Low-order non-classical continuum models for the improved prediction of an anisotropic membrane lattice’s dynamics

In this work, different standard and non-standard continualization methods are applied to an anisotropic membrane lattice to obtain non-classical continuum models, capable of accurately capturing its dynamic behaviour. Their performance is evaluated by comparing the continuum and discrete models through their dispersion relations, as well as their natural frequencies for the fixed-edge configuration. Moreover, the occurrence of certain physical inconsistencies in some of these models is examined. Interestingly, the novel Enriched Kinetic Energy model shows the best performance, presenting neither physical inconsistencies nor higher-order derivatives in its governing equation, thus not needing extra boundary conditions when dealing with finite solids.