On the higher order theories of piezoelectric crystal surfaces

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Abstract
This paper presents a higher order theory of crystal finite surfaces within the frame of the three‐dimensional theory of linear piezoelectricity. First, by modifying Hamilton's principle, a variational theorem is deduced. Then, this theorem together with a method of series expansion is employed to establish the theory in a systematic and consistent manner. The theory consists of a hierarchy of two‐dimensional equations of motion, charge equations of electrostatics, initial and boundary conditions, strain‐displacement and electric field‐electric potential relations, and macroscopic constitutive equations. It governs the extensional and flexural as well as torsional motions of piezoelectric crystal shells and plates of uniform thickness. Further, theorems of uniqueness in this theory are presented.
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