A theoretical model for a piezoelectric energy harvester with a tapered shape

A piezoelectric energy harvester made of a tapered cantilever surface bonded with piezoelectric patches is developed to harness energy from ambient vibrations. Compared with the available cantilever harvester of a uniform shape in the length direction, this harvester has a higher energy harvesting efficiency since a maximum collected power at each piezoelectric patch on the cantilever can be achieved. The current available models for cantilever harvesters are not applicable for the new developed tapered harvester due to the difficulties in dealing with the tapered shape. A corresponding finite differential model is hence developed to model the tapered harvester for estimating its efficiency by examining a governing differential equation with variable coefficients. The influences of some practical considerations, such as the geometry of the tapered cantilever and the width of piezoelectric patches on the root mean square of the generated electric power, are discussed. The results from the developed model show that an electric power up to 70 times higher than the available uniform cantilever harvesters can be achieved by the tapered harvester. This research provides an effective model for evaluating the high efficiency of the piezoelectric coupled tapered cantilevers in energy harvesting.