Torsion of a flexoelectric semiconductor rod with a rectangular cross section

We study the torsion of a flexoelectric semiconductor rod with a rectangular cross section. The macroscopic theory of flexoelectric semiconductors is used. A one-dimensional model is established from the three-dimensional theory using double power series expansion of the coordinates within the cross section. The angle of twist of the rod and warping of the cross section are taken into consideration by retaining the proper lower-order terms in the expansion. Solutions of wave propagation in an unbounded rod and static torsion of a finite rod are presented, showing that electromechanical couplings exist when warping varies along the axis of the rod. The torsional wave is essentially nondispersive, but the warping wave is dispersive with a cutoff frequency. The mobile charges concentrate at the corners of the cross section. The electric potential and charge carrier distributions produced by mechanical loads are sensitive to the geometric and physical parameters of the system. The results are potentially useful for making flexotronic devices based on torsional modes.