Mass matrices for elastic continua with micro-inertia

F. Gómez-Silva*, H. Askes

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
16 Downloads (Pure)


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

Original languageEnglish
Article number106938
JournalComputers and Structures
Publication statusPublished - 15 Jan 2023


  • High-order mass matrices
  • Length scale
  • Micro-inertia models
  • Natural frequencies
  • Numerical analysis


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