This paper tests the effect of multi-frequency vibrations on the power output of piezoelectric
energy harvesters. These tests were conducted to show how the output power scales when an energy harvester is excited not only at its eigenfrequency, but also at an off-resonance frequency and how well theoretical models predict power output under these conditions. A linear cantilever and bistable buckled beam are tested experimentally on an electrodynamic shaker and simulated using existing models to compare the accuracy of these models under such excitations. The excitation signal has one fixed frequency component, which matches the eigenfrequency of the energy harvester; and a second vibration component, which has a frequency and amplitude that are varied. For a linear cantilever, it was shown that an existing closed-parameter model can predict power output for the mechanical and electrical parameters, where the power is a summation of the power generated by each separate frequency. However, even a simple cantilever shows nonlinearity for high excitations; this is something one needs to account for if you use the model to calculate expected power output.
For a nonlinear harvester it was shown that the power output scales linear with the amplitude of vibration when subjected to a single sine. For multi-sine vibrations, the power output is only slightly increased by adding the second frequency, indicating that the beneficial bandwidth of a nonlinear energy harvester is much smaller when absorbing energy from a second frequency.