The non-linearity of a hardening-type oscillator provides a wider bandwidth and a higher energy harvesting capability under harmonic excitations. Also, both low- and high-energy responses can coexist for the same parameter combinations at relatively high excitation levels. However, if the oscillator’s response happens to coincide with the low-energy orbit then the improved performance achieved by the non-linear oscillator over that of its linear counterpart, could be impaired. This is therefore the main motivation for stabilisation of the high-energy orbit. In the present work, a schematic harvester design is considered consisting of a mass supported by two linear springs connected in series, each with a parallel damper, and a third-order non-linear spring. The equivalent linear stiffness and damping coefficients of the oscillator are derived through variation of the damper element. From this adjustment the variation of the equivalent stiffness generates a corresponding shift in the frequency–amplitude response curve, and this triggers a jump from the low-energy orbit to stabilise the high-energy orbit. This approach has been seen to require little additional energy supply for the adjustment and stabilisation, compared with that needed for direct stiffness tuning by mechanical means. Overall energy saving is of particular importance for energy harvesting applications. Subsequent results from simulation and experimentation confirm that the proposed method can be used to trigger a jump to the desirable state, thereby introducing a beneficial addition to the performance of the non-linear hardening-type energy harvester that improves overall efficiency and broadens the bandwidth.
High-energy orbit sliding mode control for nonlinear energy harvesting
