The performance of a vibrational energy harvester based on a piezoelectric film attached to a bistable laminate was characterised by measuring the power that it generates when it is shaken at different frequencies. Since this device has two stable states, it may oscillate chaotically in a wide range of frequencies, which represents an advantage over linear, narrow-bandwidth harvesting devices. This device was modelled with a modified version of the Duffing equation, to which a quadratic term was added to predict the asymmetry of the laminate. After comparing the simulations with the experimental results, it was found that this equation predicts the presence of chaotic oscillations but underestimates the amplitude of the generated voltage. By converting the vibration and voltage signals to dimensionless variables, an empirical relationship was found in which the output power can be related to the vibration characteristics, the properties of the piezoelectric material, and the resistive load.