Mass matrices for elastic continua with micro-inertia Articles uri icon

publication date

  • January 2023

start page

  • 1

end page

  • 14


  • 106938


  • 275

International Standard Serial Number (ISSN)

  • 0045-7949

Electronic International Standard Serial Number (EISSN)

  • 1879-2243


  • 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.


  • Materials science and engineering
  • Mechanical Engineering


  • high-order mass matrices; length scale; micro-inertia models; natural frequencies; numerical analysis