Performance of piezoelectric shunts for vibration reduction

Abstract

This work addresses passive reduction of structural vibration by means of shunted piezoelectric patches. The two classical resistive and resonant shunt solutions are considered. The main goal of this paper is to give closed-form solutions to systematically estimate the damping performances of the shunts, in the two cases of free and forced vibrations, whatever the elastic host structure is. Then it is carefully demonstrated that the performance of the shunt, in terms of vibration reduction, depends on only one free parameter: the so-called modal electromechanical coupling factor (MEMCF) of the mechanical vibration mode to which the shunts are tuned. Experiments are proposed and an excellent agreement with the model is obtained, thus validating it.

Balanced calibration of resonant piezoelectric RL shunts with quasi-static background flexibility correction

“…The design of piezoelectric RL shunt circuits is commonly based on a single mode representation of the structural response, whereby the electromechanical system is gov-erned by two coupled scalar equations: The modal equation of motion and the corresponding electric filter equation [20]. This format implies that the electromechanical coupling coefficient can be identified directly from the natural frequencies associated with the short-and open circuit limits of the piezoelectric transducer, or from the frequency response properties of the structure when introducing a resonant shunt circuit [38,39].…”

“…Although the electromechanical coefficient may be determined accurately, the assumed single mode representation is still an approximation, and the theoretical predictions of the resistance R and inductance L are therefore often re-calibrated [8,9] to give the desired flat plateau in the frequency response curves. In particular the electric filter frequency must be calibrated precisely, and in RL shunt circuits the inductance L is conveniently adjusted by changing the variable components of the corresponding synthetic inductor [10,20,25].…”

“…It is noted that the background flexibility 1/k 0 can be evaluated directly from (24) using only the inverse of the stiffness matrix and the stiffness k r of the resonant mode, but without evaluating dynamic properties of any of the non-resonant modes. When introducing the approximate dynamic flexibility (22) into the scalar structure equation (20), the following relation is obtained for the deformation of the transducer…”

“…It is noted that the coefficient κ r represents the square of the generalized coupling coefficient with respect to the mode r. This parameter is commonly estimated -without background flexibility correction -via the relative difference between the square of the open and short circuit natural frequencies, see for example [7,20,37].…”

A search for optimal parameters of resonance circuits ensuring damping of electroelastic structure vibrations based on the solution of natural vibration problem

“…The analysis of the literature showed that in terms of efficiency of finding the appropriate parameters for external circuits providing passive vibration damping, this approach is still most popular when analyzing the dynamic behavior of electroelastic systems with external electric circuits. In this case, the optimal values of the external circuit parameters estimated on the basis of the transfer functions can be obtained by different ways, for example, by optimizing the transfer functions with respect to 2  -or  -norms [8,17], assuming the equality of amplitudes of transfer functions at the characteristic intersection points of curves [2,6,10], using the technique for placing the poles of the transfer function ( pole placement technique) [9][10]18], etc. The result of all these peculiarities is that, depending on the ways of constructing the transfer function and selecting the optimization criterion, the optimal parameters of the external circuit parameters can take different values [2,10,17].…”