A practical power maximization design guide for piezoelectric energy harvesters inspired by avian bio-loggers

Vibrational energy harvesting has been the subject of significant recent research, and has even begun commercial deployment. Despite the research community's understanding of the fundamental mechanics of piezoelectric systems under base excitation, proper design methods and guidelines for applied systems are nonexistent. This leaves engineers with the options of either using non-ideal beams, or developing complex heuristic computational design programs. Such options are untenable given the state of research. We seek to answer a relatively simple question: Given mass, frequency, and size requirements, what would be the dimensions of the ideal bimorph harvester? By using approximations for the first natural frequency and mode shape, we are able to determine the unknown beam dimensions and modal parameters in terms of the system requirements and material properties. The result is a power equation that only depends on relative piezoelectric material thickness, and the mechanical damping ratio. With only two dependent variables, the equations can be swept in order to find the ideal beam geometry for any given damping ratio. In addition to presenting this method, two design case studies are provided as examples.