We describe and demonstrate a computational approach to analyze and design piezoelectric energy harvesting systems composed of layered plate and shell-like structures with an external harvesting circuit. We model the coupled dynamic electromechanics of a piezoelectric harvester as well as the dynamics of an electrical circuit that is connected to the harvester with the finite element method. We assume the harvester is subjected to a prescribed harmonic excitation that may have broadband frequency content. Our design approach uses topology optimization to optimally design a piezoelectric harvester by tailoring the layout of a multilayer structure consisting of structural layers, piezoelectric layers, electrodes, as well as the electrical circuit parameters. We admit the spatially tailoring of these items both in the plane and through the thickness of the multilayer plate and shell. After a description of our analysis and design approaches, we present a number of examples that demonstrate some of the capabilities of our approach and show how it can be used to explore general behavior and develop overarching principles through the study of a suite of particular problems.

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