Effect of Strain Nodes and Electrode Configuration on Piezoelectric Energy Harvesting From Cantilevered Beams

For the past five years, cantilevered beams with piezoceramic layer(s) have been frequently used as piezoelectric energy harvesters for vibration-to-electric energy conversion. Typically, the energy harvester beam is located on a vibrating host structure and the dynamic strain induced in the piezoceramic layer(s) results in an alternating voltage output across the electrodes. Vibration modes of a cantilevered piezoelectric energy harvester other than the fundamental mode have certain strain nodes where the dynamic strain distribution changes sign in the direction of beam length. It is theoretically explained and experimentally demonstrated in this paper that covering the strain nodes of vibration modes with continuous electrodes results in strong cancellations of the electrical outputs. A detailed dimensionless analysis is given for predicting the locations of the strain nodes of a cantilevered beam in the absence and presence of a tip mass. Since the cancellation issue is not peculiar to clamped-free boundary conditions, dimensionless data of modal strain nodes are tabulated for some other practical boundary condition pairs and these data can be useful in modal actuation problems as well. How to avoid the cancellation problem in energy harvesting by using segmented electrode pairs is described for single-mode and multimode vibrations of a cantilevered piezoelectric energy harvester. An electrode configuration-based side effect of using a large tip mass on the electrical response at higher vibration modes is discussed theoretically and demonstrated experimentally.