Optimal load resistance of a randomly excited nonlinear electromagnetic energy harvester with Coulomb friction

A nonlinear electromagnetic energy harvester directly powering a load resistance is considered in this manuscript. The nonlinearity includes the cubic stiffness and the unavoidable Coulomb friction, and the base excitation is confined to Gaussian white noise. Directly starting from the coupled equations, a novel procedure to evaluate the random responses and the mean output power is developed through the generalized harmonic transformation and the equivalent non-linearization technique. The dependence of the optimal ratio of the load resistance to the internal resistance and the associated optimal mean output power on the internal resistance of the coil is established. The principle of impedance matching is correct only when the internal resistance is infinity, and the optimal mean output power approaches an upper limit as the internal resistance is close to zero. The influence of the Coulomb friction on the optimal resistance ratio and the optimal mean output power is also investigated. It is proved that the Coulomb friction almost does not change the optimal resistance ratio although it prominently reduces the optimal mean output power.

[1]  Mohammed F. Daqaq,et al.  Electromechanical Modeling and Nonlinear Analysis of Axially Loaded Energy Harvesters , 2011 .

[2]  Sondipon Adhikari,et al.  The analysis of piezomagnetoelastic energy harvesters under broadband random excitations , 2011 .

[3]  Kais Atallah,et al.  The effect of Duffing-type non-linearities and Coulomb damping on the response of an energy harvester to random excitations , 2012 .

[4]  W. Zhu,et al.  Stochastic Averaging of Energy Envelope , 1991 .

[5]  Yaowen Yang,et al.  Toward Broadband Vibration-based Energy Harvesting , 2010 .

[6]  Vicenç Méndez,et al.  Efficiency of harvesting energy from colored noise by linear oscillators. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Neil D. Sims,et al.  On the identification and modelling of friction in a randomly excited energy harvester , 2013 .

[8]  S. Beeby,et al.  Strategies for increasing the operating frequency range of vibration energy harvesters: a review , 2010 .

[9]  Henry A. Sodano,et al.  A review of power harvesting using piezoelectric materials (2003–2006) , 2007 .

[10]  D. Inman,et al.  Equivalent damping and frequency change for linear and nonlinear hybrid vibrational energy harvesting systems , 2011 .

[11]  Mohammed F. Daqaq,et al.  Response of uni-modal duffing-type harvesters to random forced excitations , 2010 .

[12]  B. Mann,et al.  On the performance and resonant frequency of electromagnetic induction energy harvesters , 2010 .

[13]  S. Beeby,et al.  Optimization of an Electromagnetic Energy Harvesting Device , 2006, IEEE Transactions on Magnetics.

[14]  Sihong Zhao,et al.  Electroelastic modeling and experimental validations of piezoelectric energy harvesting from broadband random vibrations of cantilevered bimorphs , 2012 .

[15]  E. Halvorsen.  Fundamental issues in nonlinear wideband-vibration energy harvesting. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  A. Zyablovsky,et al.  Light propagation in composite materials with gain layers , 2012 .

[17]  Yoshiyuki Suzuki,et al.  Response and stability of strongly non-linear oscillators under wide-band random excitation , 2001 .

[18]  Mohammed F. Daqaq,et al.  On intentional introduction of stiffness nonlinearities for energy harvesting under white Gaussian excitations , 2012 .

[19]  Xiaoling Jin,et al.  Random vibration with inelastic impact: equivalent nonlinearization technique , 2014 .

[20]  Kais Atallah,et al.  The benefits of Duffing-type nonlinearities and electrical optimisation of a mono-stable energy harvester under white Gaussian excitations , 2012 .

[21]  N. G. Stephen,et al.  On energy harvesting from ambient vibration , 2006 .

[22]  Mohammed F. Daqaq,et al.  Transduction of a bistable inductive generator driven by white and exponentially correlated Gaussian noise , 2011 .

[23]  Marco Ferrari,et al.  Piezoelectric buckled beams for random vibration energy harvesting , 2012 .

[24]  Z. G. Ying,et al.  Stochastic averaging of energy envelope of Preisach hysteretic systems , 2009 .

[25]  Just L. Herder,et al.  Bistable vibration energy harvesters: A review , 2013 .

[26]  Einar Halvorsen.  Erratum: Fundamental issues in nonlinear wideband-vibration energy harvesting [Phys. Rev. E 87, 042129 (2013)] , 2013 .

[27]  Sihong Zhao,et al.  On the stochastic excitation of monostable and bistable electroelastic power generators: Relative advantages and tradeoffs in a physical system , 2013 .

[28]  Igor A. Khovanov,et al.  The role of excitations statistic and nonlinearity in energy harvesting from random impulsive excitations , 2011 .

[29]  S. Beeby,et al.  Energy harvesting vibration sources for microsystems applications , 2006 .

[30]  Ryan L. Harne,et al.  A review of the recent research on vibration energy harvesting via bistable systems , 2013 .

[31]  Grzegorz Litak,et al.  Magnetopiezoelastic energy harvesting driven by random excitations , 2010 .