Scattering of plane elastic waves by a multi-coated nanofiber with deformable interfaces

The scattering of in-plane P- and SV-waves by a multi-coated circular nanofiber with deformable interfaces is of interest. To this end, in the present work, after introducing two kinds of interface momenta defined as the derivative of the interface excess kinetic energy with respect to the average and relative velocities at the interface, we extend the elastostatic theory of Gurtin et al. (1998) on deformable interfaces to the elastodynamic theory and derive the interface equations of motion using Hamilton principle. The effects of the generalized interface properties including the interface inertial parameters and interface stiffness towards stretch and slip on the dynamic stress concentration factor and the scattering cross section will be examined through some numerical examples. These results reveal that the effect of the interface inertial parameters becomes significant as the frequency of the incident wave increases. Moreover, as it will be shown, in the case where the interfaces are treated to be deformable, a larger number of resonance modes are captured for low-frequency waves as a result of the compliancy of the interfaces. It will also be seen that the resonant frequencies pertinent to the local deformations of the interface, increase with the interface stiffness parameters and decrease with the interface inertial parameters introduced in this work. These results can be used for tuning the resonant frequencies by selecting appropriate geometrical sizes and materials. Such phenomena can also be useful for designing locally resonant sonic materials with nano-sized lattice parameters.