A general FEM technique to model wave propagation in cellular periodic structures

The paper describes a finite element based technique to model the propagation of elastic waves in cellular periodic structures. The technique can be applied to predict the dynamic response of repetitive structural assemblies, such as honeycombs, network grids part of deployable antennas and space trusses. In the proposed method, the unit cell of the structure is modeled using conventional elements available in commercial finite element codes. The cell finite element model is then duplicated to obtain a representation of real and imaginary fields of the propagating wave. Instead of imposing the Bloch wave conditions using complex number relations between cell edge nodes, a set of equivalent real equations is established as constraint relations to couple real and imaginary domains. This approach is effective and flexible as it can be easily implemented into the meta-parametric languages of commercial finite element codes. Existing Lanczos routines can be used to calculate the phase constant surfaces, the modes of the repeating cells as well as the structure's harmonic response.