We study extensional vibrations of a ZnO piezoelectric semiconductor fiber driven by a time-harmonic end force. A theoretical analysis is performed using a one-dimensional model based on the phenomenological theory of piezoelectric semiconductors consisting of the equations of piezoelectricity coupled to the continuity equation of electrons. A series of resonance frequencies are identified. It is found that these frequencies are lower than those of the corresponding piezoelectric dielectric fiber because the mobile charges in the semiconductor screen the effective polarization charges and thus weaken the piezoelectric stiffening effect. Various electromechanical fields at resonances are calculated and examined. Numerical results show that the effective surface polarization charge plays a more dominant role than the effective body polarization charge. The mobile charges can screen the body polarization charges greatly, but not the surface polarization charges.

In this work, we study the behavior of a composite rod consisting of a piezoelectric semiconductor layer and two piezomagnetic layers under an applied axial magnetic field. Based on the phenomenological theories of piezoelectric semiconductors and piezomagnetics, a one-dimensional model is developed from which an analytical solution is obtained. The explicit expressions of the coupled fields and the numerical results show that an axially applied magnetic field produces extensional deformation through piezomagnetic coupling, the extension then produces polarization through piezoelectric coupling, and the polarization then causes the redistribution of mobile charges. Thus, the composite rod exhibits a coupling between the applied magnetic field and carrier distribution through combined piezomagnetic and piezoelectric effects. The results have potential applications in piezotronics when magnetic fields are relevant.

Within the framework of nonlocal elasticity, the surface layer model is proposed to investigate the wave propagation characteristics in a single-layered nanoplate. The general solutions of nonlocal governing equations are expressed using partial wave technique and the nonclassical boundary conditions are derived. The dispersion relation with the effects of surface and nonlocal small-scale is obtained, and the size-dependent dispersion behaviour is demonstrated. The impacts of surface elasticity, residual surface stress and nonlocal parameter on the dispersion curves of the lowest-order two modes are illustrated. Numerical examples reveal that both the surface effect and nonlocal small-scale effect can obviously decrease the magnitude of phase velocity, and the thinner nanoplate corresponds to the smaller wave velocity and the narrower frequency bandwidth.