Reflection and transmission of plane waves at surfaces carrying material properties and embedded in second-gradient materials
Angela Madeo (INSA-Lyon)
SES Medal Symposium in honor of D.J. Steigmann
Tue 10:45 - 12:15
MacMillan 115
In the presented work reflection and transmission of compression and shear waves at structured interfaces between second gradient continua is investigated. Two semi-infinite spaces composed by the same second-gradient material are connected through an interface which is assumed to have its own material properties (mass density, elasticity and inertia). Using a variational principle, general balance equations are deduced for the bulk system, as well as jump duality conditions for the considered structured interfaces. The obtained equations include the effect of surface inertial and elastic properties on the motion of the overall system. In the first part of the work general 3D equations accounting for all surface deformation modes (including bending) are introduced. The application to wave propagation presented in the second part of the work, on the other hand, is based on a simplified 1D version of these equations, which we call “axial symmetric” case. We show that the effect of the surface material properties on reflection and transmission of plane waves is tangibly different from the effect of the second-gradient parameter. For three of the four tested internal constraints, the effect of the second-gradient parameter on reflection and transmission is seen to be definitely non-negligible and clearly distinguishable from the effect of the surface material properties. In particular, both the interface material properties and the second-gradient parameter of the two semi-infinite spaces give rise to reflection and transmission coefficients which are strongly frequency dependent, in opposition to what happens for standard semi-infinite Cauchy continua and for surfaces without material properties.