Characteristics of shear horizontal waves in magnetically affected ultra-thin films accounting for surface effect

• Propagation of SH waves in magnetically affected ultra-thin films is studied.
• By considering the surface energy, the dispersion relations are obtained.
• The limitations of the classical theory of elasticity are comprehensively addressed.
• Roles of thickness and magnetic field strength in dispersion curves are explored.
• Cutoff frequency and phase velocity of symmetric and asymmetric modes are discussed.

Consider a nano-scaled film which is made from highly conductive materials and is subjected to a uniform and constant magnetic field at the vicinity of its surfaces. The characteristics of the propagated shear horizontal (SH) waves within such a nanostructure are of particular interest. By decomposing the magnetically affected nanofilm into the surface layers and the bulk, surface elasticity is adopted and their equations of motion for the SH waves are constructed. The demonstrated dispersion curves reveal that the SH waves can propagate or be damped within the nanofilm in two manners: symmetric and asymmetric. Thereafter, the roles of the magnetic field strength and the thickness on the dispersion curves and phase velocities of both symmetric and asymmetric SH waves are addressed. Additionally, the limitations of the classical continuum theory in predicting the characteristics of SH waves are displayed and discussed.