Abstract
In this study, the static displacement behaviour of a three-layer axisymmetric circular piezoelectric unimorph actuator subjected to voltage and uniform pressure loads for different mechanical and geometric properties of layers was investigated. The closed-analytical model of piezoelectric actuator based on the classical laminated thin plate theory was performed. Kirchhoff’s thin plate theory for the mathematical model in closed form of the actuator was utilized. The superposition of transverse and lateral deflections expressions was used to obtain the displacement equation of the piezoelectric actuator. Then, the analytical model solutions were compared by finite element model solutions. It was observed that the results obtained from analytical model and finite element analysis were sufficiently compatible with each other. The effects of nondimensional physical and mechanical properties on the static deflection performance of the piezoelectric actuator were discussed using the analytical model. According to the results obtained, the physical and mechanical properties of the actuator had significant effects on the actuator displacement. Therefore, the results obtained in this study can be used to optimize the performance of the circular piezoelectric actuator.
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Abbreviations
- PZT:
-
Piezoelectric zirconate titanate
- CLPT:
-
Classical laminated plate theory
- r, θ, z :
-
The polar coordinate components
- R :
-
The radius of the layer
- u :
-
Lateral displacement
- w :
-
Transverse displacement
- εr, εθ :
-
Radial and tangential strains
- σr, σθ :
-
Radial and tangential stress
- \( \epsilon \) :
-
Electrical charge
- \( d_{31}^{k} \) :
-
Piezoelectric coupling coefficient
- K k :
-
Stiffness matrix of the layer
- v k :
-
Poisson ratio of the layer
- E k :
-
Young’s modulus of the layer
- N :
-
Normal force on the layer
- M :
-
Bending moment on the layer
- Q r :
-
Shear force on the layer
- P :
-
Uniform static pressure
- d 31 :
-
The piezoelectric layer coefficient
- ε :
-
Relative permittivity matrix of the piezoelectric
- E :
-
Young’s modulus matrix of the piezoelectric
- d:
-
Piezoelectric constant matrix of the piezoelectric
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Acknowledgements
This study was supported by Scientific Research Projects Unit of Sakarya University (Project Number: 2017-50-02-026) and Scientific Research Projects Unit of Sakarya University of Applied Sciences (Project Number: 2019-50-02-078).
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Asadi Dereshgi, H., Dal, H. & Sayan, M.E. Analytical analysis of a circular unimorph piezoelectric actuator in the range of low voltages and pressures. Microsyst Technol 26, 2453–2464 (2020). https://doi.org/10.1007/s00542-020-04786-w
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DOI: https://doi.org/10.1007/s00542-020-04786-w