Broadband dynamic elastic moduli of honeycomb lattice materials: A generalized analytical approach

A generic analytical framework is proposed to obtain the dynamic elastic moduli of lattice materials under steady-state vibration conditions. The deformation behaviour individual beam elements a distinct from static condition. This leads completely different global pattern material and subsequently opens up tremendous opportunity modulate amplitude phase properties lattices as function ambient vibration. stiffness approach in this article precisely captures sub-wavelength scale dynamics periodic network beams using single beam-like member. Here matrix damped element based on Timoshenko theory along with axial stretching coupled unit cell-based derive most general closed-form formulae for across whole frequency range. It systematically shown how expressions can be reduced special cases by neglecting shear deformations well classical significance developing compared conventional finite highlighted presenting detailed derivations representative numerical results. Further, it readily extended non-prismatic any spatial variation geometry intrinsic properties. In general, research activities field metamaterials dealing revolve around intuitively designing microstructural structure. we propose couple physics vibrating expand effective design space significantly. stretching-enriched addition bending conditions lead complex-valued due presence damping constituent material. amplitude, materials, quantified approach. dependence Poisson's ratio case geometrically regular found contrary common notion that ratios perfectly are only geometry. analysing applicable form two- or three-dimensional lattices, profile (different cross-sections spatially varying properties) through wide range band. derived viewed broadband generalisation well-established loading, essentially adding new exploitable dimension terms