Control and synchronization of a coupled network of mechanical structures

Abstract

This thesis work deals with the analysis of a control strategy of a network ofmechanical structures indirectly coupled through a dynamical environment. Mechanical structures are modelled assuming the Euler-Bernoulli formalism and the dynamic environment is an electrical circuit consisting of piezoelectric patches in parallel conformation with a load resistance. By means of appropriate mathematical concepts (modal approximation, harmonic balance method, D-subdivision method) and numerical simulationmethods (time series, phase portrait, amplitude response curves, bifurcation diagram, Fourier spectrum analysis, root mean square function and standard deviation function) , the dynamical behavior and the synchronization of the network of indirectly coupled mechanical structures are investigated. The main results of this study show that the increase of the electromechanical coupling parameter leads to a strong reduction of vibration amplitude on a network constituted with only two indirectly coupled structures. An extension of the number of coupled structures allows to explore the occurrence of strong amplitude reduction (SAR) phenomenon and synchronization in the network. SAR phenomenon appears in this system when global synchronization of all beams takes place. The occurrence of global synchronization, whichwas preceded by dynamical clustering, is dependent on the size of the network as well as on the load resistance of the electrical circuit which indirectly interacts with all the beams. The results further show that the SAR state can be observed for relatively veryweak coupling strength and large system-size. Finally, the effect of delay on a network is analyzed. Disturbance-induced by time-delay on the synchronization state and SAR state is also presented. It is conventionally known that delay induces instability in coupled systems, butwe find here that this delay can also contribute to stabilize these systems by synchronizing them. This work contributes to develop a control strategy which can be applied to the elements of structures of a skyscraper, lamellar structures of an aircraft, several foundations, several nearby bridges, several plates of a airplane or ship, metallic parallel floors, when those structures are subjected to an environmental excitation such as wind, moving loads, tsunami, or earthquake.