Influences of interface properties on the wave propagation in the dipolar gradient elastic solid

The present work mainly focuses on the influence of interface material parameters, namely the interface mass density, the interface elastic rigidity, and the interface inertial interaction constants, on the reflection and transmission behavior of elastic wave propagating through dipolar gradient elastic solids. First, the interface kinetic energy density and interface deformation energy density are taken into account. By application of Hamilton’s variation principle, the governing equations and the boundary conditions of the dipolar gradient elastic solid are obtained. Due to the consideration of microstructure effects of the material, the interface conditions can be proposed in different forms. These interfacial conditions which include the microstructure effects and interface energy effects are then used to determine the amplitude ratio of reflection and transmission waves. A numerical example is provided for the generalized internal roller interface. The influence of the interface material parameters upon the reflection and transmission coefficients in terms of energy fluxes ratio is discussed based on the numerical results. It is revealed that the reflection and transmission behavior can be manipulated by the elaborated design of the interface at both the macroscale and the microscale.