Optimum tuning of series and parallel LR circuits for passive vibration suppression using piezoelectric elements

Abstract

Bending vibration of flexible structures can be suppressed passively using piezoelectric electromechanical transducers and optimally tuned LR circuits. Since these systems include both mechanical and electrical elements, the governing equations consist of electrically coupled equations of motion. This paper describes a new method for deriving the governing equations that describe a system's vibration suppression based on the equilibrium of force principle and using an equivalent mechanical model of a piezoelectric element. Both series and parallel LR circuits are considered in the modeling approach. The optimum values for a mechanical vibration absorber can be formulated by using the two fixed points method. However, exact optimal values for the resistances of the LR circuits have not been formulated in the research literature thus far, and approximate values have been used. Analytical formulations are derived in this paper, and optimum values of the LR circuits are presented, not only in displacement, but also in terms of velocity and acceleration. The effects of the stiffness of the adhesive bond between the host structure and piezoelectric element, the dielectric loss in a piezoelectric element, and the internal resistance of an inductor are considered in the theoretical analysis. The effectiveness of the described analytical method is validated through simulations and experiments.

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

“…Piezoelectric transducers are very versatile and may be used as for example actuator/sensor pairs in active control schemes [3,4,5], as semi-active devices based on vari-from [7] has been modified slightly by Yamada et al [24] to exactly follow the procedure used for classic mechanical tuned mass absorbers [22]. Alternatively, it has been demonstrated by Kim et al [5] and Kozlowski et al [25] that the governing equations of the piezoelectric RL shunt circuits are analogous to those of slightly modified mechanical absorber configurations, and calibration expressions have been derived based on these modified models.…”

Optimum values of electrical circuit for energy harvesting using a beam and piezoelectric elements

“…(7), (8), and (17) the equivalent mechanical model of the piezoelectric element and electrical circuit is drawn as Fig. 3(b) (Yamada et al, 2010). Here,…”

“…Equation (66) is the optimum natural frequency ratio derived using two fixed points method when the additional vibration system is excited by the external force, and mobility is evaluated in passive vibration suppression (Yamada et al, 2010). Equation (66) can be used for energy harvesting as the suboptimum value because the mobility is defined as Yamada, Kurata, Utsuno and Murakami, Mechanical Engineering Journal, Vol.4, No.4 (2017) [DOI: 10.1299/mej.17-00023] the reciprocal of the mechanical impedance, and the mechanical impedance is the broad definition of the damping.…”

“…The optimum resistance ratio for passive vibration suppression has been derived using the two fixed points method (Yamada et al, 2010). However, this optimum resistance ratio is not optimum for energy harvesting because the value minimizes the maximum value of the magnitude of the mobility, and the value does not maximize the damping effect of the vibration absorber on the additional vibration system.…”

“…The reason that an LR circuit has been seldom used in energy harvesting is that an actual inductor becomes too large for practical applications. In the case of passive vibration suppression, a generalized impedance converter is usually used instead of an actual inductor (Yamada et al, 2010). A generalized impedance converter requires two operational amplifiers.…”