Couplings in parametrically excited inclined cables systems

Cables in stayed bridges are subjected to important dynamic solicitations for which dynamic model are now well established. Due to their design, such structures highlight resonance phenomena and instabilities frequently observed. Nevertheless, some structures exhibit important vibration amplitudes that can not be explained simply. Measurement recently performed on a bridge point a coupling of the cable with the deck or the pillar. The present paper suggests to consider the deck flexibility coupled to the nonlinear dynamic of the inclined cable. Results of previous study are used. The retained nonlinear model of the cable include two degrees of freedom for the in-plane motion. Considering the bridge mass and deck rigidity adds one DOF, assumed linear in a first approach. The excitation is created on the deck, which produce an external force(such as the wind or the car traffic for example). An experimental set-up uses a specific device in order to highlight expected coupling phenomena on the parametric instabilities. It is composed of a flexible blade which represents the deck, and an inclined cable. Both elements are linked to a mass forced to move vertically, and which represent the anchor point and the equivalent mass of a section of the deck. Therefore, the cable has a given initial static tension. An electrodynamic shaker applies a force close to blade clumping. The transmitted force from the shaker to the structure is measured thanks to a piezo-electric sensor. The instantaneous cable tension is measured via a Shape force sensor. And a high resolution laser sensor captures without contact the in-plane motion of the cable. Analytically, the multiple scales method is applied to solve the nonlinear equations of motion. In-plane vibration of the cable and stability in the vicinity of the primary resonance w1 and sub-harmonic resonance 2w1 are computed. The competition between the behaviour at 2w1 and w2 are of particular interest, as it is observed experimentally

Maximal monotone model with delay term of convolution

Mechanical models are governed either by partial differential equations with boundary conditions and initial conditions (e.g., in the frame of continuum mechanics) or by ordinary differential equations (e.g., after discretization via Galerkin procedure or directly from the model description) with the initial conditions. In order to study dynamical behavior of mechanical systems with a finite number of degrees of freedom including nonsmooth terms (e.g., friction), we consider here problems governed by differential inclusions. To describe effects of particular constitutive laws, we add a delay term. In contrast to previous papers, we introduce delay via a Volterra kernel. We provide existence and uniqueness results by using an Euler implicit numerical scheme; then convergence with its order is established. A few numerical examples are given

Étude des couplages câbles-tabliers sous excitations paramétriques

Cet article concerne l’étude expérimentale et la compréhension par modèle à petit nombre de degré de liberté, des vibrations d’un câble incliné relié à une poutre - modèle simplifié d’un ouvrage d’art. L’excitation extérieure est effectuée sur la poutre. Le câble attaché à l’extrémité de celle-ci est soumis à une sollicitation verticale sinusoïdale multi-fréquentielle due à la réponse de la poutre de raideur finie. L’excitation du câble bien que plus riche est comparable à celle utilisée lors de travaux antérieurs. Un système de guidage de l’extrémité de la poutre assure cette excitation au prix d’une possible variation de la tension horizontale dans le câble introduisant une excitation paramétrique supplémentaire. L’analyse de premiers résultats expérimentaux en résonance principale et secondaire permet d’envisager des modèles explicatifs à un degré de liberté obtenus par projection du modèle continu tridimensionnel du câble sur un mode convenable d’Irvine. Le traitement de ces systèmes simples nourri des données du dispositif expérimental montre un agrément qualitatif satisfaisant des premières expérimentations et des modèles

Un modèle rhéologique discret non classique en dynamique

Nous rappelons brièvement les résultats obtenus concernant les modèles dynamiques discrets construits à partir d'assemblages en série ou en parallèle d'éléments rhéologiques simples (ressorts linéaires ou non, amortisseurs, éléments de Saint-Venant). Nous étudions ensuite en régime dynamique le modèle géphyroïde introduit en régime quasi-statique par Persoz en 1969. Sa formulation à l'aide d'inclusions différentielles permet l'étude théorique puis numérique et l'illustration du caractère géphyroïde du modèle

Bifurcation analysis of Nonlinear Normal Modes with the Harmonic Balance Method

International audienceThis work presents a frequency-domain method based on the Harmonic Balance Method (HBM) to perform bifurcation and stability analysis of Nonlinear Normal Modes (NNM). To do so, a frequency phase condition has been adapted from time domain in order to fix the non-uniqueness of the solution of the autonomous equation of motion. Then, a small damping coefficient has been introduced in the equation of motion to make invertible the matrices used during the pseudo-arc length continuation process. Finally, a shifted quadratic eigenvalue problem has been used to perform stability and bifurcation analysis. The resulting HBM-based algorithm permits the continuation of NNMs, the precise computation of bifurcation points as well as branch switching

Alternative mass sensing techniques based on nonlinear phenomena in M/NEMS resonators

International audienceThis paper investigates alternative mass sensing techniques that take advantage of multi-stability and bifurcations observed in the nonlinear regime. A finite-degree-of-freedom reduced-order model of an electrostatically-actuated microbeam with small added mass is considered. Strategies are proposed for robust real-time detection, quantification and localization of the added mass

A parametrically excited oscillator involving coupling between inclined cable system and deck of stayed bridges

This paper is concerned with the experimental study of the dynamic behaviour of an inclined cable linked to a continuous beam modelling a simplified version of deck and cable of a bridge. External excitation is exerted on the beam. The cable attached to the end of the beam is submitted to a vertical sinusoidal solicitation due to the response of the finite stiffness beam. A guided device located at the end of the beam ensures the excitation with a variation of the horizontal component of the cable tension that introduces a new parametric excitation. Analysis of preliminary experimental results for main and secondary resonances permits us to consider simple modelling with one degree of freedom systems obtained by projection of the continuous three-dimensional model of the cable on adapted Irvine mode. Analytical treatment of these models involving data from the experimental devices shows a correct qualitative agreement between preliminary experiments and theoretical and numerical results

Experimental and theoretical investigation on nonlinear behavior of cable-stayed bridges

This paper deals with experimental study and with understanding via a finite number of degrees of freedom model of the vibrations of an inclined cable linked to a continuous beam. This is a simplified version of deck and cable of a bridge. External excitation is exerted on the beam. The cable attached to the end of the beam is submitted to a vertical sinusoidal solicitation due to the response of the finite stiffness beam. The excitation of the cable though it is more complex looks similar to the excitation used in previous works. A guided device located at the end of the beam ensures the excitation with a variation of the horizontal component of the cable tension that introduces a new parametric excitation. Analysis of preliminary experimental results for main and secondary resonances permits us to consider simple modeling with one degree of freedom systems obtained by projection of the continuous three-dimensional model of the cable on adapted Irvine mode. Analytical treatment of these models involving data from the experimental devices shows a correct qualitative agreement between preliminary experiments and theoretical. Continuation techniques are used to highlight the influence of physical parameters