An experimentally validated analytical model for the coupled electromechanical dynamics of linear vibration energy harvesting systems

Recent technological advancements in the efficiency of microprocessors, sensors, and other digital logic systems have increased research effort in vibration energy harvesting, where trace amounts of energy are scavenged from the ambient environment to provide power. Due to the complexity and nonlinearity of most vibration energy harvesting systems, existing research has relied primarily on numerical and finite element methods for harvester design and validation. Although these methods are useful, a vetted analytical model provides intuitive understanding of the governing dynamics and is useful for obtaining rough calculations when designing vibration energy harvesting systems. In this article, an analytical framework for linear electromechanical transducer modeling is developed into the coupled electromechanical model; a transfer function characterizing the dynamics of second-order VEH systems, which includes inputs for mechanical and electrical domain lumped parameters as complex impedances. The coupled electromechanical model transfer function is validated against frequency sweep data from a linear vibration energy harvesting experimental setup. The experimental setup demonstrated good correlation with the coupled electromechanical model, with not more than 0.9% error in natural frequency overall, 6% error in damping ratio for purely resistive loads, and 11% for reactive loads.