Dionisio Del Vescovo

Comparison of piezoelectronic networks acting as distributed vibration absorbers

Abstract 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 .

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

This review paper intends to gather and organize a series of works which discuss the possibility of exploiting the mechanical properties of distributed arrays of piezoelectric transducers. The concept can be described as follows: on every struc- tural member one can uniformly distribute an array of piezoelectric transducers whose electric terminals are to be connected to a suitably optimized electric waveguide. If the aim of such a modification is identified to be the suppression of mechanical vibrations then the optimal electric waveguide is identified to be the ‘electric analog’ of the considered structural member. The obtained electromechanical systems were called PEM (PiezoElectroMechanical) structures. The authors especially focus on the role played by Lagrange methods in the design of these analog circuits and in the study of PEM structures and we suggest some possible research developments in the conception of new devices, in their study and in their technological application. Other potential uses of PEMs, such as Structural Health Monitoring and Energy Harvesting, are described as well. PEM structures can be regarded as a particular kind of smart materials, i.e. materials especially designed and engineered to show a specific and well-defined response to external excitations: for this reason, the authors try to find connection between PEM beams and plates and some micromorphic materials whose properties as carriers of waves have been studied recently. Finally, this paper aims to establish some links among some concepts which are used in different cultural groups, as smart structure, metamaterial and functional structural modifications, showing how appropriate would be to avoid the use of different names for similar concepts.

Structural-acoustic coupling in complex shaped cavities

Abstract Structural-acoustic interaction is a topic of increasing interest in the study of vehicle noise control. During recent years particular attention has been devoted towards analytical and numerical methods for the analysis of acoustic problems of complex shaped cavities. Among them non-local methods are very appropriate for the low and medium frequency range. The integral formulation of the Helmholtz equation allows the sound pressure level, radiated by a vibrating panel, to be determined. The method may be used to account for the acoustic structural coupling and can be straightforwardly extended to consider interconnected cavities, internal vibrating panels, internal barriers and absorbing materials. Comparisons with experimental results as well as with modal methods are presented which show satisfactory agreement.

Variational Feedback Control for a nonlinear beam under an earthquake excitation

The present paper reports on the application of the VFC (Variational Feedback Control) to the mitigation of the vibrational motion of continuous structures. The control method has been very recently proposed in the context of mechanical engineering to obtain suspensions characterized by better comfort performances. In this paper the same methodology is indeed applied to a simply nonlinear supported beam that is forced by a seismic excitation. The earthquake shaking, modelled as a random displacement of the beam hinges, is moderated by the presence of a controllable damper interposed between the beam and the oscillating ground, and its damping is subjected to the VFC controller. The inputs processed by the controller are the accelerations measured by two sensors, one on the ground, and the second on the beam. Numerical results are examined and some preliminary considerations are presented in which the considered method is applied to piezoelectromechanical beams.

Experiments on Rest-to-rest Motion of a Flexible Arm

We present an experimental validation of a recently proposed solution to the problem of finding the input torque command that provides rest-to-rest motion in a given time for a one-link flexible arm. The basic idea is to design an auxiliary output such that the associated input-output transfer function has no zeros. Planning a smooth interpolating trajectory for this output imposes a unique rest-to-rest motion to the whole arm, with automatically bounded link deformations. The nominal torque is then obtained by standard inverse dynamics computation. The method is presented for a linear model of an Euler-Bernoulli flexible beam, satisfying dynamic boundary conditions and taking into account also modal damping. We illustrate the dynamic identification of the experimental flexible arm, the handling of static/viscous joint friction within the proposed method, and the way to include a stabilizing feedback based only on joint measurements. Finally, we report on comparative experimental results.

Semi-active control of a thin piezoactuated structure

Vibration damping of a cantilever plate is achieved by using a piezoelectric element simultaneously as passive single-mode device and active broad-band actuator. Control strategies are designed on the basis of a modal model of the coupled electro- mechanical structure. This model is obtained by using a suitable finite-element formulation together with a modal analysis. A purely passive single-mode control composed of an optimally tuned external RL shunt circuit and a purely active control based on classical LQG techniques are compared to a semi-active control obtained by tuning the external shunt circuit on the second vibration mode of the structure and using a LQG controller designed on the only first-mode model.

Combined polarization field gradient and strain field gradient effects in elastic flexoelectric materials

We consider a constitutive model for the behavior of elastic flexoelectric materials including strain gradient fields and polarization gradient fields. This model is based on a stored elastic energy density function which depends on four independent variables: the polarization field and the polarization field gradient as well as the strain field and the strain field gradient. A generalized Toupin variational approach is utilized to find the governing equations (constitutive relations, equilibrium equations and boundary conditions) of the material. The present model is then applied to the problem of a thick walled cylindrical tube of elastic isotropic flexoelectric material, subjected to axisymmetric loading. The resulting radial displacement field noticeably differs from the elastic and strain gradient elastic cases.

Modelling flexible multi-link robots for vibration control: Numerical simulations and real-time experiments:

In this paper, a method based on the experimental knowledge of the frequency response function at some points of a flexible multi-link robot is proposed to evaluate its deformation and, in particular, the position of the end-effector. The rationale behind the method, which can also be used for structures more complex than the one analysed in this paper, is to try to minimize the number of sensors, while maintaining a reasonable accuracy. We propose two simple control laws aimed at minimizing implementation costs and, in order to show the performance of the method, we experimentally test them on a spring steel flexible beam.

Distributed electric absorbers of beam vibrations

Several electric vibration absorbers based on distributed piezoelectric control of beam vibrations are studied. The damping devices are conceived by interconnecting with different modular electric networks an array of piezoelectric transducers uniformly distributed on a beam. Five different vibration absorbers made of five different network interconnecting topologies are considered and their damping performances are analyzed and compared. The analysis is based on homogenized models of modular piezo-electromechanical systems. The optimal parameters of these absorbers are found by adopting the criterion of critical damping of waves with a single wave number. We show that: i) there is an interconnecting network providing an optimal multimodal damping; ii) the performances required to the electr(on)ic components can be significantly decreased by increasing the number (and decreasing the dimensions) of the piezoelectric transducers.

Non-Linear Lumped-Parameter Modeling of Planar Multi-Link Manipulators with Highly Flexible Arms

The problem of the trajectory-tracking and vibration control of highly flexible planar multi-links robot arms is investigated. We discretize the links according to the Hencky bar-chain model, which is an application of the lumped parameters techniques. In this approach, each link is considered as a kinematic chain of rigid bodies, and suitable springs are added in order to model bending resistance. The control strategy employed is based on an optimal input pre-shaping and a feedback of the joint angles to treat the effects of undesired disturbances. Some numerical examples are given to show the potentialities of the proposed control, and a comparison with a standard collocated Proportional-Derivative (PD) control strategy is performed. In particular, we study the cases of a linear and a parabolic trajectory with a polynomial time law chosen to minimize the onset of possible vibrations.