A vibration energy harvester is typically composed of a spring–mass system with an electromagnetic or piezoelectric transducer connected in parallel with a spring. This configuration has been well studied and optimized for harmonic vibration sources. Recently, a dual-mass harvester, where two masses are connected in series by the energy transducer and a spring, has been proposed. The dual-mass vibration energy harvester is proved to be able to harvest more power and has a broader bandwidth than the single-mass configuration, when the parameters are optimized and the excitation is harmonic. In fact, some dual-mass vibration energy harvesters, such as regenerative vehicle suspensions and buildings with regenerative tuned mass dampers (TMDs), are subjected to random excitations. This paper is to investigate the dual-mass and single-mass vibration harvesters under random excitations using spectrum integration and the residue theorem. The output powers for these two types of vibration energy harvesters, when subjected to different random excitations, namely force, displacement, velocity and acceleration, are obtained analytically with closed-form expressions. It is also very interesting to find that the output power of the vibration energy harvesters under random excitations depends on only a few parameters in very simple and elegant forms. This paper also draws some important conclusions on regenerative vehicle suspensions and buildings with regenerative TMDs, which can be modeled as dual-mass vibration energy harvesters. It is found that, under white-noise random velocity excitation from road irregularity, the harvesting power from vehicle suspensions is proportional to the tire stiffness and road vertical excitation spectrum only. It is independent of the chassis mass, tire–wheel mass, suspension stiffness and damping coefficient. Under random wind force excitation, the power harvested from buildings with regenerative TMD will depends on the building mass only, not on the parameters of the TMD subsystem if the ratio of electrical and mechanical damping is constant.
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