Mass matrices for elastic continua with micro-inertia

In this paper, the finite element discretization of non-classical continuum models with micro-inertia is analysed. The focus on extensions one-dimensional rod model, beam bending theories Euler–Bernoulli and Rayleigh, two-dimensional membrane model. performance a variety mass matrices assessed by comparing natural frequencies their modes those associated discrete systems, it demonstrated that use higher-order reduces errors improves convergence rates. Furthermore, sizes larger than corresponding physical length scale are shown to be sufficient capture frequencies, thus facilitating numerical not only reliable but also computationally efficient.