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On the compact wave dynamics of tensegrity beams in multiple dimensions

Abstract

This work presents a numerical investigation on the nonlinear wave dynamics of tensegrity beams in 1D, 2D, and 3D arrangements. The simulation of impact loading on a chain of tensegrity prisms and lumped masses allows us to apply on a smaller scale recent results on the propagation of compression solitary waves in 1D tensegrity metamaterials. Novel results on the wave dynamics of 2D and 3D beams reveal—for the first time—the presence of compact compression waves in two- and three-dimensional tensegrity lattices with slender aspect ratio and stiffening-type elastic response. The dynamics of such systems is characterized by the thermalization of the lattice nearby the impacted regions of the boundary. The portion of the absorbed energy moving along the longitudinal direction is transported by compression waves with compact support. Such waves emerge with nearly constant speed, and slight modifications of their spatial shape and amplitude, after collisions with compression waves traveling in opposite direction. The analyzed behaviors suggest the use of multidimensional tensegrity lattices for the design and additive manufacturing of novel sound focusing devices.

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Acknowledgements

AM and GR gratefully acknowledge the financial support from the Italian Ministry of Education, University, and Research (MIUR) under the ‘FFABR’ Grant L.232/2016. FF gratefully acknowledges financial support from the Italian Ministry of Education, University, and Research (MIUR) under the ‘Departments of Excellence’ Grant L.232/2016.

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Correspondence to Fernando Fraternali.

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Supplementary material 6 (mp4 23705 KB)

Supplementary material 7 (mp4 23323 KB)

Supplementary material 8 (mp4 15495 KB)

Supplementary material 1 (mp4 20114 KB)

Supplementary material 2 (mp4 6365 KB)

Supplementary material 3 (mp4 21856 KB)

Supplementary material 4 (mp4 19742 KB)

Supplementary material 5 (mp4 15133 KB)

Supplementary material 6 (mp4 23705 KB)

Supplementary material 7 (mp4 23323 KB)

Supplementary material 8 (mp4 15495 KB)

Appendix A. Supplementary material

Appendix A. Supplementary material

Animations of the wave dynamics of the systems analyzed in this paper can be found in the online version.

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Micheletti, A., Ruscica, G. & Fraternali, F. On the compact wave dynamics of tensegrity beams in multiple dimensions. Nonlinear Dyn 98, 2737–2753 (2019). https://doi.org/10.1007/s11071-019-04986-8

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Keywords

  • Tensegrity lattices
  • Stiffening
  • Solitary waves
  • Compactons
  • Sound focusing