Response of uni-modal duffing-type harvesters to random forced excitations

The common linear energy harvesters have an inherent shortcoming in their operation concept because they operate efficiently only when the excitation frequency is very close to the fundamental frequency of the harvester. To extend the harvester’s bandwidth, some recent solutions call for utilizing energy harvesters with stiffness-type nonlinearities. From a steady-state perspective, this hardening nonlinearity can extend the coupling between the excitation and the harvester to a wider range of frequencies. In this effort, we investigate the response of such harvesters to Gaussian White and Colored excitations. For Gaussian White excitations, we solve the Fokker-Plank-Kolmogorov equation for the exact joint probability density function of the response. We show that the expected value of the output power is not even a function of the nonlinearity. As such, under White Gaussian excitations, nonlinearities in the stiffness do not provide any enhancement over the typical linear harvesters. Furthermore, we demonstrate that nonlinearities in the damping or inertia should be sought to enhance the output power. We also use the Van Kampen expansion to analyze the response to Colored excitations of different bandwidths and center frequencies. Again, we show that, regardless of the bandwidth or the center frequency, the expected value of the power is always less than that associated with a linear harvester.

[1]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[2]  David L. Churchill,et al.  Power management for energy harvesting wireless sensors , 2005, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[3]  Maarten J. IJzerman,et al.  Percutaneous neuromuscular electrical stimulation (P-NMES) for treating shoulder pain in chronic hemiplegia. Effects on shoulder pain and quality of life , 2004, Clinical rehabilitation.

[4]  L. Gammaitoni,et al.  Nonlinear energy harvesting. , 2008, Physical review letters.

[5]  Wen-Jong Wu,et al.  Tunable resonant frequency power harvesting devices , 2006, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[6]  B. Mann,et al.  Reversible hysteresis for broadband magnetopiezoelastic energy harvesting , 2009 .

[7]  Joseph A. Paradiso,et al.  Energy scavenging for mobile and wireless electronics , 2005, IEEE Pervasive Computing.

[8]  S. M. Shahruz,et al.  Limits of performance of mechanical band-pass filters used in energy scavenging , 2006 .

[9]  Jan M. Rabaey,et al.  A study of low level vibrations as a power source for wireless sensor nodes , 2003, Comput. Commun..

[10]  Alexander F. Vakakis,et al.  Vibration-Based Energy Harvesting With Essential Nonlinearities , 2007 .

[11]  N. G. Kampen,et al.  Systematic treatment of fluctuations in a nonlinear oscillator , 1976 .

[12]  Stephen G. Burrow,et al.  Energy harvesting from vibrations with a nonlinear oscillator , 2009 .

[13]  Mohammed F. Daqaq.  New Insight Into Energy Harvesting via Axially-Loaded Beams , 2009 .

[14]  D. Inman,et al.  A Review of Power Harvesting from Vibration using Piezoelectric Materials , 2004 .

[15]  Yang Zhang,et al.  Toward self-tuning adaptive vibration-based microgenerators , 2005, SPIE Micro + Nano Materials, Devices, and Applications.

[16]  Shadrach Roundy,et al.  On the Effectiveness of Vibration-based Energy Harvesting , 2005 .

[17]  Daniel J. Inman,et al.  Modeling of Piezoelectric Energy Harvesting from an L-shaped Beam-mass Structure with an Application to UAVs , 2009 .

[18]  Fred D. Discenzo,et al.  Resonant packaged piezoelectric power harvester for machinery health monitoring , 2005, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[19]  Massimo Ruzzene,et al.  . Proceedings of IDETC/CIE 2007, ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference, Las Vegas NV, USA , 2007 .

[20]  Daniel J. Inman,et al.  Generation and Storage of Electricity from Power Harvesting Devices , 2005 .

[21]  M. T. Lee,et al.  Implantable pacemakers , 1996, Proc. IEEE.

[22]  Neil D. Sims,et al.  Energy harvesting from the nonlinear oscillations of magnetic levitation , 2009 .

[23]  S. Shahruz.  Design of mechanical band-pass filters for energy scavenging , 2006 .

[24]  M. G. Prasad,et al.  A vibration energy harvesting device with bidirectional resonance frequency tunability , 2008 .

[25]  E. P. Spencer,et al.  The amelioration of the suffering associated with spinal cord injury with subperception transcranial electrical stimulation , 2003, Spinal Cord.

[26]  Paul K. Wright,et al.  A piezoelectric vibration based generator for wireless electronics , 2004 .

[27]  Kiyosi Itô.  109. Stochastic Integral , 1944 .

[28]  Daniel J. Inman,et al.  Towards autonomous sensing , 2006, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.