Imperial College London

DrLoicSalles

Faculty of EngineeringDepartment of Mechanical Engineering

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Contact

 

l.salles Website

 
 
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Assistant

 

Mr Peter Higgs +44 (0)20 7594 7078

 
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Location

 

City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
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90 results found

Lasen M, Salles L, Dini D, Schwingshackl CWet al., 2023, Tribomechadynamics Challenge 2021: A Multi-harmonic Balance Analysis from Imperial College London, Pages: 79-82, ISSN: 2191-5644

This work presents the approach and results of the Dynamics Group at Imperial College in face of the Tribomechadynamics 2021 challenge. The challenge encourages to obtain the best blind prediction of a benchmark structure so that a transversal comparison, among the groups working in nonlinear studies, is done. The approach of the Dynamics Group consists in predicting the behaviour due to friction nonlinearities at the location where more energy dissipation is observed. The results show a slight softening in the contact with an overall shifting of the linear frequency of 2.6% and a damping increase of about 1.5% with respect to the linear damping. The effect of the contact is modest, given the lack of dissipated energy and the fact that geometric nonlinearities are not considered throughout this study.

Conference paper

Vizzaccaro A, Opreni A, Salles L, Frangi A, Touzé Cet al., 2023, Higher-Order Invariant Manifold Parametrisation of Geometrically Nonlinear Structures Modelled with Large Finite Element Models, Pages: 233-236, ISSN: 2191-5644

In this contribution we present a method to directly compute asymptotic expansion of invariant manifolds of large finite element models from physical coordinates and their reduced-order dynamics on the manifold. We show the accuracy of the reduction on selected models, exhibiting large rotations and internal resonances. The results obtained with the reduction are compared to full-order harmonic balance simulations obtained by continuation of the forced response. We also illustrate the low computational cost of the present implementation for increasing order of the asymptotic expansion and increasing number of degrees of freedom in the structure. The results presented show that the proposed methodology can reproduce extremely accurately the dynamics of the systems with a very low computational cost.

Conference paper

Denimal E, Chevalier R, Renson L, Salles Let al., 2022, Shape optimisation for friction dampers with stress constraint, 40th Conference and Exposition on Structural Dynamics, Publisher: Springer International Publishing, Pages: 65-73, ISSN: 2191-5644

Friction dampers are classically used in turbomachinery for bladed discs to control the levels of vibrations at resonance and limit the risk of fatigue failure. It consists of small metal components located under the platforms of the blades, which dissipate the vibratory energy through friction when a relative displacement between the blades and the damper appears. It is well known that the shape of such component has a strong influence on the damping properties and should be designed with a particular attention. With the arrival of additive manufacturing, new dedicated shapes for these dampers can be considered, determined with specific numerical methods as topological optimisation (TO). However, the presence of the contact nonlinearity challenges the use of traditional TO methods to minimise the vibration levels at resonance. In this work, the topology of the damper is parametrised with the moving morphable components (MMC) framework and optimised based on meta-modelling techniques: here kriging coupled with the efficient global optimisation (EGO) algorithm. The level of vibration at resonance is computed based on the harmonic balance method augmented with a constraint to aim directly for the resonant solution. It corresponds to the objective function to be minimised. Additionally, a mechanical constraint based on static stress analysis is also considered to propose reliable damper designs. Results demonstrate the efficiency of the method and show that damper geometries that meet the engineers’ requirements can be identified.

Conference paper

Suriyanarayanan V, Rendu Q, Vahdati M, Salles Let al., 2022, Effect of Manufacturing Tolerance in Flow Past a Compressor Blade, Publisher: ASME, ISSN: 0889-504X

Conference paper

Sun Y, Denimal E, Yuan J, Salles Let al., 2022, Geometric design of friction ring dampers in blisks using nonlinear modal analysis and Kriging surrogate model, Structural and Multidisciplinary Optimization, Vol: 65, ISSN: 1615-1488

Integrally bladed disks (blisk) have been widely used in the turbo-machinery industry due to its high aerodynamic performance and structural efficiency. A friction ring damper (FRD) is usually integrated in the system to improve its low damping. However, the design of the geometry of this FRD become complex and computationally expensive due to the strong nonlinearities from friction interfaces. In this work, we propose an efficient modelling strategy based on advanced nonlinear modal analysis and Kriging surrogate models to design and optimize the geometry of a 3D FRD attached to a high fidelity full-scale blisk. The 3D ring damper is parametrised with a few key geometrical parameters. The impact of each geometric parameter and their sensitivities to nonlinear dynamic response can be efficiently assessed using Kriging meta-modelling based on a few damped nonlinear normal modes. Results demonstrate that the damping performances of ring dampers can be substantially optimized through the proposed modelling strategy whilst key insights for the design of the rings are given. It is also demonstrated that the distribution of the contact normal load on the contact interfaces has a strong influence on the damping performances and can be effectively tuned via the upper surface geometry of the ring dampers.

Journal article

Denimal E, Renson L, Wong C, Salles Let al., 2022, Topology optimisation of friction under-platform dampers using moving morphable components and the efficient global optimization algorithm, Structural and Multidisciplinary Optimization: computer-aided optimal design of stressed solids and multidisciplinary systems, Vol: 65, Pages: 1-19, ISSN: 1615-147X

Under-platform dampers (UPDs) are traditionally used in aircraft engines to reduce the risk of high cycle fatigue. By introducing friction in the system, vibrations at resonance are damped. However, UDPs are also the source of nonlinear behaviours making the analysis and the design of such components complex. The shape of such friction dampers has a substantial impact on the damping performances, and topology optimisation is seldomly utilised—particularly for nonlinear structures. In the present work, we present a numerical approach to optimise the topology of friction dampers in order to minimise the vibration amplitude at a resonance peak. The proposed approach is based on the moving morphable components framework to parametrise the damper topology, and the efficient global optimisation algorithm is employed for the optimisation. The results demonstrate the relevance of such an approach for the optimisation of nonlinear vibrations in the presence of friction. New efficient damper geometries are identified in a few iterations of the algorithm, illustrating the efficiency of the approach. Results show that the most efficient geometry divides the vibration amplitude at resonance by 3, corresponds to a lower mass (80%) and a smaller frequency shift compared to the non-optimised case. More generally, the different geometries are analysed and tools for clustering are proposed. Different clusters are identified and compared. Thus, more general conclusions can be obtained. More specifically, the most efficient geometries correspond to geometries that reduce the mass of the damper and increase the length of the contact surface. Physically, it corresponds to a reduction of the initial normal contact pressure, which implies that the contact points enter stick/slip earlier, bringing more damping. The results show how topology optimisation can be employed for nonlinear vibrations to identify efficient layouts for components.

Journal article

Yuan J, Sun Y, Schwingshackl C, Salles Let al., 2022, Computation of damped nonlinear normal modes for large scale nonlinear systems in a self-adaptive modal subspace, Mechanical Systems and Signal Processing, Vol: 162, Pages: 1-16, ISSN: 0888-3270

The concept of nonlinear modes has been proved useful to interpret a wide class of nonlinear phenomena in mechanical systems such as energy dependent vibrations and internal resonance. Although this concept was successfully applied to some small scale structures, the computational cost for large-scale nonlinear models remains an important issue that prevents the wider spread of this nonlinear analysis tool in industry. To address this challenge, in this paper, we describe an advanced adaptive reduced order modelling (ROM) technique to compute the damped nonlinear modes for a large scale nonlinear system with frictional interfaces. The principle of this new ROM technique is that it enables the nonlinear modes to be computed in a reduced self-adaptive modal subspace while maintaining similar accuracy to classical reduction techniques. The size of such self-adaptive subspace is only proportional to the number of active slipping nodes in friction interfaces leading to a significant reduction of computing time especially when the friction interface is in a micro-slip motion. The procedure of implementing this adaptive ROM into the computation of steady state damped nonlinear mode is presented. The case of an industrial-scale fan blade system with dovetail joints in aero-engines is studied. Damped nonlinear normal modes based on the concept of extended periodic motion is successfully calculated using the proposed adaptive ROM technique. A comparison between adaptive ROM with the classical Craig-Bampton method highlights the capability of the adaptive ROM to accurately capture the resonant frequency and modal damping ratio while achieving a speedup up to 120. The obtained nonlinear modes from adaptive ROM are also validated by comparing its synthesized forced response against the directly computed ones using Craig-Bampton (CB) method. The study further shows the reconstructed forced frequency response from damped nonlinear modes are able to accurately capture reference for

Journal article

Yuan J, Salles L, Schwingshackl C, 2022, Effects of the geometry of friction interfaces on the nonlinear dynamics of jointed structure, Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics 2022, Publisher: Springer International Publishing, Pages: 67-74, ISSN: 2191-5644

Conference paper

Zhu Y-P, Yuan J, Lang ZQ, Schwingshackl CW, Salles L, Kadirkamanathan Vet al., 2021, The data-driven surrogate model-based dynamic design of aeroengine fan systems, Journal of Engineering for Gas Turbines and Power: Transactions of the ASME, Vol: 143, Pages: 1-8, ISSN: 0742-4795

High-cycle fatigue failures of fan blade systems due to vibrational loads are of great concern in the design of aeroengines, where energy dissipation by the relative frictional motion in the dovetail joints provides the main damping to mitigate the vibrations. The performance of such a frictional damping can be enhanced by suitable coatings. However, the analysis and design of coated joint roots of gas turbine fan blades are computationally expensive due to strong contact friction nonlinearities and also complex physics involved in the dovetail. In this study, a data-driven surrogate model, known as the Nonlinear in Parameter AutoRegressive with eXegenous input (NP-ARX) model, is introduced to circumvent the difficulties in the analysis and design of fan systems. The NP-ARX model is a linear input–output model, where the model coefficients are nonlinear functions of the design parameters of interest, such that the Frequency Response Function (FRF) can be directly obtained and used in the system analysis and design. A simplified fan-bladed disc system is considered as the test case. The results show that using the data-driven surrogate model, an efficient and accurate design of aeroengine fan systems can be achieved. The approach is expected to be extended to solve the analysis and design problems of many other complex systems.

Journal article

Vizzaccaro A, Shen Y, Salles L, Blahos J, Touze Cet al., 2021, Direct computation of nonlinear mapping via normal form for reduced-order models of finite element nonlinear structures, Computer Methods in Applied Mechanics and Engineering, Vol: 384, ISSN: 0045-7825

The direct computation of the third-order normal form for a geometrically nonlinear structure discretised with the finite element (FE) method, is detailed. The procedure allows to define a nonlinear mapping in order to derive accurate reduced-order models (ROM) relying on invariant manifold theory. The proposed reduction strategy is direct and simulation free, in the sense that it allows to pass from physical coordinates (FE nodes) to normal coordinates, describing the dynamics in an invariant-based span of the phase space. The number of master modes for the ROM is not a priori limited since a complete change of coordinate is proposed. The underlying theory ensures the quality of the predictions thanks to the invariance property of the reduced subspace, together with their curvatures in phase space that accounts for the non-resonant nonlinear couplings. The method is applied to a beam discretised with 3D elements and shows its ability in recovering internal resonance at high energy. Then a fan blade model is investigated and the correct prediction given by the ROMs are assessed and discussed. A method is proposed to approximate an aggregate value for the damping, that takes into account the damping coefficients of all the slave modes, and also using the Rayleigh damping model as input. Frequency–response curves for the beam and the blades are then exhibited, showing the accuracy of the proposed method.

Journal article

Vizzaccaro A, Opreni A, Salles L, Frangi A, Touzé Cet al., 2021, High order direct parametrisation of invariant manifolds for model order reduction of finite element structures: application to large amplitude vibrations and uncovering of a folding point, Publisher: arXiv

This paper investigates model-order reduction methods for geometricallynonlinear structures. The parametrisation method of invariant manifolds is usedand adapted to the case of mechanical systems expressed in the physical basis,so that the technique is directly applicable to problems discretised by thefinite element method. Two nonlinear mappings, respectively related todisplacement and velocity, are introduced, and the link between the two is madeexplicit at arbitrary order of expansion. The same development is performed onthe reduced-order dynamics which is computed at generic order following thedifferent styles of parametrisation. More specifically, three different stylesare introduced and commented: the graph style, the complex normal form styleand the real normal form style. These developments allow making betterconnections with earlier works using these parametrisation methods. Thetechnique is then applied to three different examples. A clamped-clamped archwith increasing curvature is first used to show an example of a system with asoftening behaviour turning to hardening at larger amplitudes, which can bereplicated with a single mode reduction. Secondly, the case of a cantileverbeam is investigated. It is shown that the invariant manifold of the first modeshows a folding point at large amplitudes which is not connected to an internalresonance. This exemplifies the failure of the graph style due to the foldingpoint, whereas the normal form style is able to pass over the folding. Finally,A MEMS micromirror undergoing large rotations is used to show the importance ofusing high-order expansions on an industrial example.

Working paper

Yuan J, Fantetti A, Denimal E, Bhatnagar S, Pesaresi L, Schwingshackl C, Salles Let al., 2021, Propagation of friction parameter uncertainties in the nonlinear dynamic response of turbine blades with underplatform dampers, Mechanical Systems and Signal Processing, Vol: 156, Pages: 1-19, ISSN: 0888-3270

Underplatform dampers are widely used in turbomachinery to mitigate structural vibrations by means of friction dissipation at the interfaces. The modelling of such friction dissipation is challenging because of the high variability observed in experimental measurements of contact parameters. Although this variability is not commonly accounted for in state-of-the-art numerical solvers, probabilistic approaches can be implemented to include it in dynamics simulations in order to significantly improve the estimation of the damper performance. The aim of this work is to obtain uncertainty bands in the dynamic response of turbine blades equipped with dampers by including the variability observed in interfacial contact parameters. This variability is experimentally quantified from a friction rig and used to generate uncertainty bands by combining a deterministic state-of-the-art numerical solver with stochastic Polynomial Chaos Expansion (PCE) models. The bands thus obtained are validated against experimental data from an underplatform damper test rig. In addition, the PCEs are also employed to perform a variance-based global sensitivity analysis to quantify the influence of contact parameters on the variation in the nonlinear dynamic response via Sobol indices. The analysis highlights that the influence of each contact parameter in vibration amplitude strongly varies over the frequency range, and that Sobol indices can be effectively used to analyse uncertainties associated to structures with friction interfaces providing valuable insights into the physics of such complex nonlinear systems.

Journal article

Sun Y, Yuan J, Vizzaccaro A, Salles Let al., 2021, Comparison of different methodologies for the computation of damped nonlinear normal modes and resonance prediction of systems with non-conservative nonlinearities, Nonlinear Dynamics, Vol: 104, Pages: 3077-3107, ISSN: 0924-090X

The nonlinear modes of a non-conservative nonlinear system are sometimes referred to as damped nonlinear normal modes (dNNMs). Because of the non-conservative characteristics, the dNNMs are no longer periodic. To compute non-periodic dNNMs using classic methods for periodic problems, two concepts have been developed in the last two decades: complex nonlinear mode (CNM) and extended periodic motion concept (EPMC). A critical assessment of these two concepts applied to different types of non-conservative nonlinearities and industrial full-scale structures has not been thoroughly investigated yet. Furthermore, there exist two emerging techniques which aim at predicting the resonant solutions of a nonlinear forced response using the dNNMs: extended energy balance method (E-EBM) and nonlinear modal synthesis (NMS). A detailed assessment between these two techniques has been rarely attempted in the literature. Therefore, in this work, a comprehensive comparison between CNM and EPMC is provided through two illustrative systems and one engineering application. The EPMC with an alternative damping assumption is also derived and compared with the original EPMC and CNM. The advantages and limitations of the CNM and EPMC are critically discussed. In addition, the resonant solutions are predicted based on the dNNMs using both E-EBM and NMS. The accuracies of the predicted resonances are also discussed in detail.

Journal article

Niedergesass B, Papangelo A, Grolet A, Vizzaccaro A, Fontanela F, Salles L, Sievers AJ, Hoffmann Net al., 2021, Experimental observations of nonlinear vibration localization in a cyclic chain of weakly coupled nonlinear oscillators, Journal of Sound and Vibration, Vol: 497, Pages: 1-10, ISSN: 0022-460X

Experimental results on nonlinear vibration localization in a cyclic chain of weakly coupled oscillators with clearance nonlinearity are reported. Numerical modelling and analysis complements the experimental study. A reduced order model is derived and numerical analysis based on the harmonic balance method demonstrates the existence of multiple classes of stable spatially localized nonlinear vibration states. The experiments agree very well with the numerical results. The findings suggest that vibration localization due to fundamentally nonlinear effects may also arise in mechanical structures with relevance in engineering.

Journal article

Sun Y, Yuan J, Denimal E, Salles Let al., 2021, Nonlinear modal analysis of frictional ring damper for compressor blisk, Journal of Engineering for Gas Turbines and Power: Transactions of the ASME, Vol: 143, Pages: 1-8, ISSN: 0742-4795

The use of integrally blisk is becoming popular because of the advantages in aerodynamic efficiency and mass reduction. However, in an integrally blisk, the lack of the contact interface leads to a low structural damping compared to an assembled bladed disk. One emerging damping technique for the integrally blisk is based on the use of friction ring damper, which exploits the contact interfaces at the underneath of the disk. In this paper, three different geometries of the ring dampers are investigated for damping enhancement of a blisk. A full-scale compressor blisk is considered as a case study where a node-to-node contact model is used to compute the contact forces. The dynamic behavior of the blisk with the ring damper is investigated by using nonlinear modal analysis, which allows a direct estimation of the damping generated by the friction interface. The damping performance for the different ring dampers is evaluated and compared. It appears that the damping efficiency as well as the shift in the resonant frequency for the different geometries is highly related to the nodal diameter and contact pressure/gap distributed within contact interface. The geometry of the ring damper has significant impact on the damping performance.

Journal article

Yuan J, Schwingshackl C, wong C, Salles Let al., 2021, On an improved adaptive reduced order model for the computation of steady state vibrations in large-scale non-conservative system with friction joints, Nonlinear Dynamics, Vol: 103, Pages: 3283-3300, ISSN: 0924-090X

Joints are commonly used in many large-scale engineering systems to ease assembly, and ensure structural integrity and effective load transmission. Most joints are designed around friction interfaces, which can transmit large static forces, but tend to introduce stick-slip transition during vibrations, leading to a nonlinear dynamic system. Tools for the complex numerical prediction of such nonlinear systems are available today, but their use for large-scale applications is regularly prevented by high computational cost. To address this issue, a novel adaptive reduced-order model (ROM) has recently been developed, significantly decreasing the computational time for such high fidelity simulations. Although highly effective, significant improvements to the proposed approach is presented and demonstrated in this paper, further increasing the efficiency of the ROM. An energy-based error estimator was developed and integrated into the nonlinear spectral analysis, leading to a significantly higher computational speed by removing insignificant static modes from the stuck contact nodes in the original reduced basis, and improving the computational accuracy by eliminating numerical noise. The effectiveness of the new approach was shown on an industrial-scale fan blades system with a dovetail joints, showing that the improved adaptive method can be 2–3 times more computationally efficient than the original adaptive method especially at high excitation levels but also effectively improve the accuracy of the original method.

Journal article

Fontanela F, Vizzaccaro A, Auvray J, Niedergesäß B, Grolet A, Salles L, Hoffmann Net al., 2021, Nonlinear vibration localisation in a symmetric system of two coupled beams, Nonlinear Dynamics, Vol: 103, Pages: 3417-3428, ISSN: 0924-090X

We report nonlinear vibration localisation in a system of two symmetric weakly coupled nonlinear oscillators. A two degree-of-freedom model with piecewise linear stiffness shows bifurcations to localised solutions. An experimental investigation employing two weakly coupled beams touching against stoppers for large vibration amplitudes confirms the nonlinear localisation.

Journal article

Shen Y, Vizzaccaro A, Kesmia N, Yu T, Salles L, Thomas O, Touze Cet al., 2021, Comparison of reduction methods for finite element geometrically nonlinear beam structures, Vibration, Vol: 4, Pages: 175-204, ISSN: 2571-631X

The aim of this contribution is to present numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures. Three different methods are compared: the implicit condensation and expansion (ICE), the quadratic manifold computed from modal derivatives (MD), and the direct normal form (DNF) procedure, the latter expressing the reduced dynamics in an invariant-based span of the phase space. The methods are first presented in order to underline their common points and differences, highlighting in particular that ICE and MD use reduction subspaces that are not invariant. A simple analytical example is then used in order to analyze how the different treatments of quadratic nonlinearities by the three methods can affect the predictions. Finally, three beam examples are used to emphasize the ability of the methods to handle curvature (on a curved beam), 1:1 internal resonance (on a clamped-clamped beam with two polarizations), and inertia nonlinearity (on a cantilever beam).

Journal article

Denimal E, Wong C, Salles L, Pesaresi Let al., 2021, On the efficiency of a conical underplatform damper for turbines, Journal of Engineering for Gas Turbines and Power: Transactions of the ASME, Vol: 143, Pages: 1-9, ISSN: 0742-4795

Underplatform dampers (UPDs) are commonly used in aircraft engines to limit the risk of high-cycle fatigue of turbine blades. The latter is located in a groove between two consecutive blades. The dry friction contact interface between the damper and the blades dissipates energy and so reduces the vibration amplitudes. Two common geometries of dampers are used nowadays, namely wedge and cylindrical dampers, but their efficiency is limited when the blades have an in-phase motion (or a motion close to it), since the damper tends to have a pure rolling motion. The objective of this study is to analyze a new damper geometry, based on a conical shape, which prevents from this pure rolling motion of the damper and ensures a high kinematic slip. The objective of this study is to demonstrate the damping efficiency of this geometry. Hence, in a first part, the kinematic slip is approximated with analytical considerations. Then, a nonlinear dynamic analysis is performed, and the damping efficiency of this new geometry is compared to the wedge and the cylindrical geometries. The results demonstrate that the conical damper has a high damping capacity and is more efficient and more robust than the two others.

Journal article

Denimal E, El Haddad F, Wong C, Salles Let al., 2021, Topological optimization of under-platform dampers with moving morphable components and global optimization algorithm for nonlinear frequency response, Journal of Engineering for Gas Turbines and Power: Transactions of the ASME, Vol: 143, Pages: 1-9, ISSN: 0742-4795

To limit the risk of high cycle fatigue, underplatform dampers (UDPs) are traditionally used in aircraft engines to control the level of vibration. Many studies demonstrate the impact of the geometry of the damper on its efficiency, thus the consideration of topological optimization (TO) to find the best layout of the damper seems natural. Because of the nonlinear behavior of the structure due to the friction contact interface, classical methods of TO are not usable. This study proposes to optimize the layout of an UDP to reduce the level of nonlinear vibrations computed with the multiharmonic balance method (MHBM). The approach of TO employed is based on the moving morphable components (MMC) framework together with the Kriging and the efficient global optimization algorithm to solve the optimization problem. The results show that the level of vibration of the structure can be reduced to 30% and allow for the identification of different efficient geometries.

Journal article

Tufekci M, Rendu Q, Yuan J, Dear JP, Salles L, Cherednichenko AVet al., 2021, Stress and modal analysis of a rotating blade and the effects of nonlocality, ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition, Publisher: American Society of Mechanical Engineers, Pages: 1-12

This study focuses on the quasi-static stress and modal analyses of a rotor blade by using classical and nonlocal elasticity approaches. The finite element method with an additional numerical integration process is used to evaluate the integral equation of nonlocal contionuum mechanics. The blade is assumed to be made of a linear elastic material of weak nonlocal characteristic. Such materials can be composites, metallic foams, nanophased alloys etc. A full-scale fan blade model is chosen as the test case to represent the rotor blade for a modern high bypass ratio turbofan engine. The boundary conditions and loads are chosen based on the steady-state cruising operating conditions of such blades. The nonlocal stresses are calculated by processing the calculated local stresses. To calculate the nonlocal stresses, the integral form of nonlocal elasticity is employed in the discretised domain. The results of the two cases are compared and discussed.

Conference paper

Sun Y, Yuan J, Denimal E, Salles Let al., 2021, Nonlinear Modal Analysis of Frictional Ring Damper for Compressor Blisk, ASME Turbo expo 2020

Conference paper

Vizzaccaro A, Givois A, Longobardi P, Shen Y, Deü J-F, Salles L, Touzé C, Thomas Oet al., 2020, Non-intrusive reduced order modelling for the dynamics of geometrically nonlinear flat structures using three-dimensional finite elements, Computational Mechanics, Vol: 66, Pages: 1293-1319, ISSN: 0178-7675

Non-intrusive methods have been used since two decades to derive reduced-order models for geometrically nonlinear structures, with a particular emphasis on the so-called STiffness Evaluation Procedure (STEP), relying on the static application of prescribed displacements in a finite-element context. We show that a particularly slow convergence of the modal expansion is observed when applying the method with 3D elements, because of nonlinear couplings occurring with very high frequency modes involving 3D thickness deformations. Focusing on the case of flat structures, we first show by computing all the modes of the structure that a converged solution can be exhibited by using either static condensation or normal form theory. We then show that static modal derivatives provide the same solution with fewer calculations. Finally, we propose a modified STEP, where the prescribed displacements are imposed solely on specific degrees of freedom of the structure, and show that this adjustment also provides efficiently a converged solution.

Journal article

Vizzaccaro A, Salles L, Touzé C, 2020, Comparison of nonlinear mappings for reduced-order modellingof vibrating structures: normal form theory and quadraticmanifold method with modal derivatives, Nonlinear Dynamics, Vol: 103, Pages: 3335-3370, ISSN: 0924-090X

The objective of this contribution is to compare two methods proposed recently in order to build efficient reduced-order models for geometrically nonlinear structures. The first method relies on the normal form theory that allows one to obtain a nonlinear change of coordinates for expressing the reduced-order dynamics in an invariant-based span of the phase space. The second method is the modal derivative (MD) approach, and more specifically the quadratic manifold defined in order to derive a second-order nonlinear change of coordinates. Both methods share a common point of view, willing to introduce a nonlinear mapping to better define a reduced-order model that could take more properly into account the nonlinear restoring forces. However the calculation methods are different and the quadratic manifold approach has not the in variance property embedded in its definition. Modal derivatives and static modal derivatives are investigated, and their distinctive features in the treatment of the quadratic nonlinearity is underlined.Assuming a slow/fast decomposition allows understanding how the three methods tend to share equivalent properties. While they give proper estimations for flat symmetric structures having a specific shape of nonlinearities and a clear slow/fast decomposition between flexural and in-plane modes, the treatment of the quadratic nonlinearity makes the predictions different in the case of curved structures such as arches and shells. In the more general case, normal form approach appears preferable since it allows correct predictions of a number of important nonlinear features,including for example the hardening/softening behaviour, whatever the relationships between slave and master coordinates are.

Journal article

Sun Y, Vizzaccaro A, Yuan J, Salles Let al., 2020, An extended energy balance method for resonance prediction in forced response of systems with non-conservative nonlinearities using damped nonlinear normal mode, Nonlinear Dynamics, Vol: 103, Pages: 3315-3333, ISSN: 0924-090X

The dynamic analysis of systems with nonlinearities has become an important topic in many engineering fields. Apart from the forced response analyses, nonlinear modal analysis has been successfully extended to such non-conservative systems thanks to the definition of damped nonlinear normal modes. The energy balance method is a tool that permits to directly predict resonances for a conservative system with nonlinearities from its nonlinear modes. In this work, the energy balance method is extended to systems with non-conservative nonlinearities using the concept of the damped nonlinear normal mode and its application in a full-scale engineering structure. This extended method consists of a balance between the energy loss from the internal damping, the energy transferred from the external excitation and the energy exchanged with the non-conservative nonlinear force. The method assumes that the solution of the forced response at resonance bears resemblance to that of the damped nonlinear normal mode. A simplistic model and full-scale structure with dissipative nonlinearities and a simplistic model showing self-excited vibration are tested using the method. In each test case, resonances are predicted efficiently and the computed force–amplitude curves show a great agreement with the forced responses. In addition, the self-excited solutions and isolas in forced responses can be effectively detected and identified. The accuracy and limitations of the method have been critically discussed in this work.

Journal article

Sun Y, Yuan J, Pesaresi L, Denimal E, Salles Let al., 2020, Parametric study and uncertainty quantification of the nonlinear modal properties of frictional dampers, Journal of Vibration and Acoustics, ISSN: 0739-3717

A numerical methodology is described to study the influ-ence of the contact location and contact condition of fric-tion damper in aircraft engines. A simplified beam model isused to represent the blade for the preliminary design stage.The frictional damper is numerically analysed based on twoparameters, contact angle and vertical position of the plat-form. The nonlinear modal analysis is used to investigatethe nonlinear dynamic behaviour and damping performancesof the system. Harmonic balanced method with continua-tion technique is used to compute the nonlinear modes for alarge range of energy levels. Using such a modelling strat-egy, modal damping ratio, resonant amplitude and resonantfrequency are directly and efficiently computed for a rangeof design parameters. Monte Carlo simulations togetherwith Latin hypercube sampling is then used to assess the ro-bustness of the frictional damper, whose contact parametersinvolve much uncertainties due to manufacturing toleranceand also wear effects. The influences of those two parame-ter are obtained and the best performances of the frictionaldamper can be achieved when the contact angle is around25◦-30◦. The vertical position of the platform is highlymode-dependent and other design considerations needs to beaccounted. The results have been proved that the uncertain-ties involved contact surfaces do not have significant effects∗Address all correspondence for other issues to this author.on the performance of frictional damper.

Journal article

Tufekci M, Mace T, Özkal B, Dear J, Schwingshackl C, Salles Let al., 2020, Nonlinear dynamic behaviour of a nanocomposite: epoxy reinforced with fumed silica nanoparticles, XXV ICTAM

This study focuses on identification and modelling of vibration characteristics of a nanocomposite; an epoxy resin as thematrix and fumed silica as the reinforcement. The resin alone is manufactured and characterised. Using the same methodology,the manufacturing and characterisation of the silica-reinforced nanocomposite are performed. Following the manufacturing and theexperimental characterisation process, a nonlinear model is built to represent characterised behaviour. The model is validated by aseparate test case which is also an experimental technique to extract the damping characteristics of a structure.

Conference paper

Yuan J, Salles L, El Haddad F, Wong Cet al., 2020, An adaptive component mode synthesis method for dynamic analysis of jointed structure with contact friction interfaces, Computers and Structures, Vol: 229, ISSN: 0045-7949

Component model synthesis (CMS) has been widely used for model order reduction in dynamic analysis of jointed structures with localized non-linearities. The main drawback of these CMS methods is that their computational efficiency largely depends on the size of contact friction interfaces. This work proposes an adaptive reduction approach to improve these CMS based reduction methods in the application to the assembled structure with frictional interfaces. The main idea of this method is that, instead of retaining the whole frictional interface DOFs in the reduced model, only those DOFs in a slipping or separating condition are retained. This would significantly reduce the size of classical CMS based reduced models for dynamical analysis of jointed structure with micro-slip motion, leading to an impressive computational saving. This novel approach is based on a reformulated dynamic system that consists of a underlying linearised system and an adaptive internal variable to account the effects of non-linear contact friction force on the interface. The paper also describes the detailed implementation of the proposed approach with harmonic balance method for non-linear spectral analysis, where a new updating algorithm is put forward to enable the size of the reduced model can be automatically updated according to the contact condition of interface nodes. Two distinct FE joint models are used to validate the proposed method. It is demonstrated that the new approach can achieve a considerable computing speed-up comparing to the classic CMS approach while maintain the same accuracy.

Journal article

Denimal E, El Haddad F, Wong C, Salles Let al., 2020, Topological optimization of under-platform dampers with moving morphable components and global optimization algorithm for nonlinear frequency response

To limit the risk of High Cycle Fatigue, underplatform dampers are traditionally used in aircraft engines to control the level of vibration. Many studies demonstrate the impact of the geometry of the damper on its efficiency, thus the consideration of topological optimization to find the best layout of the damper seems natural. Because of the nonlinear behaviour of the structure due to the friction contact interface, classical methods of topological optimization are not usable. The present study proposes to optimize the layout of an underplatform damper to reduce the level of nonlinear vibrations computed with the Multi-Harmonic Balance Method. The approach of topological optimization employed is based on the Moving Morphable Components framework together with the Kriging and the Efficient Global Optimization algorithm to solve the optimization problem. The results show that the level of vibration of the structure can be reduced of 30% and allow for the identification of different efficient geometries.

Conference paper

Venkatesh S, Suzuki K, Vahdati M, Salles L, Rendu Qet al., 2020, Effect of geometric uncertainty on a one stage transonic compressor of an industrial gas turbine

The geometrical uncertainties can result in flow asymmetry around the annulus of compressor which in turn can detrimentally affect on the compressor stability and performance. Typically these uncertainties arise as a consequence of in-service degradation and/or manufacturing tolerance, both of which have been dealt with in this paper. The paper deals with effects of leading edge damage and tip gap on rotor blades. It was found that the chord-wise damage is more critical than radial damage. It was found that a zigzag pattern of arranging the damaged rotor blades (i.e. most damaged blades between two least damaged blades) would give the best possible performance and stability when performing maintenance and overhauling while a sinusoidal pattern of arrangement had the worst performance and stability. This behaviour of zigzag arrangement of random damaged blades is consonant with the behaviour of zigzag arrangement in random tip gaps. It is also shown in this work that the level of damage has a bigger impact on the compressor performance and stability than the number of damaged blades.

Conference paper

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