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

Document Type : Full Length Article

Authors

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

10.22064/tava.2020.112068.1142

Abstract

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.

Highlights

  • 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

Keywords

Main Subjects


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