Multimodal vibration damping through piezoelectric patches and optimal resonant shunt circuits

Abstract

Piezoelectric elements connected to shunt circuits and bonded to a mechanical structure form a dissipation device that can be designed to add damping to the mechanical system. Due to the piezoelectric effect, part of the vibration energy is transformed into electrical energy that can be conveniently dissipated. Therefore, by using appropriate electrical circuits, it is possible to dissipate strain energy and, as a consequence, vibration is suppressed through the added passive damping. From the electrical point of view, the piezoelectric element behaves like a capacitor in series with a controlled voltage source and the shunt circuit, commonly formed by an RL network, is tuned to dissipate the electrical energy, more efficiently in a given frequency band. It is important to know that large inductances are frequently required, leading to the necessity of using synthetic inductors (obtained from operational amplifiers). From the mechanical point of view, the vibration energy can be attenuated in a single mode, or in multiple modes, according to the design of the damping device and the frequency band of interest. This work is devoted to the study of passive damping systems for single modes or multiple modes, based on piezoelectric patches and resonant shunt circuits. The present contribution discusses the modeling of piezoelectric patches coupled to shunt circuits, where the basics of resonant shunt circuits (series and parallel topologies) are presented. Following, the devices used in passive control (piezoelectric patch and synthetic inductors) are analyzed from the electrical and experimental viewpoints. The modeling of multi-degree-of-freedom mechanical systems, including the effects of the passive damping devices is revisited, and, then a design methodology for the multi-modal case is defined. Also, it is briefly reviewed the optimization method used for design purposes, namely the LifeCycle Model. Finally, experimental results are reported, illustrating the success of using the methodology presented in passive damping applications applied to mechanical and mechatronic systems

Self-Tuning Multimodal Piezoelectric Shunt Damping

“…The addition of damping can be made later by adding resistors in series with the inductors. In general, damping provided by resistor is an important parameter to optimize the shunt performance as discussed by Viana and Steffen (2006) and Wu (1996). However, it is worth noticing that, in practice, due to the large inductance values usually required, the inductors are implemented using operational amplifiers.…”

“…In their work a two-mode resonant network was demonstrated, but few theoretical results were presented regarding the design of the shunt network parameters. Multimodal shunting was also investigated by Viana and Steffen (2006), who discussed the modeling of modeling of piezoelectric patches coupled to shunt network including a review of the basics of resonant network topologies. In addition, the modeling of multi-degree-of-freedom mechanical system was presented as well as a design methodology for the multi-modal case, although it was assumed each PZT was shunted with a parallel network of resistor and inductor designed to control a specific structural mode.…”

Vibration control of a flexible structure with electromagnetic actuators

“…In order to allow an effective operation in a wider force frequency range, [14] proposes the use of multiple degrees of freedom vibration absorbers. Other type of passive solutions can be achieved with the use of resonant circuit shunted piezoeletrics [23,25,27,31], use of viscoelastic materials [10] or shape memory alloys [9]. Alternative techniques, as the use of passive electromagnetic dampers, can be found in [22].…”

Structural vibration control using extension and shear active-passive piezoelectric networks including sensitivity to electrical uncertainties

“…In this case, the piezoelectric material serves two purposes. First, the vibration strain energy of the structure can be transferred to the shunt circuit, through the difference of electric potential induced in the piezoelectric material electrodes, and then passively dissipated in the electric components of the shunt circuit (Forward, 1979;Hagood andvon Flotow, 1991, Viana andSteffen, 2006). On the other hand, the piezoelectric material may also serve as an actuator for which a control voltage can be applied to actively control the structural vibrations.…”

“…The thickness-shear mode, originally proposed by Sun and Zhang (1995), can be obtained using longitudinallypoled piezoelectric patches that couple through-thickness electric fields/displacements and shear strains/stresses. On the other hand, although it is well-known that the performance of shunt circuits is quite sensible to the tuning of circuit parameters, little has been published about the complexities in tuning the electric circuit parameters and the effect of the parametric variations on the overall performance of the system (Viana and Steffen, 2006;Andreaus and Porfiri, 2007).…”