Affiliations: [a] Department of Engineering Mechanics, Zhejiang
University, Hangzhou, Zhejiang, China | [b] Department of Mechanical and Materials Engineering,
University of Nebraska-Lincoln, Lincoln, NE, USA
Correspondence:
[*]
Corresponding author: Jiashi Yang, Department of Mechanical and
Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588-0526,
USA. E-mail: jyang1@unl.edu
Abstract: We derive two-dimensional equations for high-frequency vibrations of
piezoelectric plates from a semi-mixed variational principle with the
mechanical displacement vector, the electric potential, and the electric
displacement vector as independent fields. This variational formulation allows
independent expansions of the three fields into power series of the plate
thickness coordinate. Similar to the shear correction factors used in Mindlin's
equations for piezoelectric plates to adjust the thickness-shear frequencies
predicted by the plate equations slightly so that they become the same as the
exact frequencies from the three-dimensional equations, a charge correction
factor is conveniently introduced in the plate equations in the present paper
so that the inaccuracy of the plate equations in the literature in predicting
the charge or current on the electrodes of an electroded plate is corrected.
The final equations obtained are convenient and accurate to use for both
electroded and unelectroded plates, and for calculating both the voltage and
the charge on the electrodes at the plate surfaces in the case of an electroded plate.
