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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.

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.

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.

As a two-terminal mechanical element, the inerter has been successfully deployed in various mechanical systems, such as automotives, multi-story buildings, and motorcycles. The introduction of the inerter allows the use of network synthesis to design a passive mechanical network, and can potentially facilitate the identification of practical and high performance mechatronic vibration absorbers. This paper provides an approach for optimal design of both the mechanical and the electrical parts for an inerter-based mechatronic device in vehicle suspension. The system considered includes a mechanical ball-screw inerter alongside an electric motor that is not driven but instead used passively with an electrical load applied across the terminals. The trade-offs in designing the ball-screw inerter and the permanent magnet electric machinery is discussed in detail. Two factors, namely, the coil resistance and the inductor resistance, are taken into account in the performance evaluation. Results show that the improvements in the road holding performance can reach 9.24% for the ideal suspension system with no diverse effect on the ride comfort and suspension travel performance, while a 5.77% improvement can be obtained when the effects of the coil resistance and the inductor are included.

This paper considers several passive shimmy-suppression devices for a dual-wheel main landing gear (MLG) and proposes a method of selecting the device parameter values for which no shimmy occurs. Two of these devices include an inerter, a novel mechanical element with the property that the applied force is proportional to the relative acceleration between its terminals. A nonlinear mathematical model is developed to represent the MLG dynamics. A bifurcation study is then carried out to investigate the effects of the shimmy-suppression devices on the gear steady-state response. The aircraft forward speed and the device damping are chosen as the continuation parameters. A range of device parameter values that ensure the aircraft is free from shimmy instability for any forward speed within its operating region are identified. It is shown that the use of a proposed spring-damper configuration can result in a more robust device in terms of the device damping over that of a conventional shimmy damper. Two inerter-based shimmy-suppression devices are then considered and yield further benefits on expanding the zero-shimmy regions in the two-parameter bifurcation diagrams.

This paper presents a case study in which the finite element model for a curved circular plate is calibrated to reproduce both the linear and nonlinear dynamic response measured from two nominally identical samples. The linear dynamic response is described with the linear natural frequencies and mode shapes identified with a roving hammer test. Due to the uncertainty in the stiffness characteristics from the manufactured perforations, the linear natural frequencies are used to update the effective modulus of elasticity of the full order finite element model (FEM). The nonlinear dynamic response is described with nonlinear normal modes (NNMs) measured using force appropriation and high speed 3D digital image correlation (3D-DIC). The measured NNMs are used to update the boundary conditions of the full order FEM through comparison with NNMs calculated from a nonlinear reduced order model (NLROM). This comparison revealed that the nonlinear behavior could not be captured without accounting for the small curvature of the plate from manufacturing as confirmed in literature. So, 3D-DIC was also used to identify the initial static curvature of each plate and the resulting curvature was included in the full order FEM. The updated models are then used to understand how the stress distribution changes at large response amplitudes providing a possible explanation of failures observed during testing.

This paper presents the possibility of using inerter-based shock strut in a landing gear to improve aircraft touch-down performance. The inerter is a mechanical element with the property that the applied force is proportional to the relative acceleration between its terminals. The baseline performance of a traditional oleo-pneumatic shock strut is established using a simplified landing gear touch-down model. Several simple layouts and general transfer functions are used to represent the shock struts and time-domain optimisations are carried out to minimise the maximum strut load transmitted to the fuselage during touch-down. The performance benefits of several inerter-based shock strut configurations with the corresponding parameter values have been identified.

This work presents a conceptually simple experiment consisting of a cantilever beam with a nonlinear spring at the tip. The configuration allows manipulation of the relative spacing between the modal frequencies of the underlying linear structure, and this permits the deliberate introduction of internal resonance. A 3:1 resonance is studied in detail; the response around the first mode shows a classic stiffening response, with the addition of more complex dynamic behaviour and an isola region. Quasiperiodic responses are also observed but in this work the focus remains on periodic responses. Predictions using Normal Form analysis and continuation methods show good agreement with experimental observations. The experiment provides valuable insight into frequency responses of nonlinear modal structures, and the implications of nonlinearity for vibration tests.

There is an increasing desire in the railway industry to improve the longevity of wheels and rails without reducing performance in other ways (e.g. worsening passenger comfort). One way of reducing track and wheel wear is to reduce the primary yaw stiffness, significantly diminishing the costs associated with maintenance and emergency repairs, resulting however in reduced passenger comfort and high-speed stability. This paper, using a two-axle railway vehicle case study, demonstrates the potential of using passive, inerter-based suspensions to concurrently improve ride comfort and reduce track wear. The industrial parameter T Gamma is used to quantify the frictional energy lost at the contact patch under curving conditions, and the lateral RMS carbody acceleration is used to quantify passenger comfort under straight running conditions, with lateral track disturbances taken from real track data. Optimisation results conclude that, with the default yaw stiffness value, compared with the default spring- damper configuration in the primary lateral suspension, employing beneficial inerter-based configurations can improve passenger comfort by up to 43%. If the yaw stiffness is reduced such that the track wear is improved, similar improvements in passenger comfort can still be achieved with lateral inerter-based suspensions; for example, an improvement of 33% can still be achieved with a 50% reduction in yaw stiffness. Furthermore, when an inerter-based lateral suspension is used together with a Hall-Bush longitudinal suspension, the passenger comfort rises to 40%, which relates to a 25% improvement when compared with a non-inerter lateral plus Hall-Bush longitudinal setup.

Pilots may experience vibrations in the cockpit during ground maneuvers because of energy being transferred from the nose landing gear to the fuselage. This indicates that the fuselage dynamics could also have an effect on the dynamics of the gear. To study this interaction, a mathematical model of a nose landing gear coupled to a fuselage model with yaw and pitch degrees of freedom is developed. Results obtained by bifurcation analysis show the nature of the interaction between the two systems; in particular, the two-degree-of-freedom fuselage does affect the onset and subsequent severity of nose landing gear shimmy.

Time delays arise in most feedback systems and have specific relevance for remotely piloted vehicles with ground-based pilots and controllers. NASA’s test facility for flight dynamics and control research using subscale vehicles, the Airborne Subscale Transport Aircraft Research facility, has developed the remotely piloted generic transport model. Analysis of a numerical model of this has previously provided insight into open-loop upset dynamics and the impact of flight controllers. However, to date, studies have not considered the effect of time delay on the system’s stability. Current developments at the Airborne Subscale Transport Aircraft Research facility are aimed at testing a subscale generic airliner model during loss-of-control conditions over extended distances and altitudes compared to the generic transport model. In developing controllers for such a remotely piloted vehicle, it is helpful to understand the effect of delay in the communication links and protocols. This paper uses bifurcation an...

In this paper, the influence of the flight control system over the off nominal behavior of a remotely operated air vehicle is evaluated. Of particular interest is the departure/upset characteristics of the closed-loop system near and beyond stall. The study vehicle is the NASA Generic Transport Model, and both fixed-gain and gain-scheduled versions of a linear quadratic regulator controller with proportional and integral components are evaluated. Bifurcation analysis is used to characterize spiral and spin behavior of the aircraft in closed-loop form and yields an understanding of the underlying vehicle dynamics outside the standard flight envelope. The use of a “gain parameter” to scale the controller gains provides information on the sensitivity of stability to gain variation, along with tracking how the controller modifies the open-loop steady states. Hence, this provides a means of assessing the effectiveness of the controller and evaluating the upset tendencies of the aircraft.

This paper proposes a model updating strategy for localised nonlinear structures. It utilises an initial finite-element (FE) model of the structure and primary harmonic response data taken from low and high amplitude excitations. The underlying linear part of the FE model is first updated using low-amplitude test data with established techniques. Then, using this linear FE model, the nonlinear elements are localised, characterised, and quantified with primary harmonic response data measured under stepped-sine or swept-sine excitations. Finally, the resulting model is validated by comparing the analytical predictions with both the measured responses used in the updating and with additional test data. The proposed strategy is applied to a clamped beam with a nonlinear mechanism and good agreements between the analytical predictions and measured responses are achieved. Discussions on issues of damping estimation and dealing with data from amplitude-varying force input in the updating process are also provided.

High Static Low Dynamic Stiffness (HSLDS) mounts consist of nonlinear springs that support a high static load with low static displacement, whilst maintaining locally low stiffness near equilibrium, to give a low natural frequency and consequently good isolation properties. Recent analysis has investigated such devices when the force–displacement relationship is an odd function about the equilibrium position, and analysed the consequences of different shapes of these functions. However many devices that have the HSLDS characteristic do not meet the assumptions of this analysis, in that the force–displacement relationship is generally asymmetric about equilibrium. Furthermore, even devices that do meet this assumption may be subject to significant adjustment error, particularly in the context of air vehicles where manoeuvres such as banked turns can cause an apparent variation in gravitational acceleration, and a consequent variation in the weight of the payload. This change in static load moves the payload away from its intended region of low stiffness. The current paper provides analysis of these situations, and shows that the performance of a mount with a symmetric stiffness–displacement relationship is highly sensitive to errors in the static loading. It is then shown that a mount with an asymmetric stiffness–displacement function can offer significant performance advantages when there are adjustment errors in the loading of the mount.

Fluid dampers are an important tool for dissipating unwanted vibrations in a range of engineering structures. This paper examines the effects of amplifying the displacements transferred to a non-linear damper, to increase the effectiveness of the damper in a range of situations commonly encountered in civil engineering structures. These include, (i) the ability to ‘‘fine tune’’ the required damping for a particular size damper, (ii) the ability to have a set of the same size dampers, but with different amplification factors to achieve a specific damping task, and (iii) to increase the sensitivity of the damper to small movements which effectively extends the range over which the damper works. Through numerical simulations and experimental tests conducted on a non-linear damper, we quantify the potential advantages of adding an amplification factor and the range of parameters where the benefit to this device is significant. The example of a two-storey structure is used as a test case and real-time dynamic substructuring tests are used to assess the complete system performance using a range of different amplification factors. The results show that the structural performance is most improved for frequencies close to resonance and that the amplification factor has an effective limit that for the case considered in this study is of approximately 3. The effects of the mechanism compliance are also assessed. 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://

This paper investigates the use of an actuator and sensor pair coupled via a control system to damp out oscillations in resonant mechanical systems. Specifically the designs emulate passive control strategies, resulting in controller dynamics that resemble a physical system. Here, the use of the novel dynamically dual approach is proposed to design the vibration absorbers to be implemented as the controller dynamics; this gives rise to the dynamically dual vibration absorber (DDVA). It is shown that the method is a natural generalisation of the classical single-degree of freedom mass–spring–damper vibration absorber and also of the popular acceleration feedback controller. This generalisation is applicable to the vibration control of arbitrarily complex resonant dynamical systems. It is further shown that the DDVA approach is analogous to the hybrid numerical-experimental testing technique known as substructuring. This analogy enables methods and results, such as robustness to sensor/actuator dynamics, to be applied to dynamically dual vibration absorbers. Illustrative experiments using both a hinged rigid beam and a flexible cantilever beam are presented.

A key part of the main landing gear (MLG) of a civil aircraft is its locking mechanism that holds the gear in the deployed or down-locked state. The locking is driven by a spring mechanism and its release by the unlock actuator. This paper considers this mechanism in terms of its stability and the locking and unlocking forces required for down-locking. To study this an analytical model was developed. The equations, consisting of geometric constraints and force/moment equilibriums, were derived using the coordinate transformation method. Using numerical continuation to solve these equations, the effect ofthe unlock force on the MLG retraction cycle was analyzed. The variation of a fold bifurcation point, which indicates the transition between the locked state and the unlocked state, gives further insight into the required unlock force that governs the sizing of the unlock actuator. Moreover, some important information, such as the critical position for the lock-links’ stops, the unlock position and the unlock force, are discussed using the bifurcation diagrams for the MLG retraction/extension cycle. Then, the effect of three key geometry parameters of the locking spring (the spring stiffness, unstrained spring length and spring attachment point) on the critical over-center angle and the unlock force are investigated. Finally, an optimization of the critical unlock force is carried out with a constraint on the initial over-center angle. The results show that the spring parameters have significant effects on the MLG’s retraction performance. A 37% reduction of the required unlock force is obtained through optimizing for the gear considered here.

Nonlinear stiffness isolation mounts, which offer a high static stiffness alongside a low dynamic stiffness or even quasi-zero-stiffness (QZS) over a displacement range have been proposed. These vibration isolators offer a higher isolation frequency band of low transmissibility than conventional linear devices. Here, three kinds of nonlinear two degree-of-freedom (DOF) vibration isolators with QZS characteristic are analysed in order to further improve the isolation performance. The dynamic response is obtained using the Harmonic Balance Method (HBM) and the peak dynamic displacement is obtained using backbone curve analysis and energy balancing method. The optimum isolation performance of the nonlinear 2DOF vibration isolators are evaluated for four performance indexes and compared with three baseline vibration isolators. These are a linear and a QZS 1DOF vibration isolator as well as a linear 2DOF vibration isolator. To ensure a fair comparison, the static displacement of each vibration isolator is kept constant. Thecomparison demonstrates that a nonlinear 2DOF vibration isolator can be tuned to achieve a better isolation performance in the higher isolation frequency band than the baseline vibration isolators, while retaining a moderate peak dynamic displacement and peak transmissibility. In addition, the best vibration isolator is identified for each of the four performance indexes.

The work reported in this paper concentrates on the possibility of suppressing shimmy oscillations of landing gear more effectively using a linear passive suppression device incorporating inerter. The inerter is a one-port mechanical device with the property that the applied force is proportional to the relative acceleration between its terminals. A linear model of a Fokker 100 aircraft main landing gear equipped with a shimmy-suppression device is presented. Time-domain optimizations of the shimmy-suppression device are carried out using cost functions of the maximum amplitude and the settling time of torsional-yaw motion. Applying two types of excitations that trigger the shimmy oscillations, the performance advantages of inerter-based configurations for suppressing shimmy of main landing gear, together with corresponding parameter values, are identified.

This paper proposes a new method, the structure-immittance approach, for designing the passive vibration absorbers consisting of inerters, dampers and springs. When considering possible configurations for these elements broadly, one of two exist approaches may be taken, either a structure-based or an immittance-based approach. Both methods have their advantages and disadvantages. In this paper, the new approach combines the advantages of the existing ones. It can both consider a full set of absorber layouts together (the advantage of immittance-based approach), and restrict the complexity, topology and element values of the candidate layouts (the advantage of structure-based approach). The structural immittances covering a full set of possible networks with one damper, one inerter and at most one spring are derived and applied to a civil engineering study. This demonstrates the advantages of the new methodology in being able to identify the optimum configurations for different element constraints.

The exploitation of nonlinear behavior in vibration-based energy harvesters has received much attention over the last decade. One key motivation is that the presence of nonlinearities can potentially increase the bandwidth over which the excitation is amplified and therefore the efficiency of the device. In the literature, references to resonating energy harvesters featuring nonlinear oscillators are common. In the majority of the reported studies, the harvester powers purely resistive loads. Given the complex behavior of nonlinear energy harvesters, it is difficult to identify the optimum load for this kind of device. In this paper the aim is to find the optimal load for a nonlinear energy harvester in the case of purely resistive loads. This work considers the analysis of a nonlinear energy harvester with hardening compliance and electromagnetic transduction under the assumption of negligible inductance. It also introduces a methodology based on numerical continuation which can be used to find the optimum load for a fixed sinusoidal excitation.

A model of a three-dimensional dual-sidestay landing gear mechanism is presented and employed in an investigation of the sensitivity of the downlocking mechanism to attachment point deflections. A motivation for this study is the desire to understand the underlying nonlinear behavior, which may prevent a dual-sidestay landing gear from downlocking under certain conditions. The model formulates the mechanism as a set of steady-state constraint equations. Solutions to these equations are then continued numerically in state and parameter space, providing all state parameter dependencies within the model from a single computation. The capability of this analysis approach is demonstrated with an investigation into the effects of the aft sidestay angle on retraction actuator loads. It was found that the retraction loads are not significantly affected by the sidestay plane angle, but the landing gear’s ability to be retracted fully is impeded at certain sidestay plane angles. This result is attributed to the lan...

Ultrasonic harmonic generation measurements have shown great potential for detecting nonlinear changes in various materials. Despite this, the practical implementation of the technique in non-destructive evaluation (NDE) has typically been limited to the through transmission setup case, with which problems arise in certain situations. Recently, works in the fields of nonlinear fluids and biomedical imaging have reported different application of the harmonic generation theory by making use of reflective boundaries and beam focusing. It is thought that such techniques may be similarly applied in the field of NDE to enable single-sided nonlinear inspection of components. In this paper, we initially describe a numerical model which has been used to determine the effects of attenuation and acoustic beam diffraction on measurements of the nonlinear parameter beta. We then extend the model to incorporate first the effects of multiple reflecting boundaries in the propagation medium, then of focused source excitation. Simulations, supported by experimental data, show that nonlinear pulse-echo measurements have the potential to provide a viable (and practical) alternative to the usual through-transmission type as a means of measuring beta in solids. Furthermore, it is shown that such measurements may be optimised, both by adjusting the excitation frequency, and by focusing the acoustic source at a certain point relative to the specimen boundary.

SUMMARY: This paper proposes the use of a novel type of passive vibration control system to reduce vibrations in civil engineering structures subject to base excitation. The new system is based on the inerter, a device that was initially developed for high-performance suspensions in Formula 1 racing cars. The principal advantage of the inerter is that a high level of vibration isolation can be achieved with low amounts of added mass. This feature makes it an attractive potential alternative to traditional tuned mass dampers (TMDs). In this paper, the inerter system is modelled inside a multi-storey building and is located on braces between adjacent storeys. Numerical results show that an excellent level of vibration reduction is achieved, potentially offering improvement over TMDs. The inerter-based system is compared to a TMD system by using a range of base excitation inputs, including an earthquake signal, to demonstrate how the performance could potentially be improved by using an inerter instead of a TMD. © 2013 John Wiley & Sons, Ltd.

A study is made into the occurrence of shimmy oscillations in a dual-wheel main landing gear. Nonlinear equations of motion are developed for the system, and various effects are considered, including gyroscopic coupling, nonlinear tire properties, geometric nonlinearities, and fluid shock damping. Of particular interest in this study is the presence of freeplay: this is introduced as a lateral play at the apex of the torque link joints. Using bifurcation analysis methods, the dynamics of this system are explored as the forward velocity and loading force acting on the gear are varied. For the zero freeplay case, the system is found to be stable over its physical operating range with shimmy oscillations appearing only for extreme loading forces and speed. However, with the introduction of freeplay, shimmy may be observed over more typical operating conditions, and the resulting oscillations are found to scale linearly with freeplay magnitude. The parameter plane of forward velocity and loading force is then further subdivided into areas of different types of dynamics. With the inclusion of freeplay one observes the appearance of low-frequency and high-frequency shimmy oscillations, bistable behavior, and stationary solutions of nonzero yaw. Considering the desirable case in which no shimmy occurs, the set of allowable freeplay profiles that satisfy a conservative stability criteria is defined.

The High Static Low Dynamic Stiffness (HSLDS) concept is a design strategy for a nonlinear anti-vibration mount that seeks to increase isolation by lowering the natural frequency of the mount whilst maintaining the same static load bearing capacity. It has previously been proposed that an HSLDS mount could be implemented by connecting linear springs in parallel with the transverse flexure of a composite bistable plate - a plate that has two stable shapes between which it may snap. Using a bistable plate in this way will lead to lightweight and efficient designs of HSLDS mounts. This paper experimentally demonstrates the feasibility of this idea. Firstly, the quasi-static force-displacement curve of a mounted bistable plate is determined experimentally. Then the dynamic response of a nonlinear mass-spring system incorporating this plate is measured. Excellent agreement is obtained when compared to theoretical predictions based on the measured force-displacement curve, and the system shows a greater isolation region and a lower peak response to base excitation than the equivalent linear system. © 2013 Elsevier Ltd.

SUMMARY In this paper, a method for designing supplemental brace–damper systems in single-degree-of-freedom (SDOF) structures is presented. We include the effects of the supporting brace stiffness in the dynamic response by using a viscoelastic Maxwell model. On the basis of the study of an SDOF under ground excitation, we propose a noniterative design procedure for simultaneously specifying both the damper and the brace while assuring a desired structural performance. It is shown that to increase the damper size beyond the value delivered by the proposed criteria will not provide any improvement but actually worsen the structural response. The design method presented here shows excellent agreement with the FEMA 273 design approach but offers solutions closer to optimality. Copyright © 2013 John Wiley & Sons, Ltd.

Considering the partial differential equation model of the vibrations of an inclined cable, we are interested in applying robust control technics to stabilize the system with measurement feedback when it is submitted to external disturbances. This paper focuses indeed on the construction of a standard linear infinite dimensional state space system and an H_infinity feedback control of vibrations with partial observation of the state. The control and observation are performed using an active tendon.

This paper investigates the use of inerters for vibration suppression of a multistorey building structure. The inerter was proposed as a two-terminal replacement for the mass element, with the property that the applied force is proportional to the relative acceleration across its terminals. It completes the force-current mechanical-electrical network analogy, providing the mechanical equivalent to a capacitor. Thus allows all passive mechanical impedances to be synthesised. The inerter has been used in Formula 1 racing cars and applications to various systems such as vehicle suspension have been identified. Several devices that incoporate inerter(s), as well as spring(s) and damper(s), have also been identified for vibration suppression of building structures. These include the tuned inerter damper (TID) and the tuned viscous mass damper (TVMD). In this paper, a three-storey building model with an absorber located at the bottom subjected to base excitation is studied. Four simple absorber layouts, in terms of how spring, damper and inerter components should be arranged, have been studied. In order to minimise the maximum relative displacement of the building, the optimum parameter values for each of the layouts have been obtained with respect to the inerter's size.

This paper considers the use of a tuned inerter damper (TID) system for\ud suppressing unwanted cable vibrations. The TID consists of an inerter, a\ud device that exerts a force proportional to relative acceleration, coupled with\ud a parallel spring and damper. It may be thought of as similar to a tunedmass-damper,\ud but requiring two terminals. As a two terminal device, the\ud performance of the TID is compared to the classical use of viscous dampers\ud (VD) located close to one of the cable supports. We show that the limitation\ud that exists with VDs, where the modal damping of the cable cannot exceed a\ud maximum level for a given damper location, can be overcome through the use\ud of the TID at the same location. A practical design methodology, based on\ud the minimisation of the displacement amplitude at the mid-span of the cable\ud subjected to support excitation, is proposed. An example where a cable\ud is subjected to the El-Centro earthquake demonstrates that the system’s\ud response is improved when a TID is used instead of a VD.

A full-scale experimental test for large and complex structures is not always achievable. This can be due to many reasons, the most prominent one being the size limitations of the test. Real-time dynamic substructuring is a hybrid testing method where part of the system is modelled numerically and the rest of the system is kept as the physical test specimen. The numerical–physical parts are connected via actuators and sensors and the interface is controlled by advanced algorithms to ensure that the tested structure replicates the emulated system with sufficient accuracy. The main challenge in such a test is to overcome the dynamic effects of the actuator and associated controller, that inevitably introduce delay into the substructured system which, in turn, can destabilize the experiment. To date, most research concentrates on developing control strategies for stable recreation of the full system when the interface location is given a priori . Therefore, substructurability is mostly studied in terms of control. Here, we consider the interface location as a parameter and study its effect on the stability of the system in the presence of delay due to actuator dynamics and define substructurability as the system’s tolerance to delay in terms of the different interface locations. It is shown that the interface location has a major effect on the tolerable delays in an experiment and, therefore, careful selection of it is necessary.

Recently, there has been increased interest in using non-linear vibration techniques to detect damage in reinforced concrete beams. To understand better the non-linear behaviour of damaged concrete beams during low-amplitude vibration, modelling is necessary. This could be achieved with knowledge of the moment-relative rotation relationship of a section of beam within the damaged region. An experimental method of studying the static moment-rotation relationship over a short subsection of the beam is presented here. Tests are conducted at the mid-span of a beam, damaged by overload. Initially the stiffness of the damaged section decreases rapidly with increased damage but above 27% of failure load the change with increased damage is very small. Several possible non-linear crack mechanisms are then discussed, two of which may be assessed using the experimental data. © 2002 Elsevier Science Ltd. All rights reserved.

Many researchers have proposed methods of assessing structural damage by analysis of vibration measurements. Most approaches involve comparing vibration signals measured on the structure before and after damage, with both signals analysed using linear methods. For concrete structures, there is evidence that the actual behaviour is non-linear even at very low amplitudes of excitation. A possible alternative method is therefore to assess damage by estimating the degree of non-linearity present within a given response measurement. In this paper, tests are reported on simply supported, reinforced concrete beams subjected to increasing levels of flexural cracking at midspan. At each damage level, the degree of non-linearity is assessed by examining the variation of measured natural frequency with vibration amplitude, as determined by time-frequency analysis of transient vibrations. The results showed a sharp increase in non-linearity due to initial cracking, but then only quite small changes as the cracks grew. At very high damage levels there appeared to be a reduction in the degree of non-linearity, indicating that the non-linear mechanism present in the system was breaking down. On the basis of these findings, it is concluded that measures of non-linearity may be useful in detecting the initiation of damage, but are unlikely to be helpful in differentiating between intermediate damage levels.

This paper presents recent progress in the development of a novel multi-degree-of-freedom dynamic manoeuvre rig aimed at investigation of aircraft model nonlinear and time dependent aerodynamics in the wind tunnel. The purpose and characteristics of the rig are first described, along with a description of the data acquisition, processing and presentation system. The dynamic manoeuvre rig capabilities are demonstrated via a series of experiments involving a wind tunnel model aircraft in a closed section low-speed wind tunnel. First, an experiment illustrating low-speed wind tunnel aerodynamic model identification is presented. Then, examples of experiments involving real-time control of the rig/aircraft model are shown; these are evaluated in terms of testing productivity with a focus on the development and design of aircraft control laws.

The mechanisms by which a travelling wave propagates through a nonlinear medium are of interest due to the large research effort aimed at exploiting its potential in assessing the damage state of structures. Typically measurements are made to track changing signal nonlinearity due to damage on a single specimen geometry. In this special case relative changes in signal nonlinearity are potentially sufficient to indicate damage. A more robust technique would allow the signal nonlinearity to be related back to the strength of the underlying nonlinear mechanism. In the case of measuring harmonic signal generation in a medium exhibiting a bulk material nonlinearity, a nonlinear parameter exists that relates the material nonlinearity to the measured harmonic signal. However, it is based on the assumption that there is no damping and the excitation is continuous. This paper focuses on assessing the effects of damping, excitation type and signal processing window on the harmonic measurement. Using perturbation and multiple scales techniques, a theoretical model of the generation of nonlinearity is derived. A numerical solution is also developed and both approaches show that the nonlinear parameter first increases and then converges with propagation distance due to the presence of damping. This is experimentally verified. The models also capture the effects of excitation type and signal processing window and using them a correction factor is proposed that accounts for all these effects.

In this article, a hybrid control framework is used to design semi-active controllers for vibration reduction. It is shown that the semi-active skyhook damper, typically used for vibration reduction, can be recast in the framework of an event-driven intermittent controller. By doing this, we can then exploit the well-developed techniques associated with hybrid control theory to design the semi-active control system. Illustrative simulation examples are based on a 2 degree-of-freedom system, often used to model the dynamics of a quarter car body model. The simulation results demonstrate how hybrid control design techniques can improve the overall performance of the semi-active control system.

This paper presents a study of how different vibration modes contribute to the dynamics of an inclined cable that is parametrically excited close to a 2:1 internal resonance. The behaviour of inclined cables is important for design and analysis of cable-stayed bridges. In this work the cable vibrations are modelled by a four-mode model. This type of model has been used previously to study the onset of cable sway motion caused by internal resonances which occur due to the nonlinear modal coupling terms. A bifurcation study is carried out with numerical continuation techniques applied to the scaled and averaged modal equations. As part of this analysis, the amplitudes of the cable vibration response to support inputs is computed. These theoretical results are compared with experimental measurements taken from a 5.4 m long inclined cable with a vertical support input at the lower end. In general this comparison shows a very high level of agreement.

Measurement of the vibrations of plates can offer significant challenges to the experimentalist, particularly when the plates are lightweight, exhibit large amplitude deflections, nonlinear responses or are initially curved. The use of accelerometers adds masses which can change the dynamics of lightweight plates. Large amplitude oscillations and initial curvatures cause complications when using a laser vibrometer, as they make it difficult to get consistent reflections back to the receiver. Furthermore, large or nonlinear oscillations challenge inherent assumptions on which the vibrometer’s algorithms depend. A high speed video camera avoids these issues, but makes it hard to extract numerical data. This paper describes a method that extends the capabilities of a high speed video camera by using a mirror, allowing post-processing software to stereoscopically resolve an array of points on the plate surface to 3D coordinates, capturing the complete shape and position of the plate throughout vibration. This method avoids all the problems mentioned above and gives very clear insight into plate vibration. Some example results of this method are presented, using thermally bistable carbon laminate plates filmed at a 1000 frames per second. These plates pose the challenges described, and also exhibit an unusual oscillatory motion where the plates ‘snap’ between two statically stable states. The method is shown to provide clear insight into the rich dynamics of these plates.

In this work, the applicability of a dynamic testing technique known as real-time dynamic substructuring (RTDS) for the assessment of passive vibration suppression systems in seismic protection of buildings is analysed. RTDS is an efficient method for the assessment of dynamic and rate-dependent behaviour of systems subjected to dynamic excitation at real scale and in real scenarios. The actuators used in RTDS test introduce additional undesirable dynamics into the system, which are often not fully compensated for in the actuator controller—these dynamics are commonly approximated as a feedback delay. To guarantee the validity and accuracy of an RTDS simulation, a stability analysis of the substructured system that includes the feedback delay should be carried out. In this paper, we present explicit analyses that provide a dynamic characterization of the delay-induced phenomena in RTDS simulations when considering passive vibration suppression systems with strong nonlinearities. We present a complete set of closed-form expressions to describe the main phenomena because of delay in terms of dynamic stability in an RTDS simulation. Through an experimental study, we confirm the existence of self-sustained oscillations caused by very small delay in the feedback loop. This lead the system to instability in the form of high-frequency oscillations. Copyright © 2011 John Wiley & Sons, Ltd.

Multi-stable composites are a novel type of composites capable of adopting multiple statically stable configurations. Due to the multi-stability property this type of composite material has been considered for several applications, particularly for morphing structures. The change of shape between stable states is achieved by a nonlinear mechanism known as snap-through. Most of the research done on these composites has focused on predicting the configuration after manufacture, its static characteristics and static actuation strategies to induce snap-through. However, these structures will operate subject to dynamic loads. Yet, very little work has been carried out to examine the dynamic behaviour of bi-stable composites. This paper focuses on the study of the cross-well dynamics of a bi-stable composite plate. A simple model previously derived for the dynamics confined to a single stable state is extended to include cross-well dynamics. The rich dynamics are experimentally investigated, focusing on cross-well oscillations and the key dynamic features of snap-through. Numerical simulations are obtained and compared to the experimental results showing good agreement. In particular, experimentally observed characteristics suggesting chaotic oscillations for cross-well dynamics are captured well by the proposed model. The results herein could be used for implementing control strategies for both configuration morphing and undesired snap-through suppression of bi-stable composites.

Quasi-active damping is a method of coupled mechanical and control system design using multiple semi-active dampers. By designing the systems such that the desired control force may always be achieved using a combination of the dampers, quasi-active damping seeks to approach levels of vibration isolation achievable through active damping, whilst retaining the desirable attributes of semi-active systems. In this article a design is proposed for a quasi-active, base-isolating suspension system. Control laws are firstly defined in a generalised form, where semi-active dampers are considered as idealised variable viscous dampers. This system is used to demonstrate in detail the principles of quasi-active damping, in particular the necessary interaction between mechanical and control systems. It is shown how such a system can produce a tunable, quasi-active region in the frequency response of very low displacement transmissibility. Quasi-active control laws are then proposed which are specific for use with magnetorheological dampers. These are validated in simulation using a realistic model of the damper dynamics, again producing a quasi-active region in the frequency response. Finally, the robustness of the magnetorheological, quasi-active suspension system is demonstrated.

In this articles the authors present a review of non-linear structural control techniques. This is an area of growing importance in a range of engineering applications, where non-linear behaviour is encountered. Structural control is usually divided into three main areas: (a) passive (b) semi-active, and (c) active control. This article follows this convention, and highlights in each section the relevant state of the art for non-linear systems, with additional references to related linear approaches.

In previous work, experimental data have demonstrated the severity of idling gear rattle depends not only on the amplitude, but also the phase of an external sinusoidal forcing. One possible explanation for this is in small tooth profile errors. In this paper, we investigate this hypothesis, by deriving an equation of motion incorporating an error function and losses at the mesh interface, values of which are obtained from experimental data. By solving the equations of motion, theoretical gear rattle trajectories are obtained. Theoretical and experimental trajectories are then compared, by way of time domain plots as well as via contour plots linking the amplitude of backlash oscillation to the amplitude and phase of input forcing. For most profile error functions, good agreement is achieved between the model and experimental data. In the case where the profile errors are dominated by misalignment between the gear and shaft centres agreement is less good and suggestions of areas of further study required for model refinement are proposed.

Large-amplitude cable vibrations have been observed on many major cable-stayed bridges. One possible source of excitation is movement of the deck and/or tower. Of particular concern is parametric excitation, whereby small deck/tower motion at one frequency can cause large cable motion at half the frequency under certain conditions. More commonly, deck/tower motion causes direct excitation of the cable at the same frequency in the same plane. Since cables have low damping, the response amplitudes can be large and geometric non-linearities can become important. Current design guidelines treat the axial and transverse components of end motion separately, but for an inclined cable subject to vertical deck motion at the lower anchorage and/or in-plane horizontal motion at the upper anchorage, both components occur simultaneously, modifying the behaviour considerably. This paper gives simplified results of non-linear mathematical modelling of inclined cable dynamics, with experimental validation, with the aim of providing more reliable guidelines for use in design. The proposed guidelines are summarised an appendix .

This paper examines generalised forms of semi-active switching control in comparison to the sky-hook semi-active controller. A switching time controller is proposed and analysed, in order to determine the optimal performance, with regard to displacement transmissibility, of semi-active switching control. In addition, the model is also used to assess the optimality of the sky-hook switching conditions. An analytical solution is then derived for the optimal switching times. A generalised form of linear switching surface controller is then presented. It is demonstrated that this controller can produce near optimal performance.

The interaction between eccentricity and an external forcing fluctuation in gear rattle response is investigated experimentally. The experimental rig consists of a 1:1 ratio steel spur gear pair, the input gear being controlled in displacement and the output gear being under no load. Gear transmission errors recorded using high accuracy encoders are presented. Large variations in backlash oscillation amplitude are observed as the relative phase of the input forcing and the sinusoidal static transmission error due to eccentricity is varied. A simplified mathematical model incorporating eccentricity is developed. It is compared with experimental findings for three different gear eccentricity alignments by way of plots relating backlash oscillation amplitude to forcing amplitude and phase relative to eccentricity sinusoid. It is shown that eccentricity does not fully account for the experimentally observed large variations in amplitude. Through analysis of the experimental data, it is suggested that further tooth profiling errors may explain the discrepancies.

This paper discusses the formulation and validation of a low order model to capture the dynamics of a bi-stable composite plate, focusing on the dynamics around its stable states. More specifically, the model aims to capture the complex nonlinear subharmonic behavior observed in the dynamic response of the plate. A system identification approach is used to derive simplified equations of motion for the system. Experimental frequency response diagrams are obtained to characterize the observed dynamics in the identification process. Simulations using the identified model are presented showing excellent agreement with the experimentally observed behavior. A theoretical validation of the model is carried out studying the stability of the modes where subharmonic response was observed. Stability boundaries were computed using averaging techniques showing good agreement with experimental results.

A bond graph framework giving a unified treatment of both physical-model based control and hybrid experimental–numerical simulation (also known as real-time dynamic substructuring) is presented. The framework consists of two subsystems, one physical and one numerical, connected by a transfer system representing non-ideal actuators and sensors. Within this context, a two-stage design procedure is proposed: firstly, design and/or analysis of the numerical and physical subsystem interconnection as if the transfer system were not present; and secondly removal of as much as possible of the transfer system dynamics while having regard for the stability margins established in the first stage. The approach allows the use of engineering insight backed up by well-established control theory; a number of possibilities for each stage are given. The approach is illustrated using two laboratory systems: an experimental mass-spring-damper substructured system and swing up and hold control of an inverted pendulum. Experimental results are provided in the latter case.

In this paper the out-of-plane dynamic stability of inclined cables subjected to in-plane vertical support excitation is investigated. We compute stability boundaries for the out-of-plane modes using rescaling and averaging methods. Our study focuses on the 2:1 internal resonance phenomenon between modes that occurs when the excitation frequency is twice the first out-of-plane natural frequency of the cable. The second in-plane mode is excited directly, while the out-of-plane modes can be excited parametrically. An analytical model is developed in order to study the stability regions in parameter space. In this model we include nonlinear coupling effects with other modes, which have thus far been omitted from previous models of parametric excitation of inclined cables. Our study reflects the importance of such effects. Unstable parameter regions are defined for the selected cable configuration. The validity of the proposed stability model was tested experimentally using a small-scale cable actuator rig. A comparison between experimental and analytical results is presented in which very good agreement with model predictions was obtained.

In this paper, a modified model reference adaptive control (MRAC) strategy is developed for use on plants with noise or unmodelled high-frequency dynamics. MRAC consists of two parts, an adaptive control part and a fixed gain control part. The adaptive algorithm uses a combination of low- and high-pass filters such that the frequency range for the adaptive part of the strategy is limited. The mechanism for noise-induced gain wind-up is demonstrated analytically, and it is shown how MRAC can be modified to eliminate this wind-up. Further to this, an additional filter is proposed to improve MRAC robustness to high-frequency unmodelled dynamics. Two test plants, one with added noise and the other with unmodelled high-frequency dynamics, are considered. Both plants exhibit unstable behaviour when controlled using standard MRAC, but, with the modified strategy, robustness is significantly improved.