Single-degree-of-freedom (SDOF) mechanical oscillators have been the most common type of generators used to harvest energy from mechanical vibrations. When the excitation is harmonic, optimal performance is achieved when the device is tuned so that its natural frequency coincides with the excitation frequency. In such a situation, the harvested energy is inversely proportional to the damping in the system, which is sought to be very low. However, very low damping means that there is a relatively long transient in the harvester response, both at the beginning and at the end of the excitation, which can have a considerable effect on the harvesting performance. This paper presents an investigation into the mechanical design of a linear resonant harvester to scavenge energy from time-limited harmonic excitations to determine an upper bound on the energy that can be harvested. It is shown that when the product of the number of excitation cycles and the harvester damping ratio is greater (less) than about 0.19, then more (less) energy can be harvested from the forced phase of vibration than from the free phase of vibration at the end of the period of excitation. The analytical expressions developed are validated numerically on a simple example and on a more practical example involving the harvesting of energy from trackside vibrations due to the passage of a train.

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