A new method for accurately determining the modal equivalent stiffness ratio of bonded piezoelectric structures

This paper describes new methods for measuring the modal equivalent stiffness ratios and modal electromechanical coupling coefficients of piezoelectric elements attached to a host structure such as a beam. Modal equivalent stiffness ratios and modal electromechanical coupling coefficients are essential for estimating the performance and determining an optimum design of active vibration control and passive vibration suppression systems that use piezoelectric elements. Accurate determination of these modal parameters is also useful for other systems including piezoelectric sensors and energy generators. This paper not only describes the measurement methods but also presents the theoretical formulations derived by taking into account the effect of adhesive bonds. The formulations in this paper demonstrate the necessity of experimental measurements and the accuracy enhancements that the theoretical estimations can provide. Conventional methods for obtaining the modal equivalent stiffness ratios are sensitive to measurement errors, which result in the loss of accuracy, rendering these methods unreliable for many practical applications. The proposed methods use an inductor instead of an open circuit to address the abovementioned issue and, thereby, provide significant improvement in the accuracy. Because the loss factors of the experimental apparatus tend to compromise the accuracy of the proposed methods, a method using a negative resistor is proposed, theoretically analyzed, and confirmed to eliminate some of the errors introduced by loss factors. The advantages of the proposed methods and the effectiveness of theoretical analysis, considering the effect of adhesive bonds, are verified experimentally.