Optimal Attachment of a Secondary, Bender-Type Resonator to a Flexible Base Beam for Energy Harvesting Applications

The application of piezoelectric bender actuators as active resonators for energy harvesting may prove to be advantageous over uniaxial actuators as they can extract both rotary and translational energy from a flexible base. In addition, this minimizes the likelihood that the attachment location is the node of a mode (rotary or translational). In this paper, the equations of motion/boundary conditions are presented for a continuous two-beam system composed of a cantilevered, primary base beam with a secondary bender mounted to its surface. The secondary bender is composed of piezoelectric material. To generalize the analyses performed in this work, the equations were nondimensionalized. Using the nondimensionalized equations of motion, a tuning procedure is described to match the first natural frequency of the actuator beam to an arbitrary natural frequency of the base beam. The actuator beam was tuned to the first natural frequency of the base beam and a sensitivity study was performed to show the effect of the actuator beam attachment location on the system natural frequencies and mode shapes. Using the mode shape waterfall plots, a brief study was also performed to determine the percent strain energy in the actuator beam relative to the total system strain energy for the first four system modes.