Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation

A nonlinear analysis of an energy harvester consisting of a multilayered cantilever beam with a tip mass is performed. The model takes into account geometric, inertia, and piezoelectric nonlinearities. A combination of the Galerkin technique, the extended Hamilton principle, and the Gauss law is used to derive a reduced-order model of the harvester. The method of multiple scales is used to determine analytical expressions for the tip deflection, output voltage, and harvested power near the first global natural frequency. The results show that one- or two-mode approximations are not sufficient to produce accurate estimates of the voltage and harvested power. A parametric study is performed to investigate the effects of the nonlinear piezoelectric coefficients and the excitation amplitude on the system response. The effective nonlinearity may be of the hardening or softening type, depending on the relative magnitudes of the different nonlinearities.

[1]  Wenwu Cao,et al.  Nonlinear properties of lead zirconate–titanate piezoceramics , 2000 .

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

[3]  Luigi Fortuna,et al.  A nonlinear model for ionic polymer metal composites as actuators , 2007 .

[4]  Daniel Guyomar,et al.  Nonlinearities in Langevin transducers , 1994, 1994 Proceedings of IEEE Ultrasonics Symposium.

[5]  Mustafa Arafa,et al.  On the Nonlinear Behavior of Piezoelectric Actuators , 2004 .

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

[7]  Ali H. Nayfeh,et al.  Modeling and analysis of piezoaeroelastic energy harvesters , 2012 .

[8]  P. Hagedorn,et al.  PIEZO–BEAM SYSTEMS SUBJECTED TO WEAK ELECTRIC FIELD: EXPERIMENTS AND MODELLING OF NON-LINEARITIES , 2002 .

[9]  D. Inman,et al.  Nonlinear piezoelectricity in electroelastic energy harvesters: Modeling and experimental identification , 2010 .

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

[11]  D. Dane Quinn,et al.  The Effect of Non-linear Piezoelectric Coupling on Vibration-based Energy Harvesting , 2009 .

[12]  Daniel J. Inman,et al.  An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations , 2009 .

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

[14]  Ann Marie Sastry,et al.  Powering MEMS portable devices—a review of non-regenerative and regenerative power supply systems with special emphasis on piezoelectric energy harvesting systems , 2008 .

[15]  Daniel Guyomar,et al.  Piezoelectric Ceramics Nonlinear Behavior. Application to Langevin Transducer , 1997 .

[16]  D. Inman,et al.  On Mechanical Modeling of Cantilevered Piezoelectric Vibration Energy Harvesters , 2008 .

[17]  Paul Muralt,et al.  Ferroelectric thin films for micro-sensors and actuators: a review , 2000 .

[18]  Daniel J. Inman,et al.  A Distributed Parameter Electromechanical Model for Cantilevered Piezoelectric Energy Harvesters , 2008 .

[19]  Muhammad R. Hajj,et al.  Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters , 2012 .

[20]  Bernard H. Stark,et al.  MEMS electrostatic micropower generator for low frequency operation , 2004 .

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

[22]  N. Jalili,et al.  Modeling, Nonlinear Dynamics, and Identification of a Piezoelectrically Actuated Microcantilever Sensor , 2008, IEEE/ASME Transactions on Mechatronics.

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

[24]  R. B. Yates,et al.  Analysis Of A Micro-electric Generator For Microsystems , 1995, Proceedings of the International Solid-State Sensors and Actuators Conference - TRANSDUCERS '95.

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

[26]  P. Seshu,et al.  A finite element model for nonlinear behaviour of piezoceramics under weak electric fields , 2005 .

[27]  S. Joshi.  Non-linear constitutive relations for piezoceramic materials , 1992 .

[28]  D.P. Arnold,et al.  Review of Microscale Magnetic Power Generation , 2007, IEEE Transactions on Magnetics.

[29]  E. Crawley,et al.  Use of piezoelectric actuators as elements of intelligent structures , 1987 .

[30]  Peter Hagedorn,et al.  Nonlinear Effects of Piezoceramics Excited by Weak Electric Fields , 2003 .

[31]  Daniel J. Inman,et al.  Estimation of Electric Charge Output for Piezoelectric Energy Harvesting , 2004 .

[32]  S. Narayanan,et al.  Active control of tensegrity structures under random excitation , 2007 .

[33]  Vimal Singh,et al.  Perturbation methods , 1991 .

[34]  H. F. Tiersten,et al.  Linear Piezoelectric Plate Vibrations , 1969 .

[35]  R. Haftka,et al.  Uncertainty-based Design Optimization of a Micro Piezoelectric Composite Energy Reclamation Device , 2004 .

[36]  S. Priya.  Advances in energy harvesting using low profile piezoelectric transducers , 2007 .

[37]  A. Nayfeh.  Introduction To Perturbation Techniques , 1981 .

[38]  Jinhao Qiu,et al.  Modeling and Characterization of Piezoelectric Fibers with Metal Core , 2005 .