Balanced calibration of resonant shunt circuits for piezoelectric vibration control

Abstract

Shunting of piezoelectric transducers and suitable electric circuits constitutes an effective passive approach to resonant vibration damping of structures. Most common design concepts for resonant resistor-inductor (RL) shunt circuits rely on either maximization of the attainable modal damping or minimization of the frequency response amplitude. However, the former is suboptimal near resonance due to constructive interference of the two modes with identical frequency, and the latter results in reduced implemented damping. This article proposes an explicit pole placement–based design procedure for both series and parallel RL circuits. The procedure relies on equal modal damping and sufficient separation of the complex poles to avoid constructive interference of the two modes. By comparison with existing design procedures, it is demonstrated that the present calibration leads to a balanced compromise between large modal damping and effective response reduction with limited damping effort.

Piezoelectric vibration damping using resonant shunt circuits: an exact solution

“…The later rule maximizes the attainable modal damping by finding the value of the frequency tuning parameter for which the distinct poles coalesce in double complex conjugate pairs. Hogsberg and Krenk recently proposed a tuning rule that is a balanced compromise between these two design criteria [17]. Through the development of an equivalent mechanical model of a piezoelectric element, Yamada et al [18] introduced a new approximate analytic expression for the damping parameter that improves the PTVA performance compared to the formulae proposed in [7].…”

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

“…However, the property of equal modal damping, obtained by the proper frequency tuning of the mechanical absorber, is a desirable design property because it is independent of the particular loading and structural response, and therefore constitutes a robust design measure. As demonstrated in Krenk and Høgsberg [27] for general control formats and in Høgsberg and Krenk [28] for RL shunt circuits the balanced calibration technique with equal modal damping also leads to proper reduction of the frequency response amplitudes for both the structural response and the damper force.…”

“…The calibration is based on the principle of equal damping of the two modes generated by the electromechanical coupling with the resonant mode of the structure. This is a pole placement procedure, developed for the tuned mass damper in [26] and extended to general control formats in [27,28]. The present section constructs the generic polynomial equation with equal modal damping properties, and the calibration procedure then follows directly from parameter equivalence, as described in Section 5.…”

Shunt Damping Vibration Control Technology: A Review

“…However, the former is suboptimal near resonance due to constructive interference of the two modes with identical frequency, and the latter leads to reduced implemented damping. Hogsberg and Krenk [82][83][84] proposed an explicit pole placement-based design procedure that relies on equal modal damping and sufficient separation of the complex poles to avoid constructive interference of the two modes. The optimal parameters are [82] …”