Journal articles: 'Non smooth contact dynamics'

1

Jean, M. "The non-smooth contact dynamics method." Computer Methods in Applied Mechanics and Engineering 177, no. 3-4 (July 1999): 235–57. http://dx.doi.org/10.1016/s0045-7825(98)00383-1.

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Jean, Michel, Vincent Acary, and Yann Monerie. "Non-smooth contact dynamics approach of cohesive materials." Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 359, no. 1789 (December 15, 2001): 2497–518. http://dx.doi.org/10.1098/rsta.2001.0906.

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Fancello, Matteo, Marco Morandini, and Pierangelo Masarati. "Helicopter Rotor Sailing by Non-Smooth Dynamics Co-Simulation." Archive of Mechanical Engineering 61, no. 2 (August 15, 2014): 253–68. http://dx.doi.org/10.2478/meceng-2014-0015.

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Abstract This paper presents the application of a co-simulation approach for the simulation of frictional contact in general-purpose multibody dynamics to a rotorcraft dynamics problem. The proposed approach is based on the co-simulation of a main problem, which is described and solved as a set of differential algebraic equations, with a subproblem that is characterized by nonsmooth dynamics events and solved using a timestepping technique. The implementation and validation of the formulation is presented. The method is applied to the analysis of the droop and anti-flap contacts of helicopter rotor blades. Simulations focusing on the problem of blade sailing are conducted to understand the behavior and assess the validity of the method. For this purpose, the results obtained using a contact model based on Hertzian reaction forces at the interface are compared with those of the proposed approach.

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Caux, S., and R. Zapata. "Modeling and control of biped robot dynamics." Robotica 17, no. 4 (July 1999): 413–26. http://dx.doi.org/10.1017/s0263574799001411.

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This paper addresses the problem of modeling biped dynamics and the use of such models for the control of walking, running and jumping robots. We describe two approaches to dynamic modeling: the basic Lagrange approach and the non-regular dynamic approach. The new non-regular dynamic approach takes into account discontinuities due to rigid contact between punctual feet and the ground without computing the exact impact time. The contact is close to the physical situation given by non-linear laws (impenetrability, non-smooth contact and real friction cone). Contact dynamics can be well managed with an accurate dynamic model that respects energy consistency during all the phases encountered during a step (0, 1 or 2 contacts). With this model, we can first study the equilibrum of a biped standing on one foot by a linearisation method. In the second stage, the unified modelized equation is used to establish a general control frame based on non-regular dynamical decoupling. A comparison is made and some simulation results are given with a two degree of freedom planar biped robot.

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Haslinger, J., G. Offner, and M. Sopouch. "Non-smooth dynamics of coil contact in valve springs." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 94, no. 11 (October 20, 2014): 957–67. http://dx.doi.org/10.1002/zamm.201300254.

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Müller, Stefan, and Peter Spaeth. "Topological contact dynamics II: Topological automorphisms, contact homeomorphisms, and non-smooth contact dynamical systems." Transactions of the American Mathematical Society 366, no. 9 (December 3, 2013): 5009–41. http://dx.doi.org/10.1090/s0002-9947-2013-06123-5.

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Nguyen, Vo Anh Thuong, Stéphane Abide, Mikaël Barboteu, and Serge Dumont. "An improved normal compliance method for non-smooth contact dynamics." Banach Center Publications 127 (2024): 191–217. http://dx.doi.org/10.4064/bc127-9.

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Koch, Michael W., and Sigrid Leyendecker. "Structure Preserving Simulation of Monopedal Jumping." Archive of Mechanical Engineering 60, no. 1 (March 1, 2013): 127–46. http://dx.doi.org/10.2478/meceng-2013-0008.

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The human environment consists of a large variety of mechanical and biomechanical systems in which different types of contact can occur. In this work, we consider a monopedal jumper modelled as a three-dimensional rigid multibody system with contact and simulate its dynamics using a structure preserving method. The applied mechanical integrator is based on a constrained version of the Lagranged’Alembert principle. The resulting variational integrator preserves the symplecticity and momentum maps of the multibody dynamics. To ensure the structure preservation and the geometric correctness, we solve the non-smooth problem including the computation of the contact configuration, time and force instead of relying on a smooth approximation of the contact problem via a penalty potential. In addition to the formulation of non-smooth problems in forward dynamic simulations, we are interested in the optimal control of the monopedal high jump. The optimal control problem is solved using a direct transcription method transforming it into a constrained optimisation problem, see [14].

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Beatini, Valentina, Gianni Royer-Carfagni, and Alessandro Tasora. "A regularized non-smooth contact dynamics approach for architectural masonry structures." Computers & Structures 187 (July 2017): 88–100. http://dx.doi.org/10.1016/j.compstruc.2017.02.002.

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Zhang, Kaiming, Xudong Zheng, Zhang Chen, Bin Liang, Tianshu Wang, and Qi Wang. "Non-smooth dynamic modeling and simulation of an unmanned bicycle on a curved pavement." Applied Mathematics and Mechanics 43, no. 1 (January 2022): 93–112. http://dx.doi.org/10.1007/s10483-022-2811-5.

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AbstractThe non-smooth dynamic model of an unmanned bicycle is established to study the contact-separate and stick-slip non-smooth phenomena between wheels and the ground. According to the Carvallo-Whipple configuration, the unmanned bicycle is reduced to four rigid bodies, namely, rear wheel, rear frame, front fork, and front wheel, which are connected by perfect revolute joints. The interaction between each wheel and the ground is simplified as the normal contact force and the friction force at the contact point, and these forces are described by the Hunt-Crossley contact force model and the LuGre friction force model, respectively. According to the characteristics of flat and curved pavements, calculation methods for contact forces and their generalized forces are presented. The dynamics of the system is modeled by the Lagrange equations of the first kind, a numerical solution algorithm of the dynamic equations is presented, and the Baumgarte stabilization method is used to restrict the drift of the constraints. The correctness of the dynamic model and the numerical algorithm is verified in comparison with the previous studies. The feasibility of the proposed model is demonstrated by simulations under different motion states.

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Abide, Stéphane, Mikaël Barboteu, Soufiane Cherkaoui, and Serge Dumont. "A semi-smooth Newton and Primal–Dual Active Set method for Non-Smooth Contact Dynamics." Computer Methods in Applied Mechanics and Engineering 387 (December 2021): 114153. http://dx.doi.org/10.1016/j.cma.2021.114153.

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Larionov, Egor, Ye Fan, and Dinesh K. Pai. "Frictional Contact on Smooth Elastic Solids." ACM Transactions on Graphics 40, no. 2 (April 20, 2021): 1–17. http://dx.doi.org/10.1145/3446663.

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Frictional contact between deformable elastic objects remains a difficult simulation problem in computer graphics. Traditionally, contact has been resolved using sophisticated collision detection schemes and methods that build on the assumption that contact happens between polygons. While polygonal surfaces are an efficient representation for solids, they lack some intrinsic properties that are important for contact resolution. Generally, polygonal surfaces are not equipped with an intrinsic inside and outside partitioning or a smooth distance field close to the surface. Here we propose a new method for resolving frictional contacts against deforming implicit surface representations that addresses these problems. We augment a moving least squares (MLS) implicit surface formulation with a local kernel for resolving contacts, and develop a simple parallel transport approximation to enable transfer of frictional impulses. Our variational formulation of dynamics and elasticity enables us to naturally include contact constraints, which are resolved as one Newton-Raphson solve with linear inequality constraints. We extend this formulation by forwarding friction impulses from one time step to the next, used as external forces in the elasticity solve. This maintains the decoupling of friction from elasticity thus allowing for different solvers to be used in each step. In addition, we develop a variation of staggered projections, that relies solely on a non-linear optimization without constraints and does not require a discretization of the friction cone. Our results compare favorably to a popular industrial elasticity solver (used for visual effects), as well as recent academic work in frictional contact, both of which rely on polygons for contact resolution. We present examples of coupling between rigid bodies, cloth and elastic solids.

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Mora, Karin, Chris Budd, Paul Glendinning, and Patrick Keogh. "Non-smooth Hopf-type bifurcations arising from impact–friction contact events in rotating machinery." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2171 (November 8, 2014): 20140490. http://dx.doi.org/10.1098/rspa.2014.0490.

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We analyse the novel dynamics arising in a nonlinear rotor dynamic system by investigating the discontinuity-induced bifurcations corresponding to collisions with the rotor housing (touchdown bearing surface interactions). The simplified Föppl/Jeffcott rotor with clearance and mass unbalance is modelled by a two degree of freedom impact–friction oscillator, as appropriate for a rigid rotor levitated by magnetic bearings. Two types of motion observed in experiments are of interest in this paper: no contact and repeated instantaneous contact. We study how these are affected by damping and stiffness present in the system using analytical and numerical piecewise-smooth dynamical systems methods. By studying the impact map, we show that these types of motion arise at a novel non-smooth Hopf-type bifurcation from a boundary equilibrium bifurcation point for certain parameter values. A local analysis of this bifurcation point allows us a complete understanding of this behaviour in a general setting. The analysis identifies criteria for the existence of such smooth and non-smooth bifurcations, which is an essential step towards achieving reliable and robust controllers that can take compensating action.

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Lozovskiy, Alexander. "The modal reduction method for multi-body dynamics with non-smooth contact." International Journal for Numerical Methods in Engineering 98, no. 13 (March 7, 2014): 937–59. http://dx.doi.org/10.1002/nme.4651.

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15

Sinou, Jean-Jacques, Olivier Chiello, and Lucien Charroyer. "Non Smooth Contact Dynamics Approach for Mechanical Systems Subjected to Friction-Induced Vibration." Lubricants 7, no. 7 (July 15, 2019): 59. http://dx.doi.org/10.3390/lubricants7070059.

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The modeling of contact is one of the main features of contact dynamics in the context of friction-induced vibrations. It can have a strong impact on the numerical results and consequently on the design choices during the optimization or specification of industrial mechanical systems. This is particularly the case for scientific studies interested in brake squeal. The objective of the paper is to recall and to promote developments concerning the use of non smooth contact dynamics approach for numerical simulations based on finite element method. The specific problem of the prediction of self-excited vibration in the context of brake squeal is discussed. In order to illustrate the potential benefit for the mechanical community of using formulations and theoretical developments from the mathematical community, the stability analysis and the estimation of nonlinear vibrations of a brake system with multiple frictional interface is investigated.

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Mangoni, Dario, Alessandro Tasora, and Rinaldo Garziera. "A primal–dual predictor–corrector interior point method for non-smooth contact dynamics." Computer Methods in Applied Mechanics and Engineering 330 (March 2018): 351–67. http://dx.doi.org/10.1016/j.cma.2017.10.030.

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Lozovskiy, Alexander, and Frédéric Dubois. "The method of a floating frame of reference for non-smooth contact dynamics." European Journal of Mechanics - A/Solids 58 (July 2016): 89–101. http://dx.doi.org/10.1016/j.euromechsol.2016.01.007.

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Quezada, Juan Carlos, and Cyrille Chazallon. "Complex modulus modeling of asphalt concrete mixes using the Non-Smooth Contact Dynamics method." Computers and Geotechnics 117 (January 2020): 103255. http://dx.doi.org/10.1016/j.compgeo.2019.103255.

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19

Mudrić, Teo, Nina Čeh, Stefan Hante, and Martin Arnold. "Free Rocking of a Rigid Block on a Flexible Structure with Non-Smooth Contact Dynamics." Applied Sciences 14, no. 15 (July 25, 2024): 6483. http://dx.doi.org/10.3390/app14156483.

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When structures are subjected to dynamic loading, such as that caused by an earthquake or working machinery, the rocking behavior of objects located on parts of the loaded structure plays an important role in addressing the protection and stability of non-structural components. In this work, the free rocking of a rigid block on a flexible beam and rigid base was investigated using numerical simulations. To this end, a numerical code based on the non-smooth contact dynamics method was developed for this particular problem, and numerical simulations are compared to experimental tests when a rigid base is considered. The purpose of the study was to investigate the predictive capabilities and limitations of the numerical model and address the effect of introducing beam flexibility on the rocking response. The investigated flexibilities were such that the beam deflection under the static weight of the block remains within the common limit of 1/250 of the beam span. For a rigid base, qualitatively good correlation with the experiments was obtained, and good convergence in terms of the time-step is displayed. With the increase in beam base flexibility, it was observed that the simulation results tend to become more sensitive to mesh density and time-step size. Furthermore, we identify a limited flexibility with respect to which unreliable predictions of the overall free rocking are obtained, which corresponds to the stiffness resulting in the beam deflection under the block weight of beam-span/2500. For stiffnesses higher than that, no significant effect of beam flexibility in comparison to the rigid base was noticed in terms of tilt angle and rocking duration, which indicates the adequacy of a rigid base approximation for beams with low flexibility.

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Langlade, T., D. Bertrand, S. Grange, G. Candia, and J. C. de la Llera. "Modelling of earthquake-induced pounding between adjacent structures with a non-smooth contact dynamics method." Engineering Structures 241 (August 2021): 112426. http://dx.doi.org/10.1016/j.engstruct.2021.112426.

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Beatini, Valentina, Gianni Royer-Carfagni, and Alessandro Tasora. "A non-smooth-contact-dynamics analysis of Brunelleschi’s cupola: an octagonal vault or a circular dome?" Meccanica 54, no. 3 (February 2019): 525–47. http://dx.doi.org/10.1007/s11012-018-00934-9.

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Ferrante, Angela, Francesco Clementi, and Gabriele Milani. "Advanced numerical analyses by the Non‐Smooth Contact Dynamics method of an ancient masonry bell tower." Mathematical Methods in the Applied Sciences 43, no. 13 (February 7, 2020): 7706–25. http://dx.doi.org/10.1002/mma.6113.

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Nodargi, Nicola A., and Paolo Bisegna. "A variational-based non-smooth contact dynamics approach for the seismic analysis of historical masonry structures." Computer Methods in Applied Mechanics and Engineering 432 (December 2024): 117346. http://dx.doi.org/10.1016/j.cma.2024.117346.

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Fallahzadeh, R., F. Bozzoli, and L. Cattani. "Effect of closed-loop nanochannels on the onset of explosive boiling: a molecular dynamics simulation study." Journal of Physics: Conference Series 2685, no. 1 (January 1, 2024): 012013. http://dx.doi.org/10.1088/1742-6596/2685/1/012013.

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Abstract As a primary boiling mode, explosive boiling has shown a promising future in many applications and received much research attention. The topology of the solid surface in contact with the liquid, particularly nanostructured surfaces, significantly affects the onset time of explosive boiling of a liquid nanofilm. Most studies investigated explosive boiling on non-closed-loop (parallel) nanochannel surfaces. Here, for the first time, explosive boiling in a closed-loop nanochannel was studied by the non-equilibrium molecular dynamics simulation method. Explosive boiling of liquid argon nanofilm on solid copper surfaces with different topologies, including an ideally smooth, a non-closed-loop, and a closed-loop nanochannel, was simulated. The results showed that, compared with the ideally smooth surface, the onset time of explosive boiling decreased for the non-closed-loop and closed-loop nanochannel surfaces. However, it turned out that compared to the non-closed-loop nanochannel, using the closed-loop nanochannel has an adverse effect on heat flux and the onset time of explosive boiling.

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Marston, J. O., I. U. Vakarelski, and S. T. Thoroddsen. "Cavity formation by the impact of Leidenfrost spheres." Journal of Fluid Mechanics 699 (May 9, 2012): 465–88. http://dx.doi.org/10.1017/jfm.2012.124.

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AbstractWe report observations of cavity formation and subsequent collapse when a heated sphere impacts onto a liquid pool. When the sphere temperature is much greater than the boiling point of the liquid, we observe an inverted Leidenfrost effect where the sphere is encompassed by a vapour layer that prevents physical contact with the liquid. This creates the ultimate non-wetting scenario during sphere penetration through a free surface, producing very smooth cavity walls. In some cases during initial entry, however, the liquid contacts the sphere at the equator, leading to the formation of a dual cavity structure. For cold sphere impacts, where a contact line is observed, we reveal details of the contact line pinning, which initially forms a sawtooth pattern. We also observe surface waves on the cavity interface for cold spheres. We compare our experimental results to previous studies of cavity dynamics and, in particular, the influence of hydrophobicity on the entry of the sphere.

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Pécol, Philippe, Pierre Argoul, Stefano Dal Pont, and Silvano Erlicher. "The non-smooth view for contact dynamics by Michel Frémond extended to the modeling of crowd movements." Discrete & Continuous Dynamical Systems - S 6, no. 2 (2013): 547–65. http://dx.doi.org/10.3934/dcdss.2013.6.547.

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Renouf, Mathieu, Frédéric Dubois, and Pierre Alart. "A parallel version of the non smooth contact dynamics algorithm applied to the simulation of granular media." Journal of Computational and Applied Mathematics 168, no. 1-2 (July 2004): 375–82. http://dx.doi.org/10.1016/j.cam.2003.05.019.

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Docquier, Nicolas, Olivier Lantsoght, Frédéric Dubois, and Olivier Brüls. "Modelling and simulation of coupled multibody systems and granular media using the non-smooth contact dynamics approach." Multibody System Dynamics 49, no. 2 (January 8, 2020): 181–202. http://dx.doi.org/10.1007/s11044-019-09721-0.

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Péralès, Robert, Marc Vinches, and Claude Bohatier. "Modélisation par éléments discrets d'ouvrages 3D en génie civil. Application de la méthode Non Smooth Contact Dynamics." Revue européenne de génie civil 11, no. 9-10 (December 31, 2007): 1169–85. http://dx.doi.org/10.3166/regc.11.1169-1185.

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Cárdenas-Barrantes, Manuel, David Cantor, Jonathan Barés, Mathieu Renouf, and Emilien Azéma. "Three-dimensional compaction of soft granular packings." Soft Matter 18, no. 2 (2022): 312–21. http://dx.doi.org/10.1039/d1sm01241j.

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Du, Yujie, Fangzheng Jiao, Ping Wang, Fei Liu, and Long Li. "Nonsmooth dynamic modeling and simulation of spatial mechanisms with frictional translational clearance joints." Journal of Physics: Conference Series 2746, no. 1 (May 1, 2024): 012013. http://dx.doi.org/10.1088/1742-6596/2746/1/012013.

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Abstract This paper presents a nonsmooth dynamic approach of modeling and computation for spatial mechanism including spatial frictional translational joints (SFTJs) with small clearances. In this research, the dynamic formulation is derived in the Lie group setting, which leads to a coordinate-free and compact formulation. In the following, the normal contact interaction between the slider and guide is described by the complementarity relations between the constraint force in the normal direction. The tangent contact interaction in the SFTJ is characterized by the Coulomb’s friction law in the type of a set-valued map. Based on the horizontal linear complementarity problem (HLCP), the non-smooth dynamics can be established and calculated by combining the Lemke’s algorithm and the RK-MK time integration algorithm. Finally, A spatial crank-slider mechanism with SFTJs is shown as a numerical case. The simulation results demonstrate the correctness and effectiveness of the proposed method which can capture the nonsmooth dynamical behavior of the system.

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Nader, François, Claire Silvani, and Irini Djeran-Maigre. "Oedometric compression of a granular material: computation of energies involved during breakage with a discrete element modelling." EPJ Web of Conferences 249 (2021): 07008. http://dx.doi.org/10.1051/epjconf/202124907008.

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A numerical model able to simulate the grain breakage with the discrete element method, using the “Non-Smooth Contact Dynamics” is presented. The model reproduces 3D grains having complex shapes and is tested in single grain and in oedometric compressions. Numerical simulations are then carried out to evaluate the different energies active during breakage (surface creation and redistribution energies). The surface creation energy is estimated. Results are closed to the ones found in the literature.

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Ginzinger, Lucas, Roland Zander, and Heinz Ulbrich. "Controller Design for a Rubbing Rotor." Solid State Phenomena 147-149 (January 2009): 203–14. http://dx.doi.org/10.4028/www.scientific.net/ssp.147-149.203.

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A new approach to control a rubbing rotor by applying an active auxiliary bearing is developed. The auxiliary bearing is attached to the foundation via two unidirectional actuators. The control force is applied indirectly using the active auxiliary bearing only in case of rubbing. A framework for the development of a feedback controller for an active auxiliary bearing is presented. The theory of a robust two-phase control strategy which guarantees a smooth transition from free rotor motion to the state of full annular rub is presented. A simulation environment for the elastic rotor and the auxiliary bearing including the non-smooth nonlinear dynamics of the rubbing contact is used to develop the feedback controller. Experimental studies have been carried out at a rotor test rig. Various experiments show the outstanding success of the strategy. In case of rubbing, the contact forces are reduced up to 90%.

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Gupta, Ritesh, Franck Bourrier, Vincent Acary, and Stéphane Lambert. "Bayesian interface based calibration of a novel rockfall protection structure modelled in the non-smooth contact dynamics framework." Engineering Structures 297 (December 2023): 116936. http://dx.doi.org/10.1016/j.engstruct.2023.116936.

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Zhao, Yanling, Gang Zhou, and Qiyu Wang. "Discrete Dynamics of Balls in Cageless Ball Bearings." Symmetry 14, no. 11 (October 25, 2022): 2242. http://dx.doi.org/10.3390/sym14112242.

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Cageless ball bearings are often preferred as a back-up bearing for active magnetic bearings to support a falling rotor, but the contact between the balls of the cageless ball bearing may lead to the deterioration of the bearing performance and affect the dynamic stability of the rotor system. Thus, we studied the discrete dynamics of cageless ball bearings. First, a model is proposed to change the groove curvature center of the local outer raceway to control the ball velocity to achieve dispersion. Combined with the spatial geometry theory, the mathematical model of the discrete raceway is established, the collision between the balls is considered as an abruptly added constraint, and the non-smooth dynamics equation of the cageless ball bearing with a local discrete raceway is established. Then, the fourth-order Adams prediction correction algorithm is used to numerically solve the dynamic discretization of the ball, and the structural parameters of the discrete raceway are preferably selected, according to the phase diagram of the ball and the change in the angular spacing. The results show that the structure of the discrete raceway has a strong influence on the discrete dynamics of the ball.

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Yuan, Gaofei, and Yuefang Wang. "Nonlinear Dynamics and Vibration Localization of Shrouded Blisk with Contact and Friction Effects." Machines 11, no. 2 (February 6, 2023): 238. http://dx.doi.org/10.3390/machines11020238.

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Shrouds have been widely used to reduce the level of excessive vibration of blisks. However, complicated nonlinear motion can be induced by the contact and friction between shrouds. Even worse, harmful localization of vibration can be encountered due to nonsmooth behaviour at the shroud contact interfaces in the tuned disk. In this paper, the nonlinear dynamics and localization of vibration of a shrouded blisk are studied considering the spin softening. The continuous parametric model of a shrouded blisk is established, and the transition boundaries between different status (i.e., stick, slip and separation) of shrouds are determined based on the Coulomb friction model. The steady-state responses of the blisk are analysed using variable rotation speed, and the primary resonance, beat and quasi-periodic vibration are presented in connection with the non-smooth behaviour of contact. A particular type of vibration localization initiated by the contact and friction effect of the shrouds in the form of asymmetric vibration in the tuned blisk is discovered. It is found that the blades-disk coupling has strong influences on the level of the localization. The effects of the contact stiffness and localization on the blade vibration are demonstrated through the change in the powers of the blade motions.

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Fu, Chao, Zhaoli Zheng, Weidong Zhu, Zhongliang Xie, Weiyang Qin, and Kuan Lu. "Nonlinear dynamics of discontinuous uncertain oscillators with unilateral constraints." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 12 (December 2022): 123112. http://dx.doi.org/10.1063/5.0125365.

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Nonlinear dynamics of discontinuous oscillators with unilateral constraints and non-random parametric uncertainties are investigated. Nonlinear oscillators considering single- and double-sided constraints are carefully constructed to exhibit rich bifurcations, such as period-doubling and Neimark–Sacker bifurcations. In deterministic amplitude–frequency responses, both hardening and softening effects are induced by non-smooth contact-type nonlinearities. Stabilities of the solutions are determined by the shooting method and the monodromy matrix. To effectively quantify the behaviors of nonlinear oscillators in the presence of parametric uncertainties, a non-intrusive surrogate function aided by arc-length ratio interpolation is constructed. Simulation results demonstrate variabilities of nonlinear responses under different non-random uncertainties. Moreover, an accuracy verification is provided to verify the effectiveness of the non-intrusive uncertainty propagation method. It is found that the surrogate function in combination with the arc-length ratio technique has high accuracy and evolutions of turning points are captured satisfactorily regardless of complex interactions of nonlinearities and uncertainties. The findings and methodologies reported are meaningful to general nonlinear systems having complex motions, paving the road for more in-depth investigations into uncertain nonlinear dynamics.

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EDWARDS, R. "Zeno breaking, the Contact effect and sensitive behaviour in piecewise-linear systems." European Journal of Applied Mathematics 29, no. 5 (March 21, 2018): 826–44. http://dx.doi.org/10.1017/s0956792518000116.

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Non-smooth approximations of steep sigmoidal switching networks, such as those used as qualitative models of gene regulation, lead to analytic and computational challenges that arise as a result of the discontinuities in the vector fields. In order to highlight the need for care in dealing with such systems, several particular phenomena are presented here through illustrative examples, including ‘Zeno breaking’, or computing beyond the finite time convergence of an infinite sequence of threshold transitions; the ‘Contact’ effect, in which in the discontinuous limit, trajectories can pass through a ‘saddle point’ without stopping, though these solutions are not unique and other solutions stop for arbitrary time intervals; and sensitive behaviour that arises from exotic dynamics within switching regions.

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Zhao, Zhen, Caishan Liu, and Bernard Brogliato. "Planar dynamics of a rigid body system with frictional impacts. II. Qualitative analysis and numerical simulations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2107 (May 6, 2009): 2267–92. http://dx.doi.org/10.1098/rspa.2008.0520.

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The objective of this paper is to implement and test the theory presented in a companion paper for the non-smooth dynamics exhibited in a bouncing dimer. Our approach revolves around the use of rigid body dynamics theory combined with constraint equations from the Coulomb's frictional law and the complementarity condition to identify the contact status of each contacting point. A set of impulsive differential equations based on Darboux–Keller shock dynamics is established that can deal with the complex behaviours involved in multiple collisions, such as the frictional effects, the local dissipation of energy at each contact point, and the dispersion of energy among various contact points. The paper will revisit the experimental phenomena found in Dorbolo et al . ( Dorbolo et al . 2005 Phys. Rev. Lett. 95 , 044101), and then present a qualitative analysis based on the theory proposed in part I. The value of the static coefficient of friction between the plate and the dimer is successfully estimated, and found to be responsible for the formation of the drift motion of the bouncing dimer. Plenty of numerical simulations are carried out, and precise agreements are obtained by the comparisons with the experimental results.

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Lancioni, Giovanni, Davide Gentilucci, Enrico Quagliarini, and Stefano Lenci. "Seismic vulnerability of ancient stone arches by using a numerical model based on the Non-Smooth Contact Dynamics method." Engineering Structures 119 (July 2016): 110–21. http://dx.doi.org/10.1016/j.engstruct.2016.04.001.

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41

Song, Yang, Zhigang Liu, Hongrui Wang, Jing Zhang, Xiaobing Lu, and Fuchuan Duan. "Analysis of the galloping behaviour of an electrified railway overhead contact line using the non-linear finite element method." Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 232, no. 10 (April 23, 2018): 2339–52. http://dx.doi.org/10.1177/0954409718769751.

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Galloping of an electrified railway overhead contact line (also known as catenary galloping) is a large-amplitude wind-induced vibration under extreme conditions that is extremely detrimental to the railway infrastructure. This paper attempts to conduct a numerical simulation of catenary galloping and analyse its galloping behaviour. Computational fluid dynamics is utilized to calculate the aerodynamic coefficients of the contact wire with different classes of wear. The mechanism of catenary galloping is revealed by the Den Hartog theory. To describe the non-linear behaviour of catenary galloping, a non-linear finite element method is employed to establish the catenary model, which properly considers the geometrical non-linearity of the contact/messenger wire and the non-smooth non-linearity of droppers. Considering the effect of fluid-induced vibration, the self-excited forces acting on the contact wire are derived. Through several numerical examples, the galloping responses of the catenary are analysed with different tension classes and stochastic wind. The results demonstrate that the extreme wear of the contact wire caused by the long-term passage of pantograph can change the aerodynamic coefficients of the cross-sections of the contact wire and cause the system’s instability under steady wind load. It is concluded that upgrading the catenary tension class can effectively suppress catenary galloping. The stochastic wind only has small effect on the catenary galloping. The stochastic wind only has small effect on the catenary galloping.

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42

Molnar, T. G., Z. Dombovari, T. Insperger, and G. Stepan. "On the analysis of the double Hopf bifurcation in machining processes via centre manifold reduction." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2207 (November 2017): 20170502. http://dx.doi.org/10.1098/rspa.2017.0502.

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The single-degree-of-freedom model of orthogonal cutting is investigated to study machine tool vibrations in the vicinity of a double Hopf bifurcation point. Centre manifold reduction and normal form calculations are performed to investigate the long-term dynamics of the cutting process. The normal form of the four-dimensional centre subsystem is derived analytically, and the possible topologies in the infinite-dimensional phase space of the system are revealed. It is shown that bistable parameter regions exist where unstable periodic and, in certain cases, unstable quasi-periodic motions coexist with the equilibrium. Taking into account the non-smoothness caused by loss of contact between the tool and the workpiece, the boundary of the bistable region is also derived analytically. The results are verified by numerical continuation. The possibility of (transient) chaotic motions in the global non-smooth dynamics is shown.

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Tolpekina, T. V., and B. N. J. Persson. "Adhesion and Friction for Three Tire Tread Compounds." Lubricants 7, no. 3 (February 26, 2019): 20. http://dx.doi.org/10.3390/lubricants7030020.

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We study the adhesion and friction for three tire tread rubber compounds. The adhesion study is for a smooth silica glass ball in contact with smooth sheets of the rubber in dry condition and in water. The friction studies are for rubber sliding on smooth glass, concrete, and asphalt road surfaces. We have performed the Leonardo da Vinci-type friction experiments and experiments using a linear friction tester. On the asphalt road, we also performed vehicle breaking distance measurements. The linear and non-linear viscoelastic properties of the rubber compounds were measured in shear and tension modes using two different Dynamic Mechanical Analysis (DMA) instruments. The surface topography of all surfaces was determined using stylus measurements and scanned-in silicon rubber replicas. The experimental data were analyzed using the Persson contact mechanics and rubber friction theory.

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Ferrante, Angela, Ersilia Giordano, Francesco Clementi, Gabriele Milani, and Antonio Formisano. "FE vs. DE Modeling for the Nonlinear Dynamics of a Historic Church in Central Italy." Geosciences 11, no. 5 (April 27, 2021): 189. http://dx.doi.org/10.3390/geosciences11050189.

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The present research paper properly focuses on the dynamics and failure mechanisms of the masonry “Apennine Church” of Santissimo Crocifisso in Pretare, municipality of Arquata del Tronto in the province of Ascoli Piceno (Marche region, Central Italy). Such a peculiar structural type traditionally characterizes the intense seismic area of Central Italy, unfortunately almost totally damaged by the recent shock sequence of 2016. Advanced numerical modeling through discontinuous and continuous approaches were here utilized to have an insight into the dynamic properties and behavior of the structure under strong nonlinear dynamic excitations. In the discrete element approach, the non-smooth contact dynamics method, implemented in LMGC90©, was applied, adopting a full 3D detailed discretization. The church was schematized as an arrangement of rigid blocks, subjected to sliding by friction and perfect plastic collisions, with a null restitution coefficient. In the finite element approach, the concrete damaged plasticity model available in Midas FEA NX© was involved. This model allows reproducing the tensile cracking, the compressive crushing, and the degradation of the material under cyclic loads. Finally, the numerical analyses provided a valuable picture of the actual behavior of the church, thus giving useful hints for future strengthening interventions.

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Cammarata, Alessandro, Pietro Davide Maddìo, Rosario Sinatra, Andrea Rossi, and Nicola Pio Belfiore. "Dynamic Model of a Conjugate-Surface Flexure Hinge Considering Impacts between Cylinders." Micromachines 13, no. 6 (June 16, 2022): 957. http://dx.doi.org/10.3390/mi13060957.

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A dynamic model of a Conjugate-Surface Flexure Hinge (CSFH) has been proposed as a component for MEMS/NEMS Technology-based devices with lumped compliance. However, impacts between the conjugate surfaces have not been studied yet and, therefore, this paper attempts to fill this gap by proposing a detailed multibody system (MBS) model that includes not only rigid-body dynamics but also elastic forces, friction, and impacts. Two models based on the Lankarani-Nikravesh constitutive law are first recalled and a new model based on the contact of cylinders is proposed. All three models are complemented by the friction model proposed by Ambrosìo. Then, the non-smooth Moreau time-stepping scheme with Coulomb friction is described. The four models are compared in different scenarios and the results confirm that the proposed model outcomes comply with the most reliable models.

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46

Mora, Karin, Alan R. Champneys, Alexander D. Shaw, and Michael I. Friswell. "Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2237 (May 2020): 20190549. http://dx.doi.org/10.1098/rspa.2019.0549.

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The dynamics associated with bouncing-type partial contact cycles are considered for a 2 degree-of-freedom unbalanced rotor in the rigid-stator limit. Specifically, analytical explanation is provided for a previously proposed criterion for the onset upon increasing the rotor speed Ω of single-bounce-per-period periodic motion, namely internal resonance between forward and backward whirling modes. Focusing on the cases of 2 : 1 and 3 : 2 resonances, detailed numerical results for small rotor damping reveal that stable bouncing periodic orbits, which coexist with non-contacting motion, arise just beyond the resonance speed Ω p : q . The theory of discontinuity maps is used to analyse the problem as a codimension-two degenerate grazing bifurcation in the limit of zero rotor damping and Ω = Ω p : q . An analytic unfolding of the map explains all the features of the bouncing orbits locally. In particular, for non-zero damping ζ , stable bouncing motion bifurcates in the direction of increasing Ω speed in a smooth fold bifurcation point that is at rotor speed O ( ζ ) beyond Ω p : q . The results provide the first analytic explanation of partial-contact bouncing orbits and has implications for prediction and avoidance of unwanted machine vibrations in a number of different industrial settings.

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Xue, Fuchun. "Investigation of rolling wheel–rail contact using an elaborate numerical simulation." Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 234, no. 10 (November 6, 2019): 1198–209. http://dx.doi.org/10.1177/0954409719886171.

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In this paper, a non-linear model is developed for analyzing rolling wheel–rail contact in a wheel–track–infrastructure system. Because of the random irregularity across the surface of the rail, the process of the wheel accelerating from rest and rolling forward at its expected speed can be simulated and verified. The dynamic characteristics of the rolling wheel–rail contact at the expected speed are also carefully investigated. The results showed that the top of the rail consists of spatially curved planes due to the deformation induced by the rolling wheel. In addition to the adhesion and slipping zones, there was also a disengaging zone existing within the contact area. The random irregularity throughout the top of the rail significantly reduced the area of contact between the wheel and the rail. By comparing the Hertz contact theory with a smooth rail top, significant differences were observed in the vertical contact stress distribution mode throughout the contact area for the real wheel–rail rolling contact, with a sharp increase in the absolute values of contact pressure. The stress distribution in the contact area was highly non-uniform, and a severe local concentration of dynamic stress was observed.

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48

Sokolenko, B. V., N. V. Shostka, and D. A. Poletaev. "Determination of the refractive index profile and surface topography of optically smooth objects using interference of optical vortices." Journal of Physics: Conference Series 2103, no. 1 (November 1, 2021): 012166. http://dx.doi.org/10.1088/1742-6596/2103/1/012166.

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Abstract In this paper, we present the results of the propagational dynamics of vortex beams in the scope of their possible applications for interferometric non-contact robust and precision optical surface profilometry with nanoscale longitudinal resolution. The result of coaxial superposition of the reference plane wave with singly charged vortex beams represents a dynamically changing intensity distribution. The nature of this changes, namely, rotational effects of intensity zeros, allows to determine directly the optical path difference which is introduced by the surfaces and internal structure of test object. We have proposed the experimental setup for examination of reflecting and transmitting objects.

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Sánchez, Paul, Mathieu Renouf, Emilien Azéma, and Rémy Mozul. "LMGC90: a Contact Dynamics open source code for the simulation of granular asteroid with realistic regolith shapes. Application to the accretion process." EPJ Web of Conferences 249 (2021): 14007. http://dx.doi.org/10.1051/epjconf/202124914007.

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Granular asteroids are naturally occurring gravitational aggregates (rubble piles) bound together by gravitational forces. For this reason, it is reasonable to use the theoretical concepts and numerical tools developed for granular media to study them. In this paper, we extend the field of applicability of the Contact Dynamic (CD) method, a class of non smooth discrete element approach, for the simulation of three dimensional granular asteroids. The CD method is particularly relevant to address the study of dense granular assemblies of a large number of particles of complex shape and broad particles size distribution, since it does not introduces numerical artefacts due to contact stiffness. We describe how the open source software LMGC90, interfaced with an external library for the calculation of self-gravity, is used to model the accretion process of spherical and irregular polyhedral particles.

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Andersson, C., and T. Dahlberg. "Wheel/rail impacts at a railway turnout crossing." Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit 212, no. 2 (March 1, 1998): 123–34. http://dx.doi.org/10.1243/0954409981530733.

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The vertical dynamics of a common Swedish railway turnout under the load of moving vehicles is investigated. The turnout is described by a linear finite element model with modal damping. The model of the turnout (a section of it) has a length of 36 sleeper spans surrounding the crossing. Rails and sleepers are modelled with uniform Rayleigh-Timoshenko beam elements. The rails are connected via railpads (linear springs) to the sleepers, which rest on an elastic foundation. The vehicles which model the dynamic behaviour of trains are discrete systems of masses, springs and dampers. They pass the turnout on the through rails at a constant speed and only vertical dynamics (including roll and pitch motions) is studied. The wheel/rail contact is modelled by use of a non-linear Hertzian spring. The train/track interaction problem is solved numerically by using an extended state space vector approach in conjunction with modal superposition for the turnout. The analyses show that the rail discontinuity at the crossing leads to an increase in the wheel/rail contact force. Both smooth and irregular transitions of the wheels from the wing rail to the crossing nose have been examined for varying speeds of the vehicle. Under perfect conditions, the wheels will change quite smoothly from rolling on the wing rail to rolling on the nose. The impact at the crossing will then be small, giving a maximum wheel/rail contact force which is only 30-50 per cent larger than the static contact force. For uneven transitions, the severity of the impact loading at the crossing depends strongly on the train speed. The increase in the contact force, as compared with the static force, is of the order of 100 per cent at 70 km/h and 200 per cent at 150 km/h.

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Journal articles on the topic 'Non smooth contact dynamics'

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