Title: Wave propagation and homogenization in 2D and 3D lattices: a semi-analytical approach,
Abstract: Wave motion in two- and three-dimensional periodic lattices of beam members
supporting longitudinal and flexural waves is considered. An analytic method
for solving the Bloch wave spectrum is developed, characterized by a
generalized eigenvalue equation obtained by enforcing the Floquet condition.
The dynamic stiffness matrix is shown to be explicitly Hermitian and to admit
positive eigenvalues. Lattices with hexagonal, rectangular, tetrahedral and
cubic unit cells are analyzed. The semi-analytical method can be asymptotically
expanded for low frequency yielding explicit forms for the Christoffel matrix
describing wave motion in the quasistatic limit.