Effet du couplage modal sur le contrôle du comportement vibratoire de passerelles

Abstract

Modern footbrigdes are lightweight and flexible structures that have to meet strict comfort criteria as far as their acceleration levels under dynamic loading are concerned. Given their slenderness, external dampers are a typical solution to keep these accelerations under thresholds. The most commonly used damping devices are tuned mass dampers (TMD). One of their main limitation though is their allowed mass. Furthermore, their design is usually based on simplifying asumptions that do not account for modal coupling. Yet, this can have a significant impact on their dynamic response, especially when eigen frequencies are closely spaced.

This paper investigates the viability of a new damping technology for harmonic loading, in the instance of inerter dampers. It is shown that they outperform conventional TMD thanks to their mass amplification effect. Then, modal coupling is studied by means of a mathematical method coming from perturbations theory. This allows to set up a closed-form expression for the transfer matrix of a coupled system. This one is general, simple, but meaningful. This tool is then used to derive analytical elementary expressions for the coupled or uncoupled design of dampers. The basic understanding of modal coupling also enables a totally new approach proposing to use only one damper to control two closey-spaced modes of vibration. Applicability criteria for the method as well as the parameters to be provided for the damper and its suitable positions are also derived in an analytical manneer. The use of inerter dampers appears very convenient for the purpose of this method. The latter is finally applied on a real-life case study and happens to be competitive with conventional damping techniques (use of 2 dampers for 2 modes).