Energy Harvesting From Broadband Random Vibrations: Comparison of Single-Mode and Multi-Mode Electroelastic Solutions

Vibration-based energy harvesting has been heavily researched over the last decade with a primary focus on resonant excitation. However, ambient vibrational energy often has broader frequency content than a single harmonic, and in many cases it is entirely stochastic. As compared to the literature of deterministic energy harvesting, very few authors presented modeling approaches for energy harvesting from broadband random vibrations. These efforts have combined the input statistical information with the single-degree-of-freedom (SDOF) dynamics of the energy harvester to express the statistical electromechanical response characteristics. In most cases, the motion input (base acceleration) is assumed to be ideal white noise. White noise has a flat power spectral density (PSD) that might in fact excite higher vibration modes of an electroelastic energy harvester. In particular, piezoelectric energy harvesters constitute such continuous electroelastic systems with more than one vibration mode. This paper presents modeling and simulations of piezoelectric energy harvesting from broadband random vibrations based on distributed-parameter electroelastic solution. For white noise–type base acceleration of a given PSD level, first the general solution of the distributed-parameter problem is given. Closed-form representations are extracted for the single-mode case and these are analogous to the SDOF equations reported in the literature of energy harvesting. It is reported that the single-mode predictions might result in significant mismatch as compared to multi-mode predictions. Using the electroelastic solution, soft and hard piezoelectric power generators are compared under broadband random excitation. Shunt damping effect of power generation on the stochastic vibration response under broadband random excitation is also reported.