Nonlinear dynamic modeling of bimorph piezoelectric actuators using modified constitutive equations caused by material nonlinearity

References

• N. Chattaraj and R. Ganguli, “Electromechanical analysis of piezoelectric bimorph actuator in static state considering the nonlinearity at high electric field,” Mech. Adv. Mater. Struct., vol. 23, no. 7, pp. 802–810, 2016. DOI: 10.1080/15376494.2015.1029168.
   Web of Science ®Google Scholar
• G. Wang, C. Tan, and F. Li, “A contact resonance viscometer based on the electromechanical impedance of a piezoelectric cantilever,” Sens. Actuators A, vol. 267, pp. 401–408, 2017. DOI: 10.1016/j.sna.2017.10.041.
   Google Scholar
• H. Ghafarirad, S. M. Rezaei, M. Zareinejad, and A. A. D. Sarhan, “Disturbance rejection-based robust control for micropositioning of piezoelectric actuators,” C. R. Méc., vol. 342, no. 1, pp. 32–45, 2014. DOI: 10.1016/j.crme.2013.11.003.
   Web of Science ®Google Scholar
• B. Ghosh, R. K. Jain, S. Majumder, S. S. Roy, and S. Mukhopadhyay, “Experimental performance evaluation of smart bimorph piezoelectric actuator and its application in micro robotics,” Microsyst. Technol., vol. 23, no. 10, pp. 4619–4635, Oct. 2017. DOI: 10.1007/s00542-017-3273-4.
   Web of Science ®Google Scholar
• D. Olender, P. Wild, and P. Byrnes, “A piezoelectric force sensor for mill-scale chip refiners,” Proc. Inst. Mech. Eng., Part E, vol. 222, no. 2, pp. 115–122, 2008. DOI: 10.1243/09544089JPME172.
   Google Scholar
• M. N. Fakhzan and A. G. A. Muthalif, “Harvesting vibration energy using piezoelectric material: Modeling, simulation and experimental verifications,” Mechatronics, vol. 23, no. 1, pp. 61–66, 2013. DOI: 10.1016/j.mechatronics.2012.10.009.
   Web of Science ®Google Scholar
• M. Lugovy, V. Slyunyayev, and N. Orlovskaya, “Two-layered cantilever sensor: A simplified mechanical analysis of dimensional limitations,” Mech. Adv. Mater. Struct., vol. 17, no. 4, pp. 280–286, 2010. DOI: 10.1080/15376490903556634.
   Web of Science ®Google Scholar
• I. A. Ivan, M. Rakotondrabe, P. Lutz, and N. Chaillet, “Quasistatic displacement self-sensing method for cantilevered piezoelectric actuators,” Rev. Sci. Instrum., vol. 80, no. 6, pp. 065102, 2009. DOI: 10.1063/1.3142486.
   PubMed Web of Science ®Google Scholar
• N. Jalili, Piezoelectric-Based Vibration Control from Macro to Micro/Nano Scale Systems. New York, NY: Springer, 2010.
   Google Scholar
• M. J. Shirazi, H. Salarieh, A. Alasty, and R. Shabani, “Tip tracking control of a micro-cantilever Timoshenko beam via piezoelectric actuator,” J. Vib Control, vol. 19, no. 10, pp. 1561–1574, 2013. DOI: 10.1177/1077546312447837.
   Web of Science ®Google Scholar
• H. Ghafarirad, S. M. Rezaei, A. A. D. Sarhan, and M. Zareinejad, “Continuous dynamic modelling of bimorph piezoelectric cantilevered actuators considering hysteresis effect and dynamic behaviour analysis,” Math. Comput. Modell. Dyn. Syst., vol. 21, no. 2, pp. 130–152, 2014. DOI: 10.1080/13873954.2014.906472.
   Web of Science ®Google Scholar
• V. Hassani and T. Tjahjowidodo, “A hysteresis model for a stacked-type piezoelectric actuator,” Mech. Adv. Mater. Struct., vol. 24, no. 1, pp. 73–87, 2017. DOI: 10.1080/15376494.2015.1107668.
   Web of Science ®Google Scholar
• S. N. Mahmoodi, N. Jalili, and M. F. Daqaq, “Modeling, nonlinear dynamics, and identification of a piezoelectrically actuated microcantilever sensor,” IEEE/ASME Trans. Mechatronics, vol. 13, no. 1, pp. 58–65, 2008. DOI: 10.1109/TMECH.2008.915823.
   Web of Science ®Google Scholar
• S. P. Joshi, “Non-linear constitutive relations for piezoceramic materials,” Smart Mater. Struct., vol. 1, no. 1, pp. 80, 1992. DOI: 10.1088/0964-1726/1/1/012.
   Google Scholar
• D. Guyomar, N. Aurelle, and L. Eyraud, “Piezoelectric ceramics nonlinear behavior. Application to langevin transducer,” J. Phys. III France, vol. 7, no. 6, pp. 1197–1208, 1997. DOI: 10.1051/jp3:1997183.
   Google Scholar
• M. Arafa and A. Baz, “On the nonlinear behavior of piezoelectric actuators,” J. Vib. Control, vol. 10, pp. 387–398, 2004. DOI: 10.1177/1077546304033365.
   Web of Science ®Google Scholar
• S. C. Stanton, A. Erturk, B. P. Mann, E. H. Dowell, and D. J. Inman, “Nonlinear nonconservative behavior and modeling of piezoelectric energy harvesters including proof mass effects,” J. Intell. Mater. Syst. Struct., vol. 23, no. 2, pp. 183–199, 2012. DOI: 10.1177/1045389X11432656.
   Web of Science ®Google Scholar
• Y. Yang and D. Upadrashta, “Modeling of geometric, material and damping nonlinearities in piezoelectric energy harvesters,” Nonlinear Dyn., vol. 84, no. 4, pp. 2487–2504, Jun. 2016. DOI: 10.1007/s11071-016-2660-1.
   Web of Science ®Google Scholar
• S. Leadenham and A. Erturk, “Unified nonlinear electroelastic dynamics of a bimorph piezoelectric cantilever for energy harvesting, sensing, and actuation,” Nonlinear Dyn., vol. 79, no. 3, pp. 1727–1743, Feb. 2015. DOI: 10.1007/s11071-014-1770-x.
   Web of Science ®Google Scholar
• D. Tan, P. Yavarow, and A. Erturk, “Resonant nonlinearities of piezoelectric macro-fiber composite cantilevers with interdigitated electrodes in energy harvesting,” Nonlinear Dyn., vol. 92, no. 4, pp. 1935–1945, 2018. doi.org/10.1007/s11071-018-4172-7.
   Web of Science ®Google Scholar
• D. Tan, P. Yavarow, and A. Erturk, “Nonlinear elastodynamics of piezoelectric macro-fiber composites with interdigitated electrodes for resonant actuation,” Compos. Struct., vol. 187, pp. 137–143, 2018. DOI: 10.1016/j.compstruct.2017.12.056.
   Web of Science ®Google Scholar