Two models of nonsmooth dynamical systems

International audienceTwo examples of nonsmooth systems are considered. The first one is a two degrees of freedom oscillator in the presence of a stop. A discontinuity appears when the system position reaches a critical value. The second example consists of coupled oscillators excited by dry friction. In this case, the discontinuity occurs when the system's velocities take a critical value. For both examples, the dynamical system can be partitioned into different configurations limited by a set of boundaries. Within each configuration, the dynamical model is linear and the close form solution is known. Periodic orbits, including several transitions between the various configurations of the system, are found in analytical form. The stability of these orbits is investigated by using the Poincaré map modeling

New events in stick slip oscillators behaviour

International audienceA two-degree-of-freedom oscillator excited by dry friction is considered. The system consists of two masses connected by a linear spring, one of which is connected to a fixed wall by another spring. The second mass is in contact with a driving belt moving at a constant velocity. Coulomb's friction force acts between the mass and the belt. Periodic orbits including stick phases and slip phases, during which the mass in contact with the belt moves faster than the belt, are found analytically. The stability of these "overshooting" orbits is also investigated

Analytical investigation of periodic solutions for a coupled oscillator with dry friction

International audienceIn this paper, we present an analytical method to investigate the behavior of a two degrees of freedom oscillator excited by dry friction. The system consists of two masses connected by linear springs. These two masses are in contact with a driving belt moving at a constant velocity. The contact forces between the masses and the belt are obtained from Coulomb's friction laws. A set of periodic solutions involving a global sticking phase followed by several other phases where one or both masses are slipping, are found in close form. Stability conditions related to these solutions are obtained

New limit cycles of dry friction oscillators under harmonic load

International audienceWe consider a system composed of two masses connected by linear springs. One of the masses is in contact with a driving belt moving at a constant velocity. Friction force, with Coulomb's characteristics, acts between the mass and the belt. Moreover, the mass is also subjected to a harmonic external force. Several periodic orbits including stick phases and slip phases are obtained. In particular, the existence of periodic orbits including a part where the mass in contact with the belt moves in the same direction at a higher speed than the belt itself is proved. Non-sticking orbits are also found for a non-moving belt. We prove that this kind of solution is symmetric in space and in time

Dynamics of coupled oscillators excited by dry friction

International audienceIn this paper, we present an analytical method to investigate the behavior of a two-degree-of-freedom oscillator excited by dry friction. The system consists of two masses connected by linear springs. These two masses are in contact with a driving belt moving at a constant velocity. The contact forces between the masses and the belt are obtained assuming Coulomb's friction law. Two families of periodic motions are found in closed form. The first one includes stick-slip oscillations with two switches per period, the second one is also composed of stick-slip motion, but includes three switches per period. In both cases, the initial conditions and the time duration of each kind of motions (stick or slip phases) are obtained in analytical form

Dynamics and Stability of a Two Degree of Freedom Oscillator With an Elastic Stop

International audienceA two-degree-of-freedom oscillator with a colliding component is considered. The aim of the study is to investigate the dynamic behavior of the system when the stiffness obstacle changes to a finite value to an infinite one. Several cases are considered. First, in the case of rigid impact and without external excitation, a family of periodic solutions are found in analytical form. In the case of soft impact, with a finite time duration of the shock, and no external excitation, the existence of periodic solutions, with an arbitrary value of the period, is proved. Periodic motions are also obtained when the system is submitted to harmonic excitation, in both cases of rigid or soft impact. The stability of these periodic motions is investigated for these four cases

Modular simulation and optimization of an 12MW industrial gasifier

In this work, a flexible model, built from elementary modules, is developed for an industrial waste gasification process, in an industrial moving bed reactor located in Morcenx (France). This gasifier is able to treat more than 46,875 ton/year of RDF (Refused Derived Fuel) waste for producing 12 MW. Drying, pyrolysis, combustion / gasification and plasma polishing are used to convert waste directly into a synthesis gas composed of carbon monoxide and hydrogen. This synthesis gas is then used for producing electricity via gas engine

Intra-session absolute and relative reliability of pressure pain thresholds in the low back region of vine-workers:effect of the number of trials

BACKGROUND: Pressure pain thresholds (PPT) are commonly used to quantify mechanical pain sensitivity of deep structures. Excellent PPT reliability has been previously reported among the low back of healthy subjects. However, there is a lack of studies assessing PPT over the low back of workers exposed to biomechanical risk factors of low back pain. Thus, the purpose of this study was threefold: (1) to evaluate the intra-session absolute and relative reliability as well as minimal detectable change (MDC) values of PPT within 14 locations covering the low back region of vine-workers and (2) to determine the number of trial required to ensure reliable PPT assessments and (3) to assess the effect of modifier factors such as gender, age, body mass index (BMI) and pain intensity on PPT reliability. METHODS: Twenty-nine vine-workers voluntarily participated in this study. Twenty-two reported low intensity of low-back pain while seven were pain-free. PPTs were assessed among 14 anatomical locations in the lower back region. Three trials were performed on each location with an interval time of at least one minute. Reliability was assessed computing intraclass correlation coefficients (ICC), standard error of measurement (SEM) for all possible combinations between trials. Bland-Altman plots were also generated to assess potential bias in the dataset. Finally, a repeated measure analysis of variance (RM-ANOVA) with the number of trials used as within subject factor was performed on (1) PPT, (2) ICC and (3) SEM values. RESULTS: ICC ranged from 0.86 to 0.99 for all anatomical locations and for all possible combinations between trials. SEM for comparison between trial 1–2, 2–3, 1–3 and, 1-2-3 ranged from respectively, 36.7–77.5, 27.8–77.7, 50–95.2 and, 39.3–80.8 kPa. ICC and SEM remained similar to the ones obtained for the entire population when taking modifier factors in consideration. The visual analysis of Bland-Altman plots suggested small measurement errors for all anatomical locations and for all possible combinations between trials. CONCLUSIONS: The assessment of PPTs of the lower back among vine-workers was found to have excellent relative and absolute reliability. Moreover, reliable measurements can be equally achieved when using the mean of three PPT measurement or with the first one