Vibration control in plates by uniformly distributed PZT actuators interconnected via electric networks

In this paper a novel device aimed at controlling the mechanical vibrations of plates by means of a set of electrically-interconnected piezoelectric actuators is described. The actuators are embedded uniformly in the plate wherein they connect every node of an electric network to ground, thus playing the two-fold role of capacitive element in the electric network and of couple suppliers. A mathematical model is introduced to describe the propagation of electro-mechanical waves in the device; its validity is restricted to the case of wave-forms with wave-length greater than the dimension of the piezoelectric actuators used. A self-resonance criterion is established which assures the possibility of electro-mechanical energy exchange. Finally the problem of vibration control in simply supported and clamped plates is addressed; the optimal net-impedance is determined. The results indicate that the proposed device can improve the performances of piezoelectric actuationComment: 22 page

Models to detect scientific creativity: Why something simpler than Fréchet Metric Manifolds?

We claim that the models needed to describe scientific creativity (and, in particular, suitable to effectively detect it) have to be very sophisticated. Indeed, the process of creating original and predictive scientific theories is manifestly the most complex ever investigated by the human mind (There are also some paradoxical aspects in the action of a mind that is investigating its own way of functioning, but we are confident that it will be possible to avoid them). In mathematical physics one of the most complex state space structures is given by Frechet Metric Manifolds. We conjecture that they will be needed to model the state of complexity of the mind of a scientist (However, we will not be surprised if an even more complex structure could be needed). The obtained models have a very important application: they are essential to design and rule the selection process that assigns a university chair (or a research grant). Recently some algorithms have been introduced to calculate some bibliometric indices. We claim that it is not reasonable to use them to evaluate the scientific quality of researchers, chair or grant holders, departments or whole universities. Instead, the only presently viable process must involve carefully designed procedures, similar to those used for forming juries. These procedures must be enforced to rule the formation and functioning of ad hoc peer committees entrusted to evaluate academic institutions and nominate professors, chairs or research grant holders. Bibliometrics and Scientometrics are too young as disciplines and therefore it is not possible yet, by means of the theoretical insight gained thanks to them, to design a more effective evaluation process. Only when game and artificial intelligence theories become sufficiently advanced will it become possible to efficiently replace selection peers committees (i.e. academic juries)

Exegesis of Sect. III.B from “Fundamentals of the Mechanics of Continua” by E. Hellinger

This is our third and last exegetic essay on the fundamental review article DIE ALLGEMEINEN ANSÄTZE DER MECHANIK DER KONTINUA in the Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Bd. IV-4, Hft. 5 (1913) by Ernst Hellinger which contains the translation and the commentary of the remaining text starting from p. 663. The six subsections, No. 9–15, deal with the applications of the previously developed conceptual tools to formulate: an effective theory of elasticity, the dynamics of ideal fluids, models for internal friction and elastic hysteresis, a theory of capillarity, optics, the fundamental equations of electrodynamics, an introduction of the thermodynamical foundations and the relationship between the theory of continua and the theory of relativity. Hellinger refers to relevant literature while consolidating in an effective way the contemporary knowledge in 1913. Considering notational differences as being irrelevant for the characterization of the presented scientific content, Hellinger's article shows that an effective compendium of a large part of the insights given in Truesdell and Toupin and Truesdell and Noll has already been available in 1913. We include in this paper an assessment of the different roles played by pioneers, who are innovating their scientific discipline, and by erudite scholars whose role consists in re-ordering existent knowledge and advertising to a wider audience the most important technical results already obtained in a given discipline

Structural-Damage Detection by Distributed Piezoelectric Transducers and Tuned Electric Circuits

A novel technique for damage detection of structures is introduced and discussed. It is based on purely electric measurements of the state variables of an electric network coupled to the main structure through a distributed set of piezoelectric patches. The constitutive parameters of this auxiliary network are optimized to increase the sensitivity of global measurements- as the frequency, response functions relative to selected electric degrees of freedom-with respect to a given class of variations in the structural-mechanical properties. Because the proposed method is based on purely electric input and output measurements, it allows for accurate results in the identification and localization of damages. Use of the electric frequency-response function to identify the mechanical damage leads to nonconvex optimization problems; therefore the proposed sensitivity-enhanced identification procedure becomes computationally efficient if an a priori knowledge about the damage is available.Comment: 18 page

Optimal piezo-electro-mechanical coupling to control plate vibrations

A new way of coupling electrical and mechanical waves, using piezoelectric effect, is presented here. Since the energy exchange between two systems supporting wave propagation is maximum when their evolution is governed by similar equations, hence, an optimal electromechanical coupling is obtained by designing an electric network which is "analog" to the mechanical structure to be controlled. In this paper, we exploit this idea to enhance the coupling, between a Kirchhoff-Love plate and one possible synthesis of its circuital analog, as obtained by means of a set of piezoelectric actuators uniformly distributed upon the plate. It is shown how this approach allows for an optimal energy exchange between the mechanic and the electric forms independent of the modal evolution of the structure. Moreover, we show how an efficient electric dissipation of the mechanical energy can be obtained adding dissipative elements in the electric network.Comment: 9 page