implemented ideally, is normally said to generate a force proportional to the relative acceleration between its two terminals. However, this is applicable only if the inerter does not rotate, so the only relative motion between the device’s terminals is axial. In many applications, this restriction is acceptable, such as in car suspension systems. However, in this paper, it is shown that the relationship between the terminal accelerations and the generated force is more complex if the inerter is used in a 2-dimensional (2D) or 3-dimensional (3D) environment, such as within a multi-bar mechanism (e.g., robotic arms or railway pantographs). Specifically, the inerter force is not given by simply the relative acceleration between the two terminals. The centripetal acceleration, resulting from the rotation of the inerter, needs to be accounted for to find the second derivative of the inerter length, which defines the generated force. Two case studies are presented to demonstrate the effects of this normally neglected centripetal acceleration term. It is shown that when an inerter is operating in a 2D or 3D environment, significant errors may occur in evaluating the inerter force and also the system response if the centripetal acceleration term is neglected. Equations are provided for both modelling the inerter in different coordinate systems and for incorporating the inerter in 2D and 3D multibody systems.

Performance of a passive vehicle suspension can be improved with the help of an active actuator, however, with potentially problematic control requirements, such as high energy consumption and large actuator forces. To maximize performance benefits without requiring significant control efforts, the passive and active parts need to be designed and work synergistically. In this paper, a novel combined passive and active vibration suppression approach of which the passive part is enhanced by an inerter is proposed for improving the trade-off between dynamic performance and control requirements. Via this approach, the optimal passive configuration consisting of inerter(s), spring(s) and damper(s) with pre-determined numbers and the optimal active control parameter can be identified. The approach is demonstrated using a case study where the combined suspension is designed considering a quarter-car model and a typical active controller (i.e., the skyhook control). It will be shown that, compared with a conventional passive part of a spring-damper, adding an inerter in parallel can significantly improve the pareto optimality between the ride comfort and power (or force) requirements. The improvement is further enhanced by systematically exploring all passive network possibilities with a pre-determined complexity via the structure-immittance technique. This approach is also applicable to the vibration suppression of other engineering structures.

Targeted energy transfer (TET) represents the phenomenon where energy in a primary system is irreversibly transferred to a nonlinear energy sink (NES). This only occurs when the initial energy in the primary system is above a critical level. There is a natural asymmetry in the system due to the desire for the NES to be much smaller than the primary structure it is protecting. This asymmetry is also essential from an energy transfer perspective. To explore how the essential asymmetry is related to TET, this work interprets the realization of TET from a symmetry breaking perspective. This is achieved by introducing a symmetrized model with respect to the generically asymmetric original system. Firstly a classic example, which consists of a linear primary system and a nonlinearizable NES, is studied. The backbone curve topology that is necessary to realize TET is explored and it is demonstrated how this topology evolves from the symmetric case. This example is then extended to a more general case, accounting for nonlinearity in the primary system and linear stiffness in the NES. Exploring the symmetry-breaking effect on the backbone curve topologies, enables the regions in the NES parameter space that lead to TET to be identified.

Model order reduction of geometrically nonlinear dynamic structures is often achieved via a static condensation procedure, whereby high-frequency modes are assumed to be quasi-statically coupled to a small set of lower frequency modes, which form the reduction basis. This approach is mathematically justifiable for structures characterized by slow/fast dynamics, such as thin plates and slender beams, and has been shown to provide highly accurate results. Nevertheless, selecting the reduction basis without a priori knowledge of the full-order dynamics is a challenging task; retaining redundant modes will lead to computationally suboptimal reduced-order models (ROMs), while omitting dynamically significant modes will lead to inaccurate results, and important features such as internal resonances may not be captured. In this study, we demonstrate how the error associated with static condensation can be efficiently approximated during model reduction. This approximate error can then be used as the basis of a method for predicting when dynamic modal interactions will occur, which will guide the reduction basis selection process. Equivalently, this may serve as a tool for verifying the accuracy of ROMs without the need for full-order simulations. The proposed method is demonstrated using a simple oscillator and a finite element model of a clamped–clamped beam.

This paper presents a novel approach to identify inerter-based suspension struts, which can provide significant performance enhancement for passenger vehicles. The inerter has been used on Formula 1 racing cars, and several beneficial devices incorporating inerters have also been identified for ride comfort enhancement. However, previous investigations either were limited to simple network configurations with moderate performance improvement, or resulted in complicated configurations with a large number of elements which are impractical for real-life applications. In addition, some important practical performance constraints have not been taken into consideration, such as high-frequency dynamic stiffness which influences the NVH performance, and frequency content consideration of the sprung mass acceleration which more directly relates to passenger perception. In this paper, a quarter-car model including top mount is studied, with the performance of a conventional suspension strut presented as baseline. The structure-immittance approach, which can cover all networks with pre-determined numbers of each element type, is adopted for the identification of the optimal suspension configurations. Several configurations with up to a 14.7% performance improvement are identified with all other practical performance indices to be no worse than the baseline. The suspension devices proposed in previous works are also considered for a sake of comparison, demonstrating significant advantages of the structure-immittance approach. Subsequently, a sensitivity analysis against the sprung and unsprung mass changes is carried out, which represents cargo and tyre weight variations, respectively. Time domain response and other reality checks are then conducted for the out-performing configurations, which reconfirm the ride comfort enhancement and ensure no unexpected behaviour occurs.

This paper presents a novel method for gust loads alleviation in a truss-braced wing in which an inerter-based device located in the truss-structure is used to reduce peak-loads during a discrete “1-cosine” gust. Three candidate layouts are considered, and the device parameters are optimized to target the response of the first three structural modes. It is demonstrated that either a single damper or a combination of inerter-based devices can be used to achieve a reduction of approximately 4% for spanwise locations inboard of the strut attachment point and that this reduction is consistent across the full range of gust gradients. Furthermore, it is noted that the inerter-based device has a significantly smaller damping coefficient than the case where just a damper is used and that the device parameter values are viable within the scope of an aerospace application.

The use of reduced-order models (ROMs) for nonlinear systems has received significant attention due to their potential to greatly reduce computational cost, compared to full nonlinear finite-element models. Here, we consider and compare two indirect methods; the applied modal force and enforced modal displacement techniques, paying particular attention to the effect of nonlinear cross-coupling terms. The analysis we present shows that the applied modal force technique is able to account for some effects arising from modes that are not retained in the ROMs, but the resulting accuracy of the ROM depends on the amplitudes selected for the set of forces used to estimate the coefficients of the ROMs. This analysis also shows that the enforced modal displacement technique does not compensate for the effect of modal interactions with modes that are not included in the ROM, but its accuracy is independent of the amplitude of the forces used to estimate the coefficients. The mechanisms that lead to the differences between these techniques is firstly demonstrated using a two conceptually-simple, discrete systems, before a nonlinear beam model is considered.

Improving the track friendliness of a railway vehicle can make a significant contribution to improving the overall cost effectiveness of the rail industry. Rail surface damage in curves can be reduced by using vehicles with a lower Primary Yaw Stiffness (PYS); however, a lower PYS can reduce high-speed stability and have a negative impact on ride comfort. Previous studies have shown that this trade-off between track friendliness and passenger comfort can be successfully combated by using an inerter in the primary suspension; however, these previous studies used simplified vehicle models, contact models, and track inputs. Considering a realistic four-axle passenger vehicle model, this paper investigates the extent to which the vehicle's PYS can be reduced with inertance-integrated primary lateral suspensions without increasing Root Mean Square (RMS) lateral accelerations when running over a 5km example track. The vehicle model, with inertance-integrated primary lateral suspensions, has been created in VAMPIRE, and the vehicle dynamics are captured over a range of vehicle velocities and wheel-rail equivalent conicities. Based on systematic optimisations using network-synthesis theory, several beneficial inertance-integrated configurations are identified. It is found that with such beneficial configurations, the PYS can be reduced by up to 47% compared to a base case vehicle, without increasing lateral RMS accelerations. This could result in a potential Network Rail Variable Usage Charge saving of 26%. With the beneficial inertance-integrated suspensions, further simulations are carried out to investigate the vehicle's performance in curve transitions and when subject to one-off peak lateral track irregularities.

This paper investigates the potential for improving the performance of hydraulic engine mounts through fluid passageway designs. In previous studies, a few simple inertia track designs have been investigated with moderate improvements obtained. However, there are countless alternative design possibilities existing; while analyzing each one of them in turn is impracticable. To this end, this paper introduces a systematic methodology to optimize fluid passageway designs in a hydraulic engine mount. First, beneficial fluid passageway configurations are systematically identified using a linearized low-frequency model that captures the relative displacement transmissibility. A nonlinear model is then used to fine-tune the fluid passageway designs for the low-frequency transmissibility improvement, and also for the assessment of high-frequency dynamic stiffness performance. The obtained beneficial designs present performance advantages over a wide frequency range. The design approach introduced in this study is directly applicable to other engine mount models and performance criteria.

Control-based continuation (CBC) is a general and systematic method to probe the dynamics of nonlinear experiments. In this paper, CBC is combined with a novel continuation algorithm that is robust to experimental noise and enables the tracking of geometric features of the response surface such as folds. The method uses Gaussian process regression to create a local model of the response surface on which standard numerical continuation algorithms can be applied. The local model evolves as continuation explores the experimental parameter space, exploiting previously captured data to actively select the next data points to collect such that they maximise the potential information gain about the feature of interest. The method is demonstrated experimentally on a nonlinear structure featuring harmonically-coupled modes. Fold points present in the response surface of the system are followed and reveal the presence of an isola, i.e. a branch of periodic responses detached from the main resonance peak., Comment: 22 pages, 12 figures

In this paper, a nonlinear dynamic landing gear model considering the influence of the coupling of the shock absorber stroke variation and the landing gear longitudinal motion with an anti-skid PID braking control system that captures gear walk is established. This gear walk model is verified by comparing with the response from a virtual prototype model. Then a parameter sensitivity analysis is carried out to find out the parameters with greater effects on gear walk and braking performance. The short time Fourier transform is employed to study the transient gear walk amplitude-frequency response, whose results are used to define the optimization constraints. A feedforward controller is proposed as part of the braking control law. Single-objective optimizations are then carried out to improve the gear walk performance while maintaining the braking efficiency. It is shown that the feedforward control, together with the PID feedback controller, can provide 25.68% reduction of the maximum gear walk angle while satisfying other constraints. The stability and robustness of the optimized braking law is verified under different working conditions. Multi-objective optimization is then used to highlight the trade-off between the gear walk vibration and the braking efficiency.

Experimental studies into aircraft stability and performance can be enhanced by using a rig in which the aircraft model support approximates free flight within a wind tunnel. Such multi-degree-of-freedom wind tunnel rigs often impose kinematic restrictions on the aircraft model's translational motion. This study investigates these kinematic effects, with particular attention to a spherical constraint where the aircraft is held at the end of afixed length pivoting arm. Here the motions of the aircraft and kinematic constraints are derived as differential-algebraic equations and assessed numerically. The impact is found mainly on translational motion with negligible effect on the aircraft's rotation. A concept to reduce these kinematic effects on the aircraft's motion by applying an external force onto the aircraft is proposed. This compensation, which partially accounts for the constraints on the aircraft motion, is shown to reduce the effects of the arm, allowing for improved physical simulation.

The high incidence aerodynamics of a lightweight jet trainer aircraft model has been investigated using a novel five degree-of-freedom (DoF) dynamic manoeuvre rig, recently updated with improved actuation and data acquisition systems, in the 7' x 5' closed-section low-speed wind tunnel at the University of Bristol. The major focus was to identify the nonlinear and unsteady aerodynamic characteristics specific to the stall region and which affect free-to-move aircraft model behaviour. First, the unstable equilibrium states in the limit cycle regions were stabilized, and so observed, over a wide range of angles of attack using a simple elevator feedback control law based on pitch angle and pitch-rate sensor measurements.Tests with two degrees-of-freedom, namely the aircraft model and rig arm pitch angles, revealed the existence of static hysteresis in the normal force acting on the aircraft model in the stall region. Unlocking the aircraft model in roll and yaw accompanied by feedback stabilization of the lateral-directional modes of motion demonstrated onset of asymmetric aerodynamic rolling and yawing moments in this four degree-of-freedom configuration. This observation implicitly indicates a link between the static hysteresis in the normal aerodynamic force with an onset of aerodynamic asymmetry. The experimental results show the efficiency of the updated multi-degree-of-freedom actively controlled manoeuvre rig in providing insight into complicated aerodynamic effects within the stall region.

This article presents a detailed study of the robust control of a cable’s vibrations, with emphasis on considering a model of infinite dimension. Indeed, using a partial differential equation model of the vibrations of an inclined cable with sag, we are interested in studying the application of $\mathcal H_{\infty }$ -robust feedback control to this infinite dimensional system. The approach relies on Riccati equations to stabilize the system under measurement feedback when it is subjected to external disturbances. Henceforth, this article focuses on the construction of a standard linear infinite dimensional state space description of the cable under consideration before writing its approximation of finite dimension and studying the $\mathcal H_{\infty }$ feedback control of vibrations with partial observation of the state in both cases. The closed-loop system is numerically simulated to illustrate the effectiveness of the resulting control law.

It is well known that a linear-based controller is only valid near the point from which the linearised system is obtained. The question remains as to how far one can move away from that point before the linear and nonlinear responses differ significantly, resulting in the controller failing to achieve the desired performance. In this paper, we propose a method to quantify these differences. By appending a harmonic oscillator to the equations of motion, the frequency responses at different operating points of a nonlinear system can be generated using numerical continuation. In the presence of strong nonlinearities, subtle differences exist between the linear and nonlinear frequency responses, and these variations are also reflected in the step responses. A systematic way of comparing the discrepancies between the linear and the nonlinear frequency responses is presented, which can determine whether the controller performs as predicted by linear-based design. We demonstrate the method on a simple fixed-gain Duffing system and a gain-scheduled reduced-order aircraft model with a manoeuvre-demand controller; the latter presents a case where strong nonlinearities exist in the form of multiple attractors. The analysis is then expanded to include actuator rate saturation, which creates a limit-cycle isola, coexisting multiple solutions (corresponding to the so-called flying qualities cliff), and chaotic motions. The proposed method can infer the influence of these additional attractors even when there is no systematic way to detect them. Finally, when severe rate saturation is present, reducing the controller gains can mitigate—but not eliminate—the risk of limit-cycle oscillation.

[No Abstract]

For modern electrical rail systems, the pantograph-catenary dynamic performance is one of the most critical challenges. Too much fluctuation in contact forces leads to either accelerated wear of the contacting components or losses of contact and, consequently, arcing. In this work, inertance-integrated pantograph damping systems are investigated with the objective of reducing the contact force standard deviation. Firstly, a multibody pantograph model is developed with its accuracy compared with experimental data. The model is improved through the calibration of the pantograph head suspension parameters and the introduction of both non-ideal joint and flexibility effects. Using the calibrated model, beneficial inertance-integrated damping systems are identified for the pantograph suspension. The results show that the configuration with one inerter provides the best performance among other candidate layouts and contends a 40% reduction of the maximum standard deviation of the contact force over the whole operating speed range in the numerical modelling scenario analysed. Considering the identified configuration, time-domain analysis and modal analysis are investigated. It has been shown that the achieved improvement is due to the fact that with the beneficial inertance-integrated damping system, the first resonance frequency of the pantograph system coincides with the natural frequency of the catenary system.

Current methods of assessing flying qualities are based on linear system theory, which cannot capture the nonlinear phenomena commonly found at high angles of attack. Although bifurcation analysis has been proven to be a powerful tool for numerically analyzing nonlinear flight dynamics, in its standard (unforced) form, the method is unsuitable for flying qualities assessment as no information on the transient response is provided. To address this shortcoming, we propose the use of an extension of bifurcation analysis that treats the aircraft as a harmonically forced system. This facilitates the evaluation of the frequency-domain dynamics where the response is unsteady by definition. It is shown that the method can identify regions with strong nonlinearities that lead to degraded flying qualities. Time simulations of the closed-loop step responses in these undesirable regions show that despite the predictions of desirable behaviors using linear analysis, the closed-loop aircraft can still be attracted to an isola, experience control reversal, or have higher overshoot than anticipated.

This paper presents an investigation into the mathematical modelling of the dynamics of a generic candidate inceptor mechanism when system linkage flexibilities are represented. The lumped parameter approach for modelling the flexibility is proposed and applied within the multi-body dynamic modelling framework formulated by Udwadia-Kalaba to explore system resonances. A low-order multi-body mathematical model of an inceptor system is derived and frequency response characteristics numerically obtained. Through a parametric design study, results show how resonance frequencies can be tuned to meet specified levels by identifying and recommending modifications in system design configurations at early design stages. The work presented in this paper provides a framework to identify acceptable design configurations of a system and offers parametric design insights within a multi-body dynamic environment.

This paper presents a methodology for systematically studying the nonlinear frequency responses of an aircraft model using numerical continuation with periodic forcing, thereby presenting an extension of conventional bifurcation analysis in flight dynamics applications. The motivation is to identify nonlinear phenomena in the frequency domain that are absent in linearized models - upon which many control law designs are based - and which therefore risks degrading the performance or robustness of the linear-model based controllers. Since the aerospace industry typically uses linearizations in controller design, both open and closed loop behaviors are considered. When the example aircraft considered here is forced with small control surface deflections, highly nonlinear responses are observed. This includes period doubling bifurcations, fold bifurcations leading to existence of multiple solutions, quasi periodic motions, and formation of isolas. Closed-loop responses of a proportional stability augmentation controller for this aircraft become out of phase with the linear prediction at low forcing frequencies when the aircraft operates at high angle of attack. To address these behaviors, the methodology is extended by employing two-parameter continuation of the controller gain to assess its effectiveness in those nonlinear regions, where linear controller design techniques cannot be used. Time histories are used to verify the results.

Nonlinear dynamic analysis of complex engineering structures modelled using commercial finite element (FE) software is computationally expensive. Indirect reduced-order modelling strategies alleviate this cost by constructing low-dimensional models using a static solution dataset from the FE model. The applicability of such methods is typically limited to structures in which (a) the main source of nonlinearity is the quasi-static coupling between transverse and in-plane modes (i.e. membrane stretching); and (b) the amount of in-plane displacement is limited. We show that the second requirement arises from the fact that, in existing methods, in-plane kinetic energy is assumed to be negligible. For structures such as thin plates and slender beams with fixed/pinned boundary conditions, this is often reasonable, but in structures with free boundary conditions (e.g. cantilever beams), this assumption is violated. Here, we exploit the concept of nonlinear manifolds to show how the in-plane kinetic energy can be accounted for in the reduced dynamics, without requiring any additional information from the FE model. This new insight enables indirect reduction methods to be applied to a far wider range of structures while maintaining accuracy to higher deflection amplitudes. The accuracy of the proposed method is validated using an FE model of a cantilever beam.

This paper has a twofold aim: to assess the performance of tuned-inerter dampers (TIDs) to reduce vibrations in cable structures subjected to seismic ground motions; and to extend an existing TID-design method for cables to a practical scenario of multiple cables in a cable-stayed bridge. In this study, TIDs are installed between the cables and the bridge’s deck, the cables being excited at both their ends by the response of the bridge’s deck and pylon to seismic ground motions. The seismic hazard is described in a general manner by rates of earthquakes and synthetic ground-motion time histories with respect to their moment magnitudes and epicentral distances. Two approaches that use an existing deterministic method to design TIDs to reduce vibrations in cables are discussed. The first one, perhaps more effective but impractical, assumes that each cable’s response is reduced by its own independently-designed TID. The second approach, more realistic and practical, proposes the design of one single TID for all cables to reduce their mid-span response in an optimal way. Numerical results are shown for cable models in the Evripos Bridge in Greece, for which a unique TID is designed for all cables in the bridge, subjected to a hypothetical seismic-hazard scenario. It is shown that the TID-controlled cables have generally a better response, that is a lower average maximum absolute mid-span displacement for most of the cables, and lower variability in the response.

The experimental characterisation of a nonlinear structure is a challenging process, particularly for multiple degree of freedom and continuous structures. Despite attracting much attention from academia, there is much work needed to create processes that can achieve characterisation in timescales suitable for industry, and a key to this is the design of the testing procedure itself. This work proposes a passive testing method that seeks a desired degree of resonance between forcing and response. In this manner, the process automatically seeks data that reveals greater detail of the underlying nonlinear normal modes than a traditional stepped sine method. Furthermore, the method can target multiple harmonics of the fundamental forcing frequency, and is therefore suitable for structures with complex modal interactions. The method is presented with some experimental examples, using a structure with a 3:1 internal resonance.