Analytical solutions of the energy harvesting potential from vehicle vertical vibration based on statistical energy conservation

Two kinds of approaches have been proposed to harvest the vibrational energy from a running vehicle, namely using a regenerative damper to replace a traditional hydraulic suspension damper, or adding one or more dynamic vibration absorbers (DVAs). Extensive studies have been conducted by simulation or experiment on the first approach, whereas the studies on the second approach are very limited and even the energy harvesting potential is not clear. This paper tries to present an analytical solution, to uniformly reveal the energy harvesting potential from vehicle vertical vibration by both approaches, with a focus on approaches with DVAs. A generic quarter car model is proposed to represent various vibration energy harvesting configurations. With a newly enunciated statistical energy conservation property for linear vibration systems, the analytical solution of the energy harvesting potential is derived for the proposed model subjected to random excitation. It is illustrated from these analytical expressions that the total vehicle vertical vibration energy is not directly related to DVA configurations, and the vibration energy dissipated in the tire can be transferred to the absorbers. Literature results and newly implemented statistical analyses are presented to validate and demonstrate the derived solutions. Sensitivity analysis is then performed to reveal the effect of various vehicle parameters on the energy harvesting potential.