Effects of in-plane stresses on the electro-elastic coupling properties in a bent rectangular piezoelectric semiconductor plate

To study how in-plane stresses affect the mechano-electro-charge carrier coupling properties in piezoelectric semiconductor plates, this work establishes a mathematical model based on the phenomenological theory of n-type piezoelectric semiconductors and the first-order shear deformation theory. The differential quadrature method is adopted to solve the two-dimensional boundary value problem. For plates with simply supported and electrically shorted boundaries, displacement, electric potential, and perturbation carrier density exhibit biaxial symmetry. Rotation, electric field, and electric current density are symmetric about one midline and antisymmetric about the orthogonal midline. In addition, owing to the screening effect of redistributed carriers, both electric potential and electric field decline with an increase in initial carrier density. This study mainly focuses on the regulation of electro-elastic fields by in-plane stress. Numerical results show that compressive stress reduces effective bending stiffness, while tensile stress improves it. Field strength rises with increasing load magnitude. The total carrier density displays a near-exponential growth trend. The variation pattern remains nearly unchanged when the initial carrier density exceeds 1020 m−3. Further investigations into the forced vibration of piezoelectric semiconductor rectangular plates demonstrate that the change in equivalent stiffness induced by in-plane stress effectively adjusts the natural frequency of the structure. Potential barriers and wells form inside the plate at resonant frequencies. Current flow is thus restricted to regions outside these potential barriers and wells. The obtained mechanisms provide theoretical guidance for the design of smart piezotronic devices.