Dynamic buckling and free bending vibration of axially compressed piezoelectric semiconductor rod with surface effect

Many rod-and fiber-based semiconductor devices operate in the state of compression due to the external me-chanical force or the inner temperature change, which not only causes the static buckling but also plays a sig-nificant role in the dynamic buckling as well as resonance frequencies. We study the dynamic buckling and free bending vibration of an axially compressed simply supported piezoelectric semiconductor (PS) rod at the nanoscale with open-circuit and electrically isolated boundary conditions. The one-dimensional basic equations incorporating the surface effect are presented based on the classical theory of Gurtin-Muduch surface elasticity. The analytical expressions of critical dynamic buckling loads and damped resonance frequencies of the axially compressed PS rod are obtained. The influences of surface effect on the critical dynamic buckling loads and damped resonance frequencies of the PS rod are investigated in detail. The effects of axial compressive force and initial electron concentration on the effective damping ratio of the vibrating PS rod are also studied. Numerical results show that the surface effect remarkably enhances both the critical buckling loads and damped resonance frequencies of the axially compressed PS rod at nanoscale, at the same time the damped resonance frequency shift is linearly dependent on the compressive force.

Automated summary

This study investigates the dynamic buckling and free bending vibration of an axially compressed piezoelectric semiconductor (PS) rod at the nanoscale, and analyzes the effects of surface effect on the critical dynamic buckling loads and damped resonance frequencies. Furthermore, the influences of axial compressive force and initial electron concentration on the effective damping ratio of the vibrating PS rod are studied.