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Vibration-based energy harvesting has been investigated by several researchers over the last decade. The goal in this research field is to power small electronic components by converting the waste vibration energy available in their environment into electrical energy. Piezoelectric energy harvesting is a promising technique for powering small-scale standalone electronic devices.

We further proposed an effective and efficient optimization method based on bond graph for optimizing physical aspects of the piezoelectric energy harvesting systems without intensive human effort.

Since the time constant of the mechanical cantilever system and internal piezoelectric inertia are far apart, a simple model of the piezoelectric element is sufficient for this analysis. More detailed models of piezoelectric transducers are available and could be of interest in future works.

This enables the piezoelectric layer to be model as a simple current source, an internal capacitance and an internal resistance. The electrode and substructure of the harvester create a capacitor C_p with the piezoelectric material as a dielectric. The internal resistance of the dielectric is expressed by R_p. The internal capacitance and resistance for each layer can be obtained.

This paper proposes a bond graph approach that is capable of modeling piezoelectric energy harvesters. The model is parameterized enabling simple introduction of relevant physical parameters. The bond graph model is verified by comparison to examples for which analytical and graphical solutions has been published. The bond graph model is valid close to the analysed mode centre frequency and delivers results compared to analytical data.