Bilaterally flexural vibrations and instabilities of moving piezoelectric nanowires with surface effect

Vibrations of piezoelectric beam-like nanostructures have been widely examined; however, their dynamic response and instabilities in the moving state accounting for surface effect have not been investigated yet thoroughly. Given the importance of the subject and potential applications of piezoelectric nanowires in moving bodies, herein, we are interested in exploring their bidirectional-transverse vibrations in the context of the surface elasticity theory of Gurtin and Murdoch. To this end, equations of motion that describe transverse vibrations of axially moving piezoelectric nanowires are obtained by employing Rayleigh's and Timoshenko's beam theories. Using assumed mode approach in conjunction with Galerkin method, the flexural frequencies are evaluated and the explicit expressions of divergence velocities accounting for surface energy are derived. The influences of nanowire's length, axial velocity, surface energy, shear deformation effect, and voltage difference on the free transverse vibrations as well as divergence and flutter instabilities of the moving piezoelectric nanostructure are displayed. The present work can provide a solid basis for better understanding of vibrations of moving vertically aligned ensembles of piezoelectric nanowires.

Graphic abstract