Electric vibration absorbers made of distributed piezoelectric devices for the control of beam vibrations are studied. The absorbers are obtained by interconnecting an array of piezoelectric transducers uniformly distributed on a beam with different modular electric networks. Five different topologies are considered and their damping performance is analysed and compared. Their optimal parameters are found by adopting a criterion for critical damping of % k-waves: the parameters are suitably chosen to have the quickest temporal vibration decay for a single wave number % k: The analysis is based on homogenized models of the modular piezo-electromechanical systems, i.e. they are regarded as continuous systems by assuming that the number of modules per unit length is high enough with respect to the considered wave numbers. Calling % k -absorbers the corresponding optimal absorbers, we show that: (i) % k-waves are damped in % k-absorbers with an optimal decay time which is independent of the absorber interconnecting topology, while it depends only on the piezoelectric coupling coefficient; (ii) the efficiency of % k-absorbers depends significantly on the absorber interconnecting topology for k different from % k; (iii) one of the proposed absorbers (which is made of a fourth-order electric transmission line with a second-order electric dissipation) equally performs for all the wave numbers and accomplishes an effective multi-modal damping for the mechanically forced response; (iv) the optimal values of the electric parameters differently depend on the number n of used circuit modules for different interconnecting topologies and, in particular, the optimal inductance per module needed in a fourth-order electric transmission line is proportional 1=n 3 : r

Metamaterials are materials especially engineered to have a peculiar physical behaviour, to be exploited for some well-specified technological application. In this context we focus on the conception of general microstructured continua, with particular attention to piezoelectromechanical structures, having a strong coupling between macroscopic motion and some internal degrees of freedom, which may be electric or, more generally, related to some micro-motion. An interesting class of problems in this context regards the design of wave-guides aimed to control wave propagation.The description of the state of the art is followed by some hints addressed to describe some possible research developments and in particular to design optimal design techniques for bone reconstruction or systems which may block wave propagation in some frequency ranges, in both linear and non-linear fields.Metamaterials are materials which are designed to have exotic behaviour: the concept has been first conceived for optical devices. Therefore, very often one talks about mechanical metamaterials, when the exotic behaviour is limited to mechanical effects, as e.g. very negative Poisson effects. This paper is based on a really simple idea: construct a bridge between two different cultural environments which address the same relevant problems. Metamaterials are studied and conceived by physicists to tackle problems and applications not yet considered in engineering sciences; at the same time the community of continuum mechanics nearly completely ignores what physicists devise and develop in the same field. This review intends to fill a gap in order to stimulate a parallel development of the these theories and to near not communicating scientific groups.The mathematical formalism chosen thereinafter is that preferred by physicist, like Landau type variational principles, and the treated subjects are chosen, in the opinion of the authors, from those considered nowadays more important by applied mechanicians.The capability of continuum theories to describe the time evolution and the deformation of the micro-structure of complex mechanical systems was recognised in the very first formulations of continuum mechanics, as in the pioneering work by Piola (Piola, 1846). He was lead by stringent physical considerations to introduce higher gradients of displacement field, as necessary independent variables, in the constitutive equation for the deformation energy of continuous media. For a more modern interpretation of this subject refer to (Mindlin, However in a similar period, while Piola was producing his papers, Cauchy and Poisson obtained a description, with a very elegant and effective format, for continuum mechanics in which: i) the displacement from a reference configuration is the only kinematic descriptor;ii) the crucial conceptual tool is Cauchy stress which is constitutively related only to the first gradient of displacement;iii) the crucial postulates are those concerning balance of mass, linear and angular momentum and, when necessary, energy.T...

. Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network. Archive of Applied Mechanics, Springer Verlag, 2009, 79 (9), pp.859-879. hal-00798627 Ivan Giorgio · Antonio Culla · Dionisio Del VescovoMultimode vibration control using several piezoelectric transducers shunted with a multiterminal network Abstract In this paper a new approach is presented to reduce vibrations for one-and two-dimensional mechanical structures, as beam or thin plates, by means of several piezoelectric transducers shunted with a proper electric network system. The governing equations of the whole system are coupled to each other through the direct and converse piezoelectric effect. More in detail, the mechanical equations are expressed in accordance with the modal theory considering n vibration modes and the electrical equations reduce to the one-dimensional charge equation of electrostatics for each of n considered piezoelectric transducers. In this electromechanical system, a shunting electric device forms an electric subsystem working as multi degrees of freedom (dof's) damped vibration absorber for the mechanical subsystem. Herein, it is introduced a proper transformation of the electric coordinates in order to approximate the governing equations for the whole shunted system with n uncoupled, single mode piezoelectric shunting systems that can be readily damped by the methods reported in literature. A further numerical optimisation problem on the spatial distribution of the piezoelectric elements allows to achieve a better performance. Numerical case studies of two relevant systems, a double clamped beam and a fully clamped plate, allow to take into account issues relative to the proposed approach. Laboratory experiments carried out in real time on a beam clamped at both ends consent to validate the proposed technique.

. Piezo-electromechanical smart materials with distributed arrays of piezoelectric transducers: Current and upcoming applications.

The present article deals with the dynamic behavior of 2D continua representing the homogenized limit of microstructured pantographic systems, i.e., the structures in which two orders of fibers are interconnected by means of pivots. The strain energy density of the continuum model depends on the first and second gradient of the displacement. Numerical simulations on modal analysis are performed and the results are compared with the behavior of an orthotropic lamina of equal mass density. The results show the characteristic features of the dynamic behavior of higher gradient models, and in particular the difference, with respect to classical laminae, in the dependence of the eigenfrequencies on the stiffness