Propagation Of SH Wave In Nano-layered Structure With Surface Effect

Layered nanostructures, such as nanofilms and nanoplates, are the important components of micro-/nano-sensors and actuators, especially when they also possess piezoelectric property. Study on the propagation of elastic wave in layered nanostructures with surface effects is the key theoretical foundation for the design and assessment of such kind of smart structures. Based on surface elasticity theory and elastic wave theory, propagation of SH waves in layered nanostructures is systematically investigated in this work. Research focuses on:(1) For the problem of Love waves propagation with surface effects in the structure where a nanofilm is bonded on a semi-infinite elastic substrate,frequency dispersion equation and wave structure of Love waves are obtained.Research focus is put on the effects of the film thickness and surface elastic constants. Our results show that surface effects can significantly affect the frequency dispersion and wave structure of Love waves when the film thickness reduces to nanometers. In the presence of surface effects, frequency dispersion of Love waves exhibits distinct thickness-dependence and the wave phase velocity of all dispersion modes increases when the film thickness decreases or surface elastic constants increases. Moreover, surface effects may give rise to a cut-off frequency in the first dispersion mode below which Love waves will be evanescent. The cut-off frequency is found dependent of the film thickness,surface elastic constants and the elastic constants of bulk materials. As far as the wave structure is concerned, the surface effects on the film free surface(free surface effects) can reduce the vibration in the elastic film while the surface effects on the interface between the film and the substrate(interface effects) can greatly promote the vibration. Such impact becomes more prominent for larger values of surface elastic constants.(2) For the problem of Love waves propagation with surface effects in a piezoelectric nanofilm on a semi-infinite elastic substrate, frequency dispersion equation and wave structure of Love waves are deduced when the electrically-open or electrically-shorted conditions are adopted. The influence of the film thickness, surface parameters and electrical boundary conditions isdiscussed. Our research shows that for both electrically-open and electrically-shorted conditions, wave phase velocity is accelerated with reducing the film thickness or increasing the surface parameters. Under the electrically-open condition, waves of all modes will propagate in the forms of Love waves. The influence of surface effects on frequency dispersion and wave structure is similar to those in the case of elastic naofilms. Under the electrically-shorted condition, waves of the second and higher modes still spread in the forms of Love waves. However, waves of the first mode may be the Love waves or the Bleustein-Gulyaev(B-G) waves, depending on the free surface effects and the interface effects. When the free surface effects or the interface effects are taking effects alone, waves propagate as the second mode B-G waves and the first mode B-G waves, respectively. When surface effects at two positions play roles simultaneously, Love waves will exist in the structure while B-G waves are suppressed. In addition, the change of wave structure induced by surface effects is consistent with the change of wave propagation forms.(3) For the problem of SH waves propagation with surface effects in two dissimilar nanofilms, equations of frequency dispersion and wave structure of SH waves are derived and numerically solved. Analysis on the effects of film thickness, thickness ratio of two films and surface elastic constants is carried out.It is shown that the above parameters play important roles in frequency dispersion of SH waves. Furthermore, a continuum method is proposed to calculate the surface/interface constants from the wave phase velocity, using the characteristics of frequency dispersion of SH waves at low frequency range.