Low order nonstandard continualization of a beam lattice with next-nearest interactions: Enhanced prediction of the dynamic behavior

Abstract

In this work, a one-dimensional beam lattice composed of masses and rotational springs with nearest and next-nearest interactions is proposed, applying to it several nonstandard continalization procedures. The reliability of nonclassical continuum models to capture the dynamic behavior of the lattice – considered as a reference –, is evaluated through dispersion and natural frequency analyses. A detailed boundary conditions treatment is presented and the existence of physical inconsistencies in the new continuum models is examined. The novel enriched kinetic energy model proposed shows the best performance, its governing equation being of low order, thus, avoiding the use of extra boundary conditions.

Keywords:

• Beam lattice
• next-nearest interactions
• nonstandard continualization
• enriched kinetic energy
• natural frequencies

Additional information

Funding

The authors wish to acknowledge the Ministerio de Ciencia e Innovación de España and the European Social Fund for the financial support under Grants PGC2018-098218-B-I00 and PRE2019-088002.