A theoretical approach for flexural behavior of FG vibrating micro-plates with piezoelectric layers considering a hybrid length scale parameter

Document Type : Research Article


1 Associated Professor, Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak, Iran

2 MSc Student, Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak, Iran

3 M.Sc. Student, Department of Mechanical Engineering, Faculty of Engineering, Arak university, Arak, IranMSc Student, Department of Mechanical Engineering, Faculty of Engineering, Arak University, Arak, Iran



In the current study, the mechanical performance of functionally graded oscillating micro-plates bonded with piezoelectric layers is examined using the modified couple stress theory. The modified couple stress theory contains a length scale parameter that considers the size-effects of micro-plates. The various modified shear deformation theories are employed to represent the displacement field of micro-plate, such as exponential, parabolic, hyperbolic, trigonometric, and fifth-order shear deformation theories. The properties of FG micro-plate, such as Young’s modulus, density, and length scale parameter, are assumed to vary smoothly and across the micro-plate thickness based on the Power-law model. The governing equations of motion are obtained by Hamilton's principle and solved by a theoretical approach under various boundary conditions. The accuracy of the proposed model is validated based on a comparison of the results with the accepted studies. Computational analysis is carried out to clarify the impacts of mechanical and geometrical variables on the natural frequencies of micro-plates.


  • Dynamic behavior of FG micro-plates with piezoelectric layer are discussed.
  • Length-scale parameter is supposed to vary along the thickness of structure.
  • The modified couple stress theory is applied to capture size effects in the plate.
  • Various theories are used to consider the shear deformation and inertia effects.
  • Various boundary conditions are modeled by some orthogonal trigonometric functions


Main Subjects

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