Memory in random bouncing ball dynamics

The bouncing of an inelastic ball on a vibrating plate is a popular model used in various fields, from granular gases to nanometer-sized mechanical contacts. For random plate motion, so far, the model has been studied using Poincar{\'e} maps in which the excitation by the plate at successive bounces is assumed to be a discrete Markovian (memoryless) process. Here, we investigate numerically the behaviour of the model for continuous random excitations with tunable correlation time. We show that the system dynamics are controlled by the ratio of the Markovian mean flight time of the ball and the mean time between successive peaks in the motion of the exciting plate. When this ratio, which depends on the bandwidth of the excitation signal, exceeds a certain value, the Markovian approach is appropriate; below, memory of preceding excitations arises, leading to a significant decrease of the jump duration; at the smallest values of the ratio, chattering occurs. Overall, our results open the way for uses of the model in the low excitation regime, which is still poorly understood.Comment: Final published version, 5 pages, 4 figure

Experiments and numerical results on nonlinear vibrations of an impacting hertzian contact. Part 1: harmonic excitation

The purpose of this paper is to investigate experimental and numerical dynamic responses of a preloaded vibro-impacting Hertzian contact under sinusoidal excitation. Dynamic response under random excitation is analysed in the second part of this paper. A test rig is built corresponding to a double sphere-plane contact preloaded by the weight of a moving cylinder. Typical response curves are obtained for several input levels. Time traces and spectral contents are explored. Both amplitude and phase of harmonics of the dynamic response are investigated. Linearised resonance frequency and damping ratio are identified from the almost linear behaviour under very small input amplitude. Increasing the external input amplitude, the softening behaviour induced by Hertzian nonlinear stiffness is clearly demonstrated. Resonance peak is confined in a narrow frequency range. Jump discontinuities are identified for both amplitude and phase responses. Forced response spectrum exhibits several harmonics because of nonlinear Hertzian restoring force. Numerical simulations show a very good agreement with experimental results. For higher input amplitude, system exhibits vibro-impacts. Loss of contact non-linearity clearly dominates the dynamic behaviour of the vibroimpacting contact and leads to a wide frequency range softening resonance. Spectral content of the response is dominated by both the first and the second harmonics. Evolution of the experimental downward jump frequency versus input amplitude allows the identification of the nonlinear damping law during intermittent contact. Simulations of the vibroimpacting Hertzian contact are performed using a shooting method and show a very good agreement with experimental results

Response of an impacting hertzian contact to an order-2 subharmonic excitation : theory and experiments

Response of a normally excited preloaded Hertzian contact is investigated in order to analyze the subharmonic resonance of order 2. The nonlinearity associated with contact losses is included. The method of multiple scales is used to obtain the non-trivial steady state solutions, their stability, and the frequency-response curves. To this end, a third order Taylor series of the elastic Hertzian contact force is introduced over the displacement interval where the system remains in contact. A classical time integration method is also used in conjunction with a shooting method to take into account losses of contact. The theoretical results show that the subharmonic resonance constitutes a precursor of dynamic responses characterised by loss of contact, and consequently, the resonance establishes over a wide frequency range. Finally, experimental validations are also presented in this paper. To this end, a specific test rig is used. It corresponds to a double sphere-plane contact preloaded by the weight of a moving mass. Experimental results show good agreements with theoretical ones

Experiments and numerical results on nonlinear vibrations of an impacting hertzian contact. Part 2: random excitation

Non linear dynamic behaviour of a normally excited preloaded Hertzian contact (including possible contact losses) is investigated using an experimental test rig. It consists on a double sphere plane contact loaded by the weight of a rigid moving mass. Contact vibrations are generated by a external Gaussian white noise and exhibit vibroimpact responses when the input level is sufficiently high. Spectral contents and statistics of the stationary transmitted normal force are analysed. A single-degree-of-freedom non linear oscillator including loss of contact and Hertzian non linearities is built for modelling the experimental system. Theoretical responses are obtained by using the stationary Fokker-Planck equation and also Monte Carlo simulations. When contact loss occurrence is very occasional, numerical results shown a very good agreement with experimental ones. When vibroimpacts occur, results remain in reasonable agreement with experimental ones, that justify the modelling and the numerical methods described in this paper. The contact loss non linearity appears to be rather strong compared to the Hertzian non linearity. It actually induces a large broadening of the spectral contents of the response. This result is of great importance in noise generation for a lot of systems such as mechanisms using contacts to transform motions and forces (gears, ball-bearings, cam systems, to name a few). It is also of great importance for tribologists preoccupied to prevent surface dammage

Influence of Multiharmonics Excitation on Rattle Noise in Automotive Gearboxes

We consider the automotive gearbox rattle noise resulting from vibro-impacts that can occur between the idle gears under excessive velocity fluctuations of the shaft-driving gears imposed by engine torque fluctuation. Even if the rattling phenomenon has no consequence on reliability, it may be particularly annoying for vehicle interior sound quality and acoustic comfort. The main parameters governing such kind of vibrations are the excitation source associated with engine torque fluctuation which can be modeled by an imposed displacement of the driveline, the inertia of the idle gear, the drag torque acting during the free flight motion, and the impact laws. In the case of rattle, it is reasonable to assume that duration of impacts between teeth is very short compared to the excitation period. Then, these impacts are modeled by a coefficient of restitution law. The excitation source is not composed only with fundamental component but also with other harmonic components. This study presents some effects of these additional components on the dynamic response of the idle gear

Decreased sAβPPβ, Aβ38, and Aβ40 Cerebrospinal Fluid Levels in Frontotemporal Dementia.

International audienceTo improve the etiological diagnosis of neurodegenerative dementias like Alzheimer's disease (AD) or frontotemporal dementia (FTD), we evaluated the value of individual and combined measurements of the following relevant cerebrospinal fluid (CSF) biomarkers: Tau, 181p-Tau, Aβ38, Aβ40, Aβ42, sAβPPα, and sAβPPβ. This study conducted in two centers included patients with FTD (n = 34), AD (n = 52), as well as a control group of persons without dementia (CTRL, n = 42). Identical clinical criteria and pre-analytical conditions were used while CSF biomarkers were measured using commercial single and multiplex quantitative immunoassays. Thorough statistical analyses, including ROC curves, logistic regressions, and decision trees, were performed. We validated in AD the specific increase of p-Tau levels and the decrease of Aβ42 levels, two biological hallmarks of this disease. Tau concentrations were highest in AD and intermediate in FTD when compared to CTRL. The most interesting results were obtained by focusing on amyloid biomarkers as we found out in FTD a significant decrease of sAβPPβ, Aβ38, and Aβ40 levels. Aβ38 in particular was the most useful biomarker to differentiate FTD subjects from the CTRL population. Combining p-Tau and Aβ38 led us to correctly classifying FTD patients with sensitivity at 85% and specificity at 82%. Significant changes in amyloid biomarkers, particularly for Aβ38, are therefore seen in FTD. This could be quite useful for diagnosis purposes and it might provide additional evidence on the interrelationship between Tau and AβPP biology which understanding is essential to progress towards optimal therapeutic and diagnostic approaches of dementia

Clinical reporting following the quantification of cerebrospinal fluid biomarkers in Alzheimer's disease: An international overview

Introduction: The current practice of quantifying cerebrospinal fluid (CSF) biomarkers as an aid in the diagnosis of Alzheimer's disease (AD) varies from center to center. For a same biochemical profile, interpretation and reporting of results may differ, which can lead to misunderstandings and raises questions about the commutability of tests. Methods: We obtained a description of (pre-)analytical protocols and sample reports from 40 centers worldwide. A consensus approach allowed us to propose harmonized comments corresponding to the different CSF biomarker profiles observed in patients. Results: The (pre-)analytical procedures were similar between centers. There was considerable heterogeneity in cutoff definitions and report comments. We therefore identified and selected by consensus the most accurate and informative comments regarding the interpretation of CSF biomarkers in the context of AD diagnosis. Discussion: This is the first time that harmonized reports are proposed across worldwide specialized laboratories involved in the biochemical diagnosis of AD

Effet de la raideur périodique d'engrènement sur le comportement vibratoire d'une chaîne cinématique soumise à des fluctuations de couple

National audienceLes systèmes mécaniques qui présentent des transmissions par engrenages sont le siège d'excitations internes qui peuvent déboucher sur un comportement vibro-acoustique gênant pour ses utilisateurs. Ces excitations peuvent être couplées a des excitations externes associées a des variations de couple des organes amont (moteur) ou aval (récepteur). On cherche à prendre en compte les couplages multi-physiques entre les sources internes et les sources d'excitation externes. Ce type de couplage est la cause d'un enrichissement du contenu de la réponse fréquentielle. Le but de ce papier est de présenter une méthode d'analyse dynamique de ces couplages. Les phénomènes sont illustrés a travers l'analyse du comportement d'une pompe à vide soumise a une excitation fluidique