Embodiments of the invention couple a non-linear force to a vibration element such as a piezoelectric cantilever to introduce chaotic, i.e., non-resonant vibration in the vibration element and thereby improve the non-resonant response of the vibration element. By doing so, the vibration element is responsive to a wider frequency range of vibrations and thus may be more efficient in scavenging energy in environments where the vibration frequency is not constant, e.g., in environment subject to multi-mode or random vibration sources.
 The invention was supported in whole or in part by Contract/Grant No. DE-FC26-06NT42795 from the Department of Energy and Contract/Grant No. DAAB07-03-D-B010/TO-0198 from the United States Navy. The Government has certain rights in the invention.