Analysis of transmission and reflection characteristics of linear plane waves in pantographic lattices

In this paper, linear wave propagation in pantographic lattices is investigated. It is assumed that the pantographic lattice is attached to a material modeled by the classical first-gradient continuum with a structured interface having its own material properties. By using a variational principle, governing equations and jump conditions at the structured interface are obtained. To this end, the pantographic lattice is modeled by a well-known second-gradient continuum model. Transmission and reflection characteristics are investigated considering four different types of constraints at the structured interface, namely generalized internal clamp, generalized internal hinge, generalized internal roller, and generalized internal free ends. The effects of elastic moduli and material properties of both continua and the structured interface are analyzed by conducting a parameter study for each considered constraint.