This paper investigates the possibility of developing a novel vibration absorber aimed towards slender continuous structures such as wings or blades. The absorber essentially consists an axially elastic tendon guided along a series of points along the span of cantilevered laboratory beam demonstrator, such that an aggregate of its induced extensional activity is observed at a specific location. The central idea is to introduce a discrete absorber at this strategically selected point, with the tendon providing the stiffness between the absorber and the primary structure. To explore the concept, the presented experiment is aimed at providing a comparison against a reduced 2 degree of freedom representation of the combined and mutually coupled absorber system. The specific focus of this arrangement is to support the interpretation of the underlying modal characteristics of the proposed concept.

Abstract Whirl flutter is an aeroelastic instability that affects aircraft with propellers/rotors. With their long and flexible rotor blades, tiltrotor aircraft are particularly susceptible. Whirl flutter is known to have destroyed aircraft and in the best case it constitutes a fatigue hazard. The complexity of whirl flutter analysis increases significantly with the addition of nonlinearities, due to the more complex dynamical behaviours that emerge as a result. Most whirl flutter stability analyses in current literature are grounded in linear theory, preventing the full discovery of the nonlinearities’ effects. Continuation and bifurcation methods (CBM) may instead be used to fully appreciate and analyse the effects of the presence of nonlinearities. Previous CBM-based work on nonlinear gimballed hub rotor-nacelle models, representing those found on tiltrotor aircraft, are capable of whirl flutter in parametric regions declared safe by linear analysis. Furthermore, it was found that they are capable of complex behaviours including limit cycle oscillations, quasi-periodic behaviour and even chaos, though the whirl flutter implications of such behaviours has not been explored. This paper investigates the impact of a smooth structural nonlinearity on the whirl flutter stability of a basic gimballed rotor-nacelle model, compared to its baseline linear stiffness version. A 9-DoF model with quasi-steady aerodynamics, a flexible wing and blades that can move both cyclically and collectively in both flapping and lead-lag motions, producing gimbal flap-like behaviour, was adopted from existing literature. A smooth stiffness nonlinearity was introduced in the blade flapping stiffness and CBM was used to find the new whirl flutter behaviours created by the presence of the nonlinearity. Time simulations, Poincaré sections and spectral analysis were then used to investigate the various behaviours found. This in turn allowed recommendations to be made concerning preferable and/or hazardous parameter combinations of use to the tiltrotor designer.

Damping induced by vertically sloshing liquids at large amplitudes is of interest in the understanding of the dynamic response of aircraft wings containing fuel. This work presents the experimental investigation of sloshing-induced damping in two small rectangular tanks (L=100mm, h=37.5mm and 50mm) under vertical excitation at various frequencies (3.3 to 10.3Hz) and amplitudes (up to 1.57 tank heights). The focus is placed on large amplitudes that lead to violent vertical interactions between the liquid and the tank and the nonlinear damping effects they cause. The sloshing-induced dissipative energy in dimensional form shows a deviation from linearity with increasing amplitude of excitation, which is attributed to force–displacement hysteresis sub-cycle formations. When increasing the frequency of excitation, it is shown that the damping increases initially, and then remains constant. These findings are confirmed by a kinematics-based ballistic–harmonic model. Optical flow and a new technique based on pixel intensity standard deviation are employed in correlation with an analysis of the hysteresis cycles in order to offer insight into the sloshing force variation within one liquid cycle of oscillation.

Fuel sloshing-induced damping is currently being studied extensively within the EU-funded SLOWD project as a means of passively reducing dynamic loads in aircraft wings. It is of interest to be able to determine which parameters have the greatest influence on the added damping from the sloshing motion. An uncertainty in the measured sloshing force has been observed when multiple consecutive and identical oscillation cycles are considered in sinusoidal excitation experiments, leading to variations in the measured energy dissipation. This current work considers liquid undergoing vertical sloshing motions for different fill level and excitation conditions (frequency and amplitude) leading to energy dissipation via several possible physical mechanisms. The sloshing dissipation is measured experimentally across a large number of excitation cycles and for each excitation amplitude, expressed in the form of Froude (Fr) numbers. Depending on the Fr number, distinct sloshing mechanisms dominate the dissipative effects and induce a particular variance across the identical cycles analysed. The sloshing-induced energy dissipation variation is quantified and correlated with different mechanisms depending on Fr number, helping to explain various non-stationary effects that are observed even in well-controlled experimental conditions. As well as improving the insights into the inherent dispersion nature of the studied phenomena, this research also establishes experimental characteristics suitable for future model validation and calibration.

All aircraft are subject to a range of loading throughout ground and flight operations, which ultimately define the sizing and weight of the aircraft structure. Active and passive loads alleviation technologies provide an approach to reduce dynamic loads arising from atmospheric gusts and turbulence, leading to more fuel-efficient aircraft designs. Within the H2020 SLOWD project, fuel sloshing is being considered as a method for alleviating loads in aircraft wings via an increase in effective damping. Recent work has considered the transient response of a vertically vibrating, single degree of freedom system coupled to a rectangular liquid-filled tank. This research revealed identifiable dissipation regions in the free vibration responses characterised by their own distinct equivalent damping ratio values. In this work, free surface displacement has been extracted from high-speed camera footage during the chosen sloshing regimes, which are representative of a decaying parametrically excited fluid. These results are compared against a fluid-structure coupled numerical model based upon smoothed particle hydrodynamics, previously shown to have good agreement with the experimental damping response. Further analysis of the free-surface response of the numerical solution notes a presence of an undesired travelling longitudinal wave. The analysis of this discrepancy between the model and experiment is then used to improve the numerical formulation, showing a requirement for modelling surface tension.

The effect of the sloshing motion of liquid in a tank on the vertical transient motion of a single degree of freedom system is investigated. Step release tests of a vertically vibrating structure, including a tank containing liquid, demonstrate that added damping from the sloshing motion depends upon the amount of fluid in the tank and the maximum acceler-ation. The maximum amount of damping was observed at a 50% fill level and the system showed three distinct response regimes during the transient decay, all related to different motions of the fluid. The first response regime, immediately at the start of the transient, is considered to be the most important to exploit for aircraft gust loads alleviation due to its dominant role in the overall energy dissipation balance. Further, to advance the under-standing of the modelling and predictive capabilities, coupled fluid-structure models of two opposing levels of fidelity were developed and evaluated. Namely, smoothed particle hydrodynamics (SPH) and an equivalent mechanical model (EMM) based on a bouncing ball model were considered to represent the fluid motion in the tank during the experi-ment. Both models are shown to provide good predictive capability in the initial impacting sloshing mode while the subsequent flow regime can be predicted with the SPH model only. The findings in this paper open routes towards improved coupled fluid-structure models and their use in improved aeroelastic wing design. (c) 2020 Elsevier Ltd. All rights reserved.

Free vibration and stability analysis of the system consisting of the Euler-Bernoulli beam axially loaded by a tendon is studied in the paper. The tendon is attached to the cantilever beam at the tip as well as in several spanwise locations using mechanical attachment points. This novel beam-tendon system is modelled using a set of partial differential equations and the coupling between the beam and the tendon is ensured by the boundary and continuity conditions. Computational free vibration analysis is conducted using a boundary value problem solver and the results are thoroughly experimentally validated using a bench-top experiment. In particular, the effect of the number of the attachment points and their location on the frequency-loading diagram of the beam-tendon system is investigated for the first time. It is found that the applied axial load causes a frequency shift of beam-dominated natural frequencies, and frequency loci veering between beam dominated and tendon-dominated modes. Both of these features are shown to be dependent on a number and location of the attachment points. In addition, the effect of the attachment points on the structural stability of the system is numerically studied and it is observed that the critical force of the system with the intermittently attached tendon is always higher than for the system with no attachment points. (c) 2021 Elsevier Ltd. All rights reserved.

An advanced rotor and propeller rig for tip Mach-scaled wind tunnel testing is the subject of dynamic analysis presented in this paper. Experimental modal analysis and finite element method are used to assess the key characteristics such as the modal properties and transfer functions, as well as their changes under varying conditions. This work aims to determine and summarize these characteristics for the purposes of further rig development and its safe operation. The research also includes analysis of the key sources of uncertainty, damping, the effect of unbalanced excitation and model-experiment correlation. The low frequency region is found to be dominated by the three weakly damped global modes whilst the following modes feature increased modal activity of the rotor shaft and the hub. The latter set of modes is also found to be more susceptible to nonlinear effects and associated increased identification and modelling uncertainty.

An investigation was performed to measure sloshing motion and damping during harmonic forced vertical motion of a rectangular tank containing fluid, with a particular focus on the amplitude dependent transition between lateral sloshing and turbulent, vertical slamming. Qualitative and quantitative explanations are provided for the damping saturation point and dissipation effects, together with metrics to distinguish the different sloshing regimes, and a ballistic-harmonic analytical model is presented capable of reproducing the physical trends. Image processing tools were used to analyse experimental high-speed video footage, illustrating potential routes to increased damping in vertically oscillating structures, and correlating well with measured fluid forces and flow regimes.

This paper presents the development of a small-scale unpowered experimental test rig with a bladed rotor along with its dynamic model. The novel attributes of this work are: (1) the use of a compact portable vertical wind tunnel and with the pendulum-like accelerometer-instrumented rotor rig, (2) assessment of the in-operation vibrations and whirling dynamics for future use in the large scale experiments, and (3) analysis of the rig-specific rotor dynamics phenomena. This work experimentally and numerically studies the proposed rotor rig with the main emphasis on its modal characteristics. Owing to its design characteristics, it is shown analytically and experimentally, that the rig features four dominant lateral backward and forward whirling vibration modes in relatively wide frequency range during its windmilling operation. Consequently, it is determined that the rotor rig represents a useful simplified low order system suitable for studies of a range or dynamic phenomena such as transient resonance crossing, whirl flutter and geometric nonlinearity effects.

In the paper, an experimental method based on the Operational Modal Analysis (OMA) approach will be developed for the estimate of the damping properties of a sloshing system. The considered system will mimic a wing-like structure carrying fluid simulating the sloshing typically occurring in a flying wing. The experimental investigation will take advantage of the environmental testing facility available at the Department of Mechanical and Aerospace Engineering of the University of Rome "La Sapienza". The sensitivity of the damping estimates to the type, direction, and level of excitation as well as to the different filling levels will be studied and compared with similar results already achieved by the Department of Aerospace Engineering of the University of Bristol. The presented results, will serve the SLOshing Wing Dynamics (SLOWD) European funded project for the accuracy assessment.

All aircraft are subjected to dynamics loads resulting from in-flight atmospheric gusts and turbulence, with the resulting stresses determining the sizing, and hence weight, of the resulting structure. There is much interest in studying active and passive approaches to alleviate these loads, leading to more fuel-efficient and environmentally friendly airplane designs. Recent work, as part of the H2020 SLOW-D project, has considered the use of fuel sloshing as a means of loads reduction, with fundamental transient response experiments, performed using a single degree of freedom system coupled to a liquid filled tank, demonstrating a multi-regime piecewise linear damping behaviour dependent on the amount of tank fill and the size of the excitation. This work continues the effort to improve the development of coupled fluid-structure sloshing models through investigation of the 2nd and 3rd transient response regions. Experimental measurements based on high frame-rate videos of the fluid surface motion and the tank vibration are used to further develop coupled structure / sloshing fluid computational models based on an SPH approach. A good comparison between the numerical model and the experimental measurements is found.

Theoretical and experimental modal analysis of the system consisting of the Euler-Bernoulli beam axially loaded by a tendon is studied in the paper. The beam-tendon system is modelled using a set of partial differential equations derived by Hamilton's principle and the coupling between the beam and the tendon is ensured by the boundary conditions. Theoretical modal analysis is conducted using a boundary value problem solver and the results are thoroughly experimentally validated using a bench-top experiment. In particular, the effect of the tendon tension on the modal properties of the system is studied. It is found that by increasing the tension, the natural frequencies of the beam decrease while the natural frequencies of the tendon increase. It is also shown that these two sets of modes interact with each other through frequency loci veering. The effect of the tendon mass is also experimentally and numerically studied and it is shown that lighter tendon produces fewer vibration modes in the studied frequency region. Two further numerical studies are conducted to demonstrate the effect of the tendon on the torsional modes of the beam, and to study the structural stability. Overall, an excellent agreement between the numerical and experimental results is obtained, giving the confidence in the derived theoretical model. (C) 2019 Elsevier Ltd. All rights reserved.

The main objective of this paper is to investigate free vibration of a rotating pre-twisted beam with bending-bending-torsion coupling that is axially loaded by a tendon. The tendon is connected to the tip of the beam, passes through its body, and is fixed and loaded at the axis of rotation. Due to their connection, the motion of the beam influences the motion of the tendon and vice versa. The equations of motion of the beam-tendon system are introduced and solved numerically by a combination of a boundary value problem solver and differential quadrature method to obtain the natural frequencies and mode shapes of the system. The numerical implementation is firstly validated against literature for a non-rotating beam-tendon system and a rotating pre-twisted blade. Then, the effect of the tendon on the free vibration of the system is studied for a wide range of loading cases and rotation speeds. From the computed modal characteristics, it is found that the presence of a tendon leads to the frequency shift of beam's natural frequencies as well as frequency loci veering between the beam-dominated and tendon-dominated modes. Both of these effects strongly depend on the beam-tendon rotation speed.

This paper presents a numerical and experimental study of coupled bending-torsion vibration of a beam loaded by a tendon-induced axial force. The rotating beam-tendon system is described using a set of partial differential equations and free vibration analysis is performed. The model is validated against a benchtop experiment which features a reinforced open-section cantilever beam subjected to tendon loading. A satisfactory agreement between the numerical and experimental results is obtained and it is shown that the tendon not only reduces the natural frequencies of the beam, but also introduces frequency loci veering. The validated model is then used to perform a case study on the Bo105 helicopter to present some benefits of incorporating a tendon in a rotorcraft blade, making a first step towards an active tendon concept. This concept should eventually allow rotorcraft to operate with a variable rotor speed, thereby increasing their performance and efficiency.

This work presents an experimental investigation into the dynamic behavior of a bolted joint beam configuration. The impact hammer is chosen as an alternative to classical harmonic excitation methods. The structural responses are explored for a range of the joint tightening toques and various levels of impulse hammer excitations. A symmetric beam assembly made of two nominally identical steel beams is studied. Symmetric modes are found to be sensitive to the test parameters. For given torque, impact-based varying joint loading conditions are used to induce the nonlinear joint effects. A linear data processing strategy is used to observe the nonlinear behavior indirectly. The dynamic joint behavior is described in the form of the modal frequency-damping ratio performance maps represented by the two-parametric approximating quadratic response surface models. This model maps the joint conditions on the corresponding dynamic characteristics of interest and it will serve as a basis for the parametric linear joint model development.

There are many benefits of variable speed rotors if the associated dynamics problems can be alleviated. Existing passive and active methods are unsuitable due to their mass/power requirements and effectiveness over the necessary frequency range. The concept of inducing controlled 'stress softening' to alter the natural frequencies of a rotating structure in a vacuum and in turn avoid resonance is explored in this research. This paper presents an experimental and computational demonstration of this concept in the context of a small scale rotor blade representation. The model is successfully validated away from and within regions of coupling in which veering was present, and was therefore used to assess the effectiveness of the concept on full sized rotorcraft blades. Full scale assessment demonstrated that adequate separation can be achieved without requiring excessively large forces. The aim of the research is to create a semi-active method for the alteration of the blade's resonant frequencies to avoid resonance within a range of rotor speeds.

This research explores possibility of improved liquid damper identification based on the systematic use of the triangular piston displacement inputs. Both static and dynamic damper characteristics are studied to ensure complete problem characterization. Static characteristics are associated with resistive hydraulic features. Dynamic or transient characteristics are primarily associated with mechanical and liquid elasticity in dampers. Measured and simulated damper responses induced by the triangular inputs are studied in order to understand transient damper behaviour. This research looks at the use of the initial transient responses acquired during triangular excitation tests for model and parameter identification. A previously developed single-state dynamic model of the symmetric damper is refined and used in these studies. Measured data acquired from the industrially deployed helicopter damper are used to evaluate the proposed model and its ability to predict transient responses. This study indicates that a more detailed non-constant compressibility model can be successfully applied in single-state damper models.

The use of modal response residuals and parameterized models forms the framework for parameter subset selection based damage detection. This research explores the novel approach in this class of methods which is characterized by the successive application of the homogeneous modal response residuals. The motivation behind this approach is to restrict the use of unknown weighting factors which are employed in cases with mixed response residuals. Particular attention is given to the parameter-effect symmetry issues and large nonlinear changes in response residuals due to increasing damage observed across multiple damage levels. A case study involving a real aluminum three-dimensional frame structure with a loose joint connection is used to demonstrate the approach and its ability to localize the damaged area.

A three storey aluminium frame structure was tested in multiple damage cases. All damage scenarios, simulated by the localized stiffness changes, were associated with joint areas of the structure. Further, between damage tests the structure was returned to its healthy reference conditions and was again measured. In this paper, a parameter subset selection methodology is applied to an updated finite element model of the structure, together with a previously demonstrated approach employing concepts of model sensitivity subspace angles, first order model representation and mixed response residuals for damage detection. The objective of this paper is the evaluation of these methods on a real experimental structure with significant complexity, represented by an imprecise reference mathematical model and in the environment with uncertain reference structural state. The questions of symmetry, mixed response residuals and semi-localized parameterization are also addressed in this work.