Transverse and longitudinal dynamic modeling of bimorph piezoelectric actuators with investigating the effect of vibrational modes

Document Type: Invited by Hamid Ahmadian


1 Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iran

2 New Technologies Research Centre, Amirkabir University of Technology, Tehran, Iran



Bimorph piezoelectric cantilevered (BPC) actuators have recently received a great deal of attention in a variety of micro-electromechanical systems (MEMS) applications. Dynamic modeling of such actuators needs to be improved in order to enhance the control performance. Previous works have usually taken transverse vibration into account without considering longitudinal vibration. This paper presents a comprehensive modeling for a set of transverse and longitudinal vibration equations for piezoelectric cantilevered actuators. In addition, dynamic behavior and exact non-minimum phase region along BPC is derived by analyzing first three vibrational modes. A simulation study is propounded to better analyze the system dynamic behavior. Finally, an experimental setup is developed to verify the proposed dynamic model. The modal frequency response of the system for the first three modes, obtained from the proposed model, is compared with those obtained from the experiment and a good consistency between them confirms the validity of the proposed dynamic model.


  • The set of transverse and longitudinal vibration equations have been derived and discretized for a BPC actuator.
  • The dynamic behavior of BPC actuator has been analyzed based on vibration equations for first three vibration modes.
  • The exact non-minimum phase region has been acquired along the actuator’s length.
  • The proposed dynamic behavior has been simulated to identify the model parameters and finally it has been verified via the experimental results.


Main Subjects

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