Enhancing efficiency of piezoelectric element attached to beam using extended spacers

This paper describes a new method that enhances the efficiency of a piezoelectric element attached to a beam, based on mechanical impedance matching. The attached piezoelectric element is often used to suppress bending vibration passively or actively. This element can also be used as a sensor or an energy-harvesting source and placement optimization is often used for enhancing its efficiency. When the efficiency is insufficient despite using placement optimization, the size or number of piezoelectric elements is increased. Although these two methods improve the efficiency of the piezoelectric element qualitatively and quantitatively, respectively, the improvements are still insufficient for practical applications. We have proposed a method based on mechanical impedance matching for enhancing the efficiency of the attached piezoelectric element and found that the width and thickness of the element were independent of the maximum value of the modal equivalent stiffness ratio, the parameter that determines the performance of passive vibration suppression under the ideal condition. However, the maximum value of the modal equivalent stiffness ratio depends on the length of the piezoelectric element. In this paper, we propose yet another new method that does not require a piezoelectric element of large length. In this method, the modal equivalent stiffness ratio is independent of the length of the piezoelectric element under the ideal condition. As this new method involves extending the region of the beam with respect to mechanical impedance matching using spacers extended in the longitudinal direction, the efficiency of the piezoelectric element is improved. Although the only difference between the new method and our previous methods is the extended parts of the spacers, the proposed method was theoretically investigated because of the need to additionally consider the effect of the extended parts. The optimum condition for the proposed method was theoretically formulated, and the effectiveness of the new method and the theoretical analysis was verified through simulations and experiments.