A continuum model for the tensegrity Maxwell chain

Luca Placidi; Julia de Castro Motta; Rana Nazifi Charandabi; Fernando Fraternali; Luca Placidi; Julia de Castro Motta; Rana Nazifi Charandabi; Fernando Fraternali

doi:10.3934/nhm.2024026

Networks and Heterogeneous Media

2024, Volume 19, Issue 2: 597-610. doi: 10.3934/nhm.2024026

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A continuum model for the tensegrity Maxwell chain

1.
International Telematic University Uninettuno, 00186 Rome, Italy
2.
Department of Civil Engineering, University of Salerno, 84084 Fisciano(SA), Italy
3.
Department of Information Engineering, Electrical Engineering and Applied Mathematics (DIEM), University of Salerno, 84084 Fisciano (SA), Italy

Received: 15 April 2024 Revised: 28 May 2024 Accepted: 06 June 2024 Published: 12 June 2024

A recent study has presented a Maxwell mass–spring model for a chain formed by two different types of tensegrity prisms alternating with lumped masses. Such a model shows tensegrity theta prisms arranged in parallel with minimal regular prisms acting as resonant substructures. It features a tunable frequency bandgap response, due to the possibility of adjusting the width of the bandgap regions by playing with internal resonance effects in addition to mass and spring contrasts. This paper expands such research by presenting a continuum modeling of the tensegrity Maxwell chain, which is useful to conduct analytic studies and to develop finite element models of the plane wave dynamics of the investigated system. In correspondence to the high wave-length limit, i.e., in the low wave number regime, it is shown that the dispersion relations of the discrete and continuum models provide similar results. Analytic solutions to the wave dynamics of physical systems are presented, which validate the predictions of the bandgap response offered by the dispersion relation of the continuum model.
- Maxwell chain,
- discrete to continuum,
- bandgap response,
- tensegrity structures
Citation: Luca Placidi, Julia de Castro Motta, Rana Nazifi Charandabi, Fernando Fraternali. A continuum model for the tensegrity Maxwell chain[J]. Networks and Heterogeneous Media, 2024, 19(2): 597-610. doi: 10.3934/nhm.2024026

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Abstract

A recent study has presented a Maxwell mass–spring model for a chain formed by two different types of tensegrity prisms alternating with lumped masses. Such a model shows tensegrity theta prisms arranged in parallel with minimal regular prisms acting as resonant substructures. It features a tunable frequency bandgap response, due to the possibility of adjusting the width of the bandgap regions by playing with internal resonance effects in addition to mass and spring contrasts. This paper expands such research by presenting a continuum modeling of the tensegrity Maxwell chain, which is useful to conduct analytic studies and to develop finite element models of the plane wave dynamics of the investigated system. In correspondence to the high wave-length limit, i.e., in the low wave number regime, it is shown that the dispersion relations of the discrete and continuum models provide similar results. Analytic solutions to the wave dynamics of physical systems are presented, which validate the predictions of the bandgap response offered by the dispersion relation of the continuum model.

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