A generalized dynamic model of nanoscale surface acoustic wave sensors and its applications in Love wave propagation and shear-horizontal vibration

Abstract

• A generalized dynamic model based on the Hamilton's principle and variational approach is established. • The model is applied to depict the wave propagation in SAW nano-devices or vibration of piezoelectric nanoplates. • The surface effect is included with the aid of the surface elasticity , surface piezoelectricity and surface permittivity. • A critical thickness value of surface acoustic wave nano-devices or piezoelectric nanoplates can be obtained. • Below the critical thickness, the size-dependent properties will become evident and should be taken into account. A generalized dynamic model to depict the wave propagation properties in surface acoustic wave nano-devices is established based on the Hamilton's principle and variational approach. The surface effect, equivalent to additional thin films, is included with the aid of the surface elasticity, surface piezoelectricity and surface permittivity. It is demonstrated that this generalized dynamic model can be reduced into some classical cases, suitable for macro-scale and nano-scale, if some specific assumptions are utilized. In numerical simulations, Love wave propagation in a typical surface acoustic wave device composed of a piezoelectric ceramic transducer film and an aluminum substrate, as well as the shear-horizontal vibration of a piezoelectric plate, is investigated consequently to qualitatively and quantitatively analyze the surface effect. Correspondingly, a critical thickness that distinguishes surface effect from macro-mechanical behaviors is proposed, below which the size-dependent properties must be considered. Not limited as Love waves, the theoretical model will provide us a useful mathematical tool to analyze surface effect in nano-devices, which can be easily extended to other type of waves, such as Bleustein-Gulyaev waves and general Rayleigh waves.