A Stabilised Micropolar Theory Derived from a Periodic Beam Lattice

Starting from the finite element equations of a periodic beam lattice, a continuum theory is derived via Taylor series expansions. The continualised equations of motion are of the micropolar type and thus contain stiffness and inertia contributions in terms of translational as well as rotational degrees of freedom. Scrutiny of the underlying energy functionals and of the model’s response to excitation via harmonic waves confirms that the continualised model is unstable. In order to stabilise the model, Padé approximation is applied to the rotational equation of motion. As a result of this process, micro-inertia terms appear in the model that are expressed as the spatial gradients of the standard rotational inertia terms. It is demonstrated by means of an analysis of dispersive waves that the Padé approximation not only stabilises the model but also improves the accuracy with which the continuum model approximates the original discrete model.