An experimental study to determine damping of piezoelectric harvesters using transient analysis of unified electromechanical voltage equation

Toward the accurate electrical and mechanical modulations of the piezoelectric harvester, this paper presents a unified electromechanical-coupled voltage equation and a damping determination method. A single differential equation for the voltage is obtained that accommodates mechanical and electrical physics for which the exact transient solution is presented. In addition, the fully coupled relationship between the voltage output, the driving vibration frequency, and the resistive electrical load is clarified. A simple method is devised to determine the damping coefficient from only the voltage time-domain measurements based on the harmonic transient voltage response (HTVR). The HTVR uses the transient characteristics of the voltage measurements. The results showed that the electromechanical-coupling effect on the harvester resonant frequency is influential for the kilo Ohm scale electrical loads. This finding is contributed to the piezoelectric harvester's frequency-matched design by calculating the accurate coupled natural frequency. The results also proved the ability of the HTVR in the accurate determination of the damping coefficient without prior modeling and using only the voltage measurements made on the piezoelectric harvester. The results also demonstrate the HTVR ability for characterizing the piezoelectric harvester by accurate damping determination under any arbitrary-frequency harmonic excitation even with noisy, polluted voltage measurements.