Before the beginning of digital-computers era, a lot of research was carried out in order to find electric circuits the governing equations of which were analogous to the ones of mechanical systems. The mentioned circuits were called ectro-mechanical analogs. They were used as analogical computers for the simulation and the design of mechanical systems. The actual technological development of piezoelectric actuators, which are devices able to efficiently transduce energy between the electrical and mechanical form, induced us to consider again those electro-mechanical analogs in order to create coupled piezo-electro-mechanical systems. Our idea is that the coupling between electro-mechanical phenomena is maximum when the propagation of both electrical and mechanical waves are governed by similar equations. Let us remark that because of the propagating mechanical wave-speed is much lower than the light-speed for every material, it is not possible to search for an efficient electro-mechanical coupling inside a piezoelectric continuum. Consequently circuits able to support the propagation of electric-potential waves have been considered. In this work, the equations for the elastica and for the plate are considered and their circuital analogs are derived using their finite-difference approximation. Afterwards, the coupling between the two structures is modelled considering piezoelectric actuators uniformly distributed on the mechanical system and connected to the nodes of the electric circuit. Then the electro-mechanical coupled equations are derived, and an analytical solution is found for a particular case. Finally some numerical simulations showing the efficiently energy exchange is presented. / Master of Science

The aim of this thesis is to show that it is possible to damp mechanical vibrations in a given frame, constituted by Euler beam governed by the equations of an elastica, by means of piezoelectric actuators glued on every beam and interconnected each other via electrical networks.Since we believe that the most efficient way to damp mechanical vibrations by means of electrical networks, is to realize a strong modal coupling between the electrical and the mechanical motion, we will synthesize a distributed circuit analog to the Euler beam.We will approach this synthesis problem following the black box approach to mechanical systems, studied by many engineers and scientists during the 1940's in an attempt to design analog computers.It will be shown that it is possible to obtain a quick energy exchange between its mechanical and electrical forms, using available piezoelectric actuators.Finally we will study a numerical simulation for the damping of transverse vibrations of a beam clamped at both ends. / Master of Science