Zareinejad Continuous dynamic modelling of bimorph piezoelectric cantilevered actuators considering hysteresis effect and dynamic behaviour analysis, Math. Inman A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters, J. Inman An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations, Smart Mater. Yang Small size piezoelectric impact drive actuator with rectangular bimorphs, Sens. Koszewnik Mu-Synthesis robust control of 3D bar structure vibration using piezo-stack actuators, Mech. Chaillet Simultaneous displacement/force self-sensing in piezoelectric actuators and applications to robust control, IEEE/ASME Trans. A spiral motion piezoelectric micromotor for autofocus and auto zoom in a medical endoscope, Appl. Lin Development of a piezoelectric micropump with novel separable design for medical applications, Sens. Saha Design and manufacturing of mobile micro manipulation system with a compliant piezoelectric actuator based micro gripper, J. Sarhan Disturbance rejection-based robust control for micropositioning of piezoelectric actuators, C. Recent progress in flexible and stretchable piezoelectric devices for mechanical energy harvesting, sensing and actuation, Extrem. Abdelkefi Accurate modeling, comparative analysis, and performance enhancement of broadband piezoelectric energy harvesters with single and dual magnetic forces, Int. Piezoelectric sensor for micro mass detection, 2016 13th International Computer Conference on Wavelet Active Media Technology and Information Processing (ICCWAMTIP), 2016, pp. A micro-fabricated force sensor using an all thin film piezoelectric active sensor, Sensors (Basel), Volume 14 (2014), pp. Fantner A monolithic MEMS position sensor for closed-loop high-speed atomic force microscopy, Nanotechnology, Volume 27 (2016) Also, in order to evaluate the accuracy of the proposed model, it is tested out of the identification range as well. Finally, the results are compared with the ones obtained experimentally and nonlinear parameters are identified considering frequency response and phase response simultaneously. Next, the method of multiple scales is used to solve the discretized nonlinear differential equations. Then, based on the obtained constitutive equations and Euler–Bernoulli beam theory, a continuous nonlinear dynamic model for a piezoelectric bending actuator is presented. In this study, first, the nonlinear stress–strain relationship of a piezoelectric material at high frequencies is modified.

For decades, many linear models have been presented to describe the dynamic behavior of this type of actuators however, in many situations, such as resonant actuation, the piezoelectric actuators exhibit a softening nonlinear behavior hence, an accurate dynamic model is demanded to properly predict the nonlinearity.

The nature of the aforementioned applications calls for the dynamic characteristics identification of actuator at the embodiment design stage. Piezoelectric bimorph actuators are used in a variety of applications, including micro positioning, vibration control, and micro robotics.

Bimorph piezo actuator solution