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

<p> Analytical expressions for the propagation impairments due to various noise sources in long-haul optical systems and fiber-to-the-home passive optical networks have been obtained. Extensive comparison has been made in this thesis for systems based on different modulation formats, and the advantage of one over the other is clearly stated.</p> <p> For long-haul fiber optical communication systems with inline amplifiers, we have studied the statistical properties of various noise sources in systems based on differential phase-shift keying (DPSK) such as the linear phase noise induced by the amplifier spontaneous emission (ASE) noise, the intra-channel four-wave mixing (IFWM) and the nonlinear phase noise induced by the interplay between ASE noise and fiber Kerr nonlinearity. The error probability of the system based on DPSK is evaluated semi-analytically. In addition, the error probability of the system based on on-off keying (OOK) is calculated taking into account the effects of ASE noise, and the intra-channel nonlinearities such as IFWM and intra-channel cross-phase modulation (IXPM). Comparison of the performance of systems based on DPSK and OOK is made thereafter.</p> <p> For fiber-to-the-home passive optical networks without inline active photonic devices, different modulation formats have been examined for the downstream and upstream data to enable full-duplex transmission. The statistical properties of Rayleigh backscattering in single-source bi-directional optical systems have been studied including the effects of the high speed external modulation signal and the laser phase noise for systems based on DPSK and OOK. The error probabilities for systems using OOK/OOK topology and DPSK/OOK topology for downstream/upstream transmission have been evaluated and compared.</p> <p> In addition, the interplay of the amplifier spontaneous emission noise, fiber nonlinearity and dispersion has been examined starting from the nonlinear Schrödinger equation on the receiver current fluctuation. The variance of the current noise has been evaluated analytically using the two dimensional perturbation theory.</p> / Thesis / Master of Applied Science (MASc)