Surface Effects on the Frequency Dispersion of Flexural Waves in Timoshenko Nanobeams

The surface effects play an important role in nanobeams. Based on a recently developed theory of surface elastodynamics, a model of the flexural wave propagation in Timoshenko nanobeams is established, in which the surface effects characterized by surface energy and surface inertia are introduced. It is found that when the size of a beam is comparable with nanometers, the surface energy effect would enhance the wave speed, while the surface inertial one would reduce it. An interesting phenomenon discovered is that with an increasing wave frequency, the dominant role transits from the surface energy effect to the surface inertial effect. The two kinds of surface effects exhibit a frequency-dependent competitive mechanism. In contrast to the macroscopic beams, due to the surface effects, the frequency dispersion of flexural waves in nanobeams becomes size-dependent. Furthermore, a comparison of the Timoshenko nanobeam and the Euler one indicates that the shear deformation effect and rotary inertial one cannot be neglected for a large wave number, which would prominently decrease the wave speed. Besides, when the size of the beam is large enough, the surface effects can be neglected and the present results can degenerate to the classical Timoshenko ones. The present results should be helpful not only for deep understanding of the dispersive mechanism of flexural waves in nanobeams, but also for optimal design of nanobeam-based acoustic wave devices.