Imperial College London

DrLoicSalles

Faculty of EngineeringDepartment of Mechanical Engineering

Research Fellow
 
 
 
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Contact

 

+44 (0)20 7594 2243l.salles Website

 
 
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Assistant

 

Mr Peter Higgs +44 (0)20 7594 7078

 
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Location

 

556City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

51 results found

Saeed Z, Jenovencio G, Arul S, Blahoš J, Sudhakar A, Pesaresi L, Yuan J, El Haddad F, Hetzler H, Salles Let al., 2020, A Test-Case on Continuation Methods for Bladed-Disk Vibration with Contact and Friction, Pages: 209-212, ISSN: 2191-5644

© 2020, Society for Experimental Mechanics, Inc. Bladed-disks in turbo-machines experience harsh operating conditions and undergo high vibration amplitudes if not properly damped. Friction at the blade-to-blade or blade-to-disk interfaces plays a key role in dampening the high amplitudes. Due to the inherent complexity of these structures and non-linearities introduced by the friction joints, accurate response prediction becomes very difficult. There are variety of methods in the literature to predict non-linear vibration due to contact friction. However, their application to the bladed-disks remains limited. Furthermore, there are not many 3D realistic test-cases in the open literature for testing those methods and serve as a benchmark. A bladed-disk representative of a real turbine is presented as an open numerical test-case for the research community. It is characterized by a blade root joint and a shroud joint. The bladed-disk sector is meshed in different ways along with component mode synthesis (CMS) model order reduction for onward non-linear computations. The steady-state solution is obtained by multi-Harmonic Balance method and then continuation method is employed to predict the non-linear frequency response. Thus, it can serve as a case for testing previous and new methods as well as a benchmark for comparative studies.

Conference paper

Sun Y, Yuan J, Pesaresi L, Denimal E, Salles Let al., Parametric Study and Uncertainty Quantification of the Nonlinear Modal Properties of Frictional Dampers, Journal of Vibration and Acoustics, ISSN: 0739-3717

Journal article

Yuan J, Salles L, El Haddad F, Wong Cet al., An adaptive component mode synthesis method for dynamic analysis of jointed structure with contact friction interfaces, Computers and Structures, ISSN: 0045-7949

Component model synthesis (CMS) has been widely used for model order re-duction in dynamic analysis of jointed structures with localized non-linearities.The main drawback of these CMS methods is that their computational efficiencylargely depends on the size of contact friction interfaces. This work proposes anadaptive reduction approach to improve these CMS based reduction methods inthe application to the assembled structure with frictional interfaces.The mainidea of this method is that, instead of retaining the whole frictional interfaceDOFs in the reduced model, only those DOFs in a slipping or separating con-dition are retained. This would significantly reduce the size of classical CMSbased reduced models for dynamical analysis of jointed structure with micro-slipmotion, leading to an impressive computational saving. This novel approach isbased on a reformulated dynamic system that consists of a underlying linearisedsystem and including an updating internal variable to account the effects ofnon-linear contact friction force on the interface. The paper also describesthe detailed implementation of the proposed approach with harmonic balancedmethod for non-linear spectral analysis, where a new updating algorithm is putforward to enable the size of the reduced model can be automatically updatedaccording to the contact condition of interface nodes. Two distinct FE joint models are used to validate the proposed method. It is demonstrated that thenew approach can achieve a considerable computing speed-up comparing to theclassic CMS approach while maintain the same accuracy.

Journal article

Pesaresi L, Fantetti A, Cegla F, Salles L, Schwingshackl CWet al., 2019, On the use of ultrasound waves to monitor the local dynamics of friction joints, Experimental Mechanics, ISSN: 0014-4851

Friction joints are one of the fundamental means used for the assembly of structural components in engineering applications. The structural dynamics of these components becomes nonlinear, due to the nonlinear nature of the forces arising at the contact interface characterised by stick-slip phenomena and separation. Advanced numerical models have been proposed in the last decades which have shown some promising capabilities in capturing these local nonlinearities. However, despite the research efforts in producing more advanced models over the years, a lack of validation experiments made it difficult to have fully validated models. For this reason, experimental techniques which can provide insights into the local dynamics of joints can be of great interest for the refinement of such models and for the optimisation of the joint design and local wear predictions. In this paper, a preliminary study is presented where ultrasound waves are used to characterise the local dynamics of friction contacts by observing changes of the ultrasound reflection/transmission at the friction interface. The experimental technique is applied to a dynamic friction rig, where two steel specimens are rubbed against each other under a harmonic tangential excitation. Initial results show that, with a controlled experimental test procedure, this technique can identify microslip effects at the contact interface.

Journal article

Fantetti A, Tamatam, Volvert, Laval, Liu, Salles L, Brake M, Schwingshackl C, Nowell Det al., 2019, The impact of fretting wear on structural dynamics: experiment and simulation, Tribology International, Vol: 138, Pages: 111-124, ISSN: 0301-679X

This paper investigates the effects of fretting wear on frictional contacts. A high frequency friction rig is used to measure the evolution of hysteresis loops, friction coefficient and tangential contact stiffness over time. This evolution of the contact parameters is linked to significant changes in natural frequencies and damping of the rig. Hysteresis loops are replicated by using a Bouc-Wen modified formulation, which includes wear to simulate the evolution of contact parameters and to model the evolving dynamic behaviour of the rig. A comparison of the measured and predicted dynamic behaviour demonstrates the feasibility of the proposed approach and highlights the need to consider wear to accurately capture the dynamic response of a system with frictional joints over its lifetime.

Journal article

Yuan J, Salles L, Wong C, Patsias Set al., 2019, A novel penalty-based reduced order modelling method for dynamic analysis of joint structures, IUTAM Symposium on Model Order Reduction of Coupled Systems, Publisher: Springer, Pages: 165-176

This work proposes a new reduced order modelling method to improve the computational efficiency for the dynamic simulation of a jointed structures with localized contact friction non-linearities. We reformulate the traditional equation of motion for a joint structure by linearising the non-linear system on the contact interface and augmenting the linearised system by introducing an internal non-linear penalty variable. The internal variable is used to compensate the possible non-linear effects from the contact interface. Three types of reduced basis are selected for the Galerkin projection, namely, the vibration modes (VMs) of the linearised system, static modes (SMs) and also the trial vector derivatives (TVDs) vectors. Using these reduced basis, it would allow the size of the internal variable to change correspondingly with the number of active non-linear DOFs. The size of the new reduced order model therefore can be automatically updated depending on the contact condition during the simulations. This would reduce significantly the model size when most of the contact nodes are in a stuck condition, which is actually often the case when a jointed structure vibrates. A case study using a 2D joint beam model is carried out to demonstrate the concept of the proposed method. The initial results from this case study is then compared to the state of the art reduced order modeling.

Conference paper

Armand J, Pesaresi L, Salles L, Wong C, Schwingshackl CWet al., 2019, A modelling approach for the nonlinear dynamics of assembled structures undergoing fretting wear, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 475, ISSN: 1364-5021

© 2019 The Author(s) Published by the Royal Society. All rights reserved. Assembled structures tend to exhibit nonlinear dynamic behaviour at high excitation levels due to the presence of contact interfaces. The possibility of building predictive models relies on the ability of the modelling strategy to capture the complex nonlinear phenomena occurring at the interface. One of these phenomena, normally neglected, is the fretting wear occurring at the frictional interface. In this paper, a computationally efficient modelling approach which enables considerations of the effect of fretting wear on the nonlinear dynamics is presented. A multiscale strategy is proposed, in which two different time scales and space scales are used for the contact analysis and dynamic analysis. Thanks to the decoupling of the contact and dynamic analysis, a more realistic representation of the contact interface, which includes surface roughness, is possible. The proposed approach is applied to a single bolted joint resonator with a simulated rough contact interface. A tendency towards an increase of real contact area and contact stiffness at the interface is clearly observed. The dynamic response of the system is shown to evolve over time, with a slight decrease of damping and an increase of resonance frequency, highlighting the impact of fretting wear on the system dynamics.

Journal article

Yuan J, El-Haddad F, Salles L, Wong Cet al., 2019, Numerical Assessment of Reduced Order Modeling Techniques for Dynamic Analysis of Jointed Structures With Contact Nonlinearities, JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER-TRANSACTIONS OF THE ASME, Vol: 141, ISSN: 0742-4795

Journal article

Fontanela F, Grolet A, Salles L, Chabchoub A, Champneys AR, Patsias S, Hoffmann Net al., 2019, Dissipative solitons in forced cyclic and symmetric structures, MECHANICAL SYSTEMS AND SIGNAL PROCESSING, Vol: 117, Pages: 280-292, ISSN: 0888-3270

Journal article

Fontanela F, Grolet A, Salles L, Hoffmann Net al., 2019, Computation of quasi-periodic localised vibrations in nonlinear cyclic and symmetric structures using harmonic balance methods, JOURNAL OF SOUND AND VIBRATION, Vol: 438, Pages: 54-65, ISSN: 0022-460X

Journal article

Filippatos A, Wollmann T, Minh N, Kostka P, Dannemann M, Langkamp A, Salles L, Gude Met al., 2019, Design and Testing of a Co-Rotating Vibration Excitation System, SENSORS, Vol: 19, ISSN: 1424-8220

Journal article

Tatar A, Salles L, Haslam AH, Schwingshackl CWet al., 2019, Comparison of computational generalized and standard eigenvalue solutions of rotating systems, Pages: 187-194, ISSN: 2191-5644

© The Society for Experimental Mechanics, Inc. 2019. Modal analysis is regularly used to compute natural frequencies and mode shapes of structures via eigenvalue solutions in vibration engineering. In this paper, the eigenvalue problem of a 6 degrees of freedom rotating system with gyroscopic effects, including axial, torsional and lateral motion, is investigated using Timoshenko beam theory. The main focus thereby is the investigation of the computational time and the numerical errors in generalized and standard eigenvalue solutions of rotating systems. The finite element method is employed to compute the global stiffness, mass and gyroscopic matrices of the rotating system. The equations of motion is expressed in the state space form to convert the quadratic eigenvalue problem into the generalized and standard forms. The number of elements in the finite element model was varied to investigate the convergence of the natural frequencies and the computational performance of the two eigenvalue solutions. The numerical analyses show that the standard eigenvalue solution is significantly faster than the generalized one with increasing number of elements and the generalized eigenvalue solution can yield wrong solutions when using higher numbers of elements due to the ill-conditioning phenomenon. In this regard, the standard eigenvalue solution gives more reliable results and uses less computational time than the generalized one.

Conference paper

Venkatesh S, Rendu Q, Vahdati M, Salles Let al., 2019, Effect of manufacturing tolerance in flow past a compressor blade

Copyright © by the Authors. This paper presents the effect of manufacturing tolerance on performance and stability boundaries of a transonic fan using a RANS simulation. The effect of tip gap and stagger angle was analysed through a series of single passage and double passage simulation; based on which an optimal arrangement was proposed for random tip gap and random stagger angle in case of a whole annulus rotor. All simulations were carried out using NASA rotor 67 as a test case and AU3D an in-house CFD solver. Results illustrate that the stagger angle mainly affects efficiency and hence its circumferential variation must be as smooth as possible. Furthermore, the tip gap affects the stability boundaries, pressure ratio and efficiency. Hence its optimal configuration mandates that the blades be configured in a zigzag arrangement around the annulus i.e. larger tip gap between two smaller ones.

Conference paper

Fontanela F, Grolet A, Salles L, Hoffmann Net al., 2019, Solitons in cyclic and symmetric structures, Pages: 175-178, ISSN: 2191-5644

© The Society for Experimental Mechanics, Inc. 2019. This research focuses on localised states arising from modulationally unstable plane waves in non-conservative cyclic and symmetric structures. The main application is on vibrations of bladed-disks of aircraft engines experiencing nonlinear effects, such as large displacements, friction dissipation, and/or complex fluid-structure interactions. The investigation is based on a minimal model composed of a chain of linearly damped Duffing oscillators under external travelling wave excitation. The computed results are based on two strategies: (1) a Non-Linear Schrödinger Equation (NLSE) approximation; and (2) the periodic and quasi-periodic Harmonic Balance Methods (HBM). In both cases, the results show that unstable plane waves may self-modulate, leading to stable and unstable single and multiple solitons configurations.

Conference paper

Lacayo R, Pesaresi L, Gross J, Fochler D, Armand J, Salles L, Schwingshackl C, Allen M, Brake Met al., 2019, Nonlinear modeling of structures with bolted joints: a comparison of two approaches based on a time-domain and frequency-domain solver, Mechanical Systems and Signal Processing, Vol: 114, Pages: 413-438, ISSN: 0888-3270

Motivated by the current demands in high-performance structural analysis, and by a need to better model systems with localized nonlinearities, analysts have developed a number of different approaches for modeling and simulating the dynamics of a bolted-joint structure. However, it is still unclear which approach might be most effective for a given system or set of conditions. To better grasp their similarities and differences, this paper presents a numerical benchmark that assesses how well two diametrically differing joint modeling approaches – a time-domain whole-joint approach and a frequency-domain node-to-node approach – predict and simulate a mechanical joint. These approaches were applied to model the Brake-Reuß beam, a prismatic structure comprised of two beams with a bolted joint interface. The two approaches were validated first by updating the models to reproduce the nonlinear response for the first bending mode of an experimental Brake-Reuß beam. Afterwards, the tuned models were evaluated on their ability to predict the nonlinearity in the dynamic response for the second and third bending modes. The results show that the two joint modeling approaches perform about equally as well in simulating the Brake-Reuß beam. In addition, the exposition highlights improvements that were made in each method during the course of this work and reveal further challenges in advancing the state-of-the-art.

Journal article

Pesaresi L, Armand J, Schwingshackl C, Salles L, Wong Cet al., 2018, An advanced underplatform damper modelling approach based on a microslip contact model, Journal of Sound and Vibration, Vol: 436, Pages: 327-340, ISSN: 0022-460X

High-cycle fatigue caused by large resonance stresses remains one of the most common causes of turbine blade failures. Friction dampers are one of the most effective and practical solutions to limit the vibration amplitudes, and shift the resonance frequencies of the turbine assemblies far from operating speeds. However, predicting the effects of underplatform dampers on the dynamics of the blades with good accuracy still represents a major challenge today, due to the complex nature of the nonlinear forces at the interface, characterised by transitions between stick, slip, and separation conditions. The most common modelling approaches developed recently are based on the explicit FE model for the damper, and on a dense grid of 3D contact elements comprised of Jenkins elements, or on a single 2D microslip element on each surface. In this paper, a combination of the two approaches is proposed. A 3D microslip element, based on a modified Valanis model is proposed and a series of these elements are used to describe the contact interface. This new approach allows to implicitly account for the microscale energy dissipation as well as the pressure-dependent contact stiffness caused by the roughness of the contact surface. The proposed model and its predicting capabilities are then evaluated against a simplified blade-damper model, based on an underplatform damper test rig recently developed by the authors. A semi-analytical contact solver is used to tune the parameters of the contact element starting from the profilometer measurements of the real damper surface. A comparison with a more simplistic modelling approach based on macroslip contact elements, highlights the improved accuracy of the new model to predict the experimental nonlinear response, when information about the surface roughness is available.

Journal article

Sun Y, Yuan J, Pesaresi L, Salles Let al., 2018, Nonlinear Vibrational Analysis for Integrally Bladed Disk Using Frictional Ring Damper, Modern Practice in Stress and Vibration Analysis (MPSVA) 2018, ISSN: 1742-6588

© Published under licence by IOP Publishing Ltd. The use of integrally bladed-disk is now very popular in turbomachinery industry since they feature significant aerodynamic and structural improvements along with a significant mass reduction. However, these integrated single structures can arise a major high cycle fatigue issue due to the lack of sufficient damping for dissipating the vibrational energy. This work describes a numerical investigation of the nonlinear dynamic behaviour and nonlinear normal mode for such a bladed-disk with frictional ring damper using the Harmonic Balanced Method (HBM) with alternating Fourier transformation. Jenkins element is used to model the nonlinear contact friction between the disc and ring damper. Using such a modeling strategy, the modal damping and resonance amplitude are directly and efficiently computed through nonlinear normal mode analysis. The initial results show the vibrational level on the blades can be effectively controlled by the parameters of the ring damper model. The effectiveness of ring damper and damping performance is evaluated. This study also indicates the nonlinear normal mode analysis based HBM may be an effective method to analyse the dynamic behaviour of the integrated bladed-disk with frictional ring damper.

Conference paper

Armand J, Salles L, Schwingshackl CW, Süß D, Willner Ket al., 2018, On the effects of roughness on the nonlinear dynamics of a bolted joint: a multiscale analysis, European Journal of Mechanics - A/Solids, Vol: 70, Pages: 44-57, ISSN: 0997-7538

Accurate prediction of the vibration response of friction joints is of great importance when estimating both the performance and the life of build-up structures. The contact conditions at the joint interface, including local normal load distribution and contact stiffness, play a critical role in the nonlinear dynamic response. These parameters strongly depend on the mating surfaces, where the surface roughness is well known to have a significant impact on the contact conditions in the static case. In contrast, its effects on the global and local nonlinear dynamic response of a build-up structure is not as well understood due to the complexity of the involved mechanisms. To obtain a better understanding of the dependence of the nonlinear dynamic response on surface roughness, a newly proposed multiscale approach has been developed. It links the surface roughness to the contact pressure and contact stiffness, and in combination with a multiharmonic balance solver, allows to compute the nonlinear dynamic response for different interface roughness. An application of the technique to a single bolted lap joint highlighted a strong impact of larger roughness values on the pressure distribution and local contact stiffness and in turn on the nonlinear dynamic response.

Journal article

Fontanela F, Grolet A, Salles L, Chabchoub A, Hoffmann Net al., 2018, Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry, JOURNAL OF SOUND AND VIBRATION, Vol: 413, Pages: 467-481, ISSN: 0022-460X

Journal article

Yuan J, El -Haddad F, Salles L, Wong Cet al., 2018, NUMERICAL ASSESSMENT OF REDUCED ORDER MODELING TECHNIQUES FOR DYNAMIC ANALYSIS OF JOINTED STRUCTURES WITH CONTACT NONLINEARITIES, ASME Turbo Expo: Turbomachinery Technical Conference and Exposition, Publisher: AMER SOC MECHANICAL ENGINEERS

Conference paper

Pesaresi L, Armand J, Schwingshackl CW, Salles L, Wong Cet al., 2017, An advanced underplatform damper modelling approach based on a microslip contact model, 17th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery

High-cycle fatigue caused by large resonance stresses remains one of the most common causes of turbine blades failures. Friction dampers are one of the most effective and practical solutions to limit the vibration amplitude, and shift the resonance frequencies of the turbine assemblies far from operating speeds. However, predicting with good accuracy the effects of underplatform dampers on the blades dynamics, still represents a major challenge today, due to the complex nature of the nonlinear forces at the interface, characterised by transitions between stick, slip, and separation conditions. The most common modelling approaches developed recently are based on the explicit FE model for the damper, and on a dense grid of 3D contact elements comprised of Jenkins elements, or on a single 2D microslip element on each surface. In this paper, a combination of the two approaches is proposed. A 3D microslip element, based on a modified Valanis model is proposed and a series of these elements are used to describe the contact interface. The proposed model and its predicting capabilities are then evaluated against a simplified blade-damper model, based on an underplatform damper test rig recently developed by the authors. A comparison with a more simplistic modelling approach based on macroslip contact elements, highlights the improved accuracy of the new model to predict the experimental nonlinear response.

Conference paper

Franz D, Salles L, Stapelfeldt S, 2017, Analysis of a Turbine Bladed Disk With Structural and Aerodynamic Mistuning, ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition

Conference paper

Brake MRW, Groß J, Lacayo RM, Salles L, Schwingshackl CW, Reuß P, Armand Jet al., 2017, Reduced order modeling of nonlinear structures with frictional interfaces, The Mechanics of Jointed Structures: Recent Research and Open Challenges for Developing Predictive Models for Structural Dynamics, Pages: 427-450, ISBN: 9783319568164

Book chapter

Lu Y, Zhao F, Salles L, Vandati Met al., 2017, AEROELASTIC ANALYSIS OF NREL WIND TURBINE, ASME Turbo Expo: Turbine Technical Conference and Exposition, Publisher: AMER SOC MECHANICAL ENGINEERS

Conference paper

Panunzio AM, Salles L, Schwingshackl CW, 2016, Uncertainty propagation for nonlinear vibrations: A non-intrusive approach, JOURNAL OF SOUND AND VIBRATION, Vol: 389, Pages: 309-325, ISSN: 0022-460X

Journal article

Salles L, Vahdati M, 2016, Comparison of Two Numerical Algorithms for Computing the Effects of Mistuning of Fan Flutter, ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition

Conference paper

Pesaresi L, Salles L, Jones A, Green JS, Schwingshackl CWet al., 2016, Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications, Mechanical Systems and Signal Processing, Vol: 85, Pages: 662-679, ISSN: 1096-1216

Underplatform dampers (UPD) are commonly used in aircraft engines to mitigate the risk of high-cycle fatiguefailure of turbine blades. The energy dissipated at the friction contact interface of the damper reduces the vibrationamplitude significantly, and the couplings of the blades can also lead to significant shifts of the resonance frequenciesof the bladed disk. The highly nonlinear behaviour of bladed disks constrained by UPDs requires an advancedmodelling approach to ensure that the correct damper geometry is selected during the design of the turbine, and thatno unexpected resonance frequencies and amplitudes will occur in operation. Approaches based on an explicit modelof the damper in combination with multi-harmonic balance solvers have emerged as a promising way to predict thenonlinear behaviour of UPDs correctly, however rigorous experimental validations are required before approaches ofthis type can be used with confidence.In this study, a nonlinear analysis based on an updated explicit damper model having different levels of detail isperformed, and the results are evaluated against a newly-developed UPD test rig. Detailed linear finite element modelsare used as input for the nonlinear analysis, allowing the inclusion of damper flexibility and inertia effects. The nonlinearfriction interface between the blades and the damper is described with a dense grid of 3D friction contact elementswhich allow accurate capturing of the underlying nonlinear mechanism that drives the global nonlinear behaviour. Theintroduced explicit damper model showed a great dependence on the correct contact pressure distribution. The use ofan accurate, measurement based, distribution, better matched the nonlinear dynamic behaviour of the test rig. Goodagreement with the measured frequency response data could only be reached when the zero harmonic term (constantterm) was included in the multi-harmonic expansion of the nonlinear problem, highlighting its importance when thecontact inter

Journal article

Armand J, Pesaresi L, Salles L, Schwingshackl CWet al., 2016, A Multiscale Approach for Nonlinear Dynamic Response Predictions With Fretting Wear, JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER-TRANSACTIONS OF THE ASME, Vol: 139, ISSN: 0742-4795

Journal article

Salles L, Staples B, Hoffmann N, Schwingshackl Cet al., 2016, Continuation techniques for analysis of whole aeroengine dynamics with imperfect bifurcations and isolated solutions, Nonlinear Dynamics, Vol: 86, Pages: 1897-1911, ISSN: 0924-090X

The analysis of whole engine rotordynamic models is an important element in the design of aerojet engines. The models include gyroscopic effects and allow for rubbing contact between rotor and stator components such as bladed discs and casing. Due to the nonlinearities inherent to the system, bifurcations in the frequency response may arise. Reliable and efficient methods to determine the bifurcation points and solution branches are required. For this purpose, a multi-harmonic balance approach is presented that allows a numerically efficient detection of bifurcation points and the calculation of both continuous and isolated branches of the frequency response functions. The method is applied to a test case derived from a commercial aeroengine. A bifurcation structure with continuous and isolated solution branches is observed and studied in this paper. The comparison with time marching based on simulations shows both accuracy and numerical efficiency of the newly developed approach.

Journal article

Papangelo A, Grolet A, Salles L, Hoffmann N, Ciavarella Met al., 2016, Snaking bifurcations in a self-excited oscillator chain with cyclic symmetry, Communications in Nonlinear Science and Numerical Simulation, Vol: 44, Pages: 108-119, ISSN: 1007-5704

Snaking bifurcations in a chain of mechanical oscillators are studied. The individual oscillators are weakly nonlinear and subject to self-excitation and subcritical Hopf-bifurcations with some parameter ranges yielding bistability. When the oscillators are coupled to their neighbours, snaking bifurcations result, corresponding to localised vibration states. The snaking patterns do seem to be more complex than in previously studied continuous systems, comprising a plethora of isolated branches and also a large number of similar but not identical states, originating from the weak coupling of the phases of the individual oscillators.

Journal article

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