Size-dependent Electromechanical Coupling Behaviors Of The Piezoelectric Microstructures Incorporating Flexoelectric Effects

Piezoelectric microstructures are extensively applied in micro sensors,micro actuators and micro resonators in microelectromechanical system(MEMS)owing to their rapid response speed,excellent electromechanical coupling properties,easily gratified driving voltage and other advantages.The properties of these microstructures are significantly dependent on the electromechanical coupling properties of piezoelectric materials.However,the mechanical properties of the microstructures show discrepancy and behave size-dependency compared with the structures in macroscale.Furthermore,the electromechanical coupling properties of the piezoelectric microstructures are in:fluenced by flexoelectric effects,which shows rapid increase when the size of structures diminish to microscale and nanoscale.This leads to the electromechanical properties of the microstructures show size-dependency.In conclusion,to explore the size-dependency of the mechanical and the electromechanical properties are of vital importance in MEMS researches.In this research,the electromechanical properties of the bilayer piezoelectric microbeam and the piezoelectric short microbeam are investigated based on the couple stress piezoelectric theory incorporating flexoelectric effects.By taking rotation gradient effects,polarization gradient effects and flexoelectric effects into account,the size-dependent model of the bilayer piezoelectric microbeam is established based on the Euler-Bernoulli beam hypothesis.The governing equations and the boundary conditions of the bilayer piezoelectric microbeam are derived from variation principle.The static bending problems under the applied voltage and the applied force along with the free vibration problems of the microbeam have been solved.The size-dependency of the electromechanical coupling properties and the natural frequency of the microbeam are analyzed through numerical method.The results indicate that under both the applied voltage and the applied force,the electromechanical response of the bilayer piezoelectric microbeam increases when the beam size is much larger than the material length scale parameters.With the continuous decrease of the bram size,the electromechanical response reaches an extreme point and turn to rapid decrease.The location of the extreme point is related with the flexoelectric coefficients.Particularly,the piezoelectric response shows steady decreases as the beam size decreases,and it decreases much quicker when the beam size approaches to the material length scale parameters.The flexoelectric response increases when the beam size is larger than the material length scale plarameters,then turn to rapid decreases when the beam size is smaller than the material ength scale parameters.The dimensionless natural frequency of the bilayer piezoelectric Euler-Bernoulli microbeam increases significantly as the beam size decreases.The dimensionless natural frequency of the bilayer piezoelectric slender microbeam shows stronger size-dependency than that of the model without considering electromechanical coupling effects,which mainly resulted from flexoelectric effects,and piezoelectric effects exerted minor influence on the beam natural frequency.By taking rotation gradient effects,polarization gradient effects and flexoelectric effects into account,the size-dependent model of the piezoelectric short microbeam is established based on the Timoshenko beam hypothesis.The static bending problems under the applied voltage and the applied force along with the free vibration problems of the microbeam have been solved.The size-dependency of the electromechanical coupling properties and the natural frequency of the microbeam are analyzed through numerical method.The results indicate that under both the applied voltage and the applied force,the electromechanical response of the piezoelectric short microbeam increases when the beam size is larger than the material length scale parameters,then turn to rapid decreases when the beam size is smaller than the material length scale parameters.The natural frequency of the piezoelectric short microbeam increases significantly as the beam size decreases.The shear deformation leads to the decrease of the beam electromechanical response and the beam natural frequency.