Modal Analysis

The first step in developing the semi-analytical model of a tapered piezoelectric energy harvester is to formulate a structural model for modal analysis of a multilayered, prismatic, tapered cantilever structure. The structure modeled here is strictly prismatic, assuming straight cuts in the structure fabrication process without undercutting. When undercutting is considered, the model can be updated to consider a taper along the structure’s thickness. The governing equation of motion for a tapered cantilever is first set up before formulating the spatial modal equation via the separation of variables.