  The paper presents an analysis of the dynamic behaviour of discrete flexural
systems composed of Euler--Bernoulli beams. The canonical object of study is
the discrete Green's function, from which information regarding the dynamic
response of the lattice under point loading by forces and moments can be
obtained. Special attention is devoted to the interaction between flexural and
torsional waves in a square lattice of Euler--Bernoulli beams, which is shown
to yield a range of novel effects, including extreme dynamic anisotropy,
non-reciprocity, wave-guiding, filtering, and the ability to create localised
defect modes, all without the need for additional resonant elements or
interfaces. The analytical study is complimented by numerical computations and
finite element simulations, both of which are used to illustrate the effects
predicted. A general algorithm is provided for constructing Green's functions
as well as defect modes. This algorithm allows the tuning of the lattice to
produce pass bands, band gaps, resonant modes, wave-guides, and defect modes,
over any desired frequency range.

Classical Physics