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Nested Bloch waves in elastic structures with configurational forces.

F Dal Corso1, D Tallarico2, N V Movchan3

  • 1DICAM, University of Trento, via Mesiano, 77 38123, Trento, Italy.

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|September 3, 2019
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Summary
This summary is machine-generated.

Configurational forces in elastic beams with sliding sleeves break band gaps, enabling axial propagation during transverse vibrations. This phenomenon allows for novel designs of mechanical devices for longitudinal actuation using flexural vibrations.

Keywords:
band-gapperiodic structuresresonance

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Area of Science:

  • Solid mechanics
  • Vibrational analysis
  • Nonlinear dynamics

Background:

  • Periodic structures composed of elastic beams are susceptible to complex vibrational behaviors.
  • Interactions at constraints, such as sliding sleeves, can introduce nonlinearities.
  • Understanding these nonlinear couplings is crucial for predicting structural response.

Purpose of the Study:

  • To analyze small axial and flexural oscillations in a periodic structure of elastic beams with sliding sleeves.
  • To investigate the role of nonlinear coupling between longitudinal and transverse displacements.
  • To explore the impact of configurational forces on vibration propagation and band gap structures.

Main Methods:

  • Application of a nested Bloch-Floquet technique.
  • Analysis of nonlinear coupling induced by configurational forces at sliding sleeve ends.
  • Examination of the interplay between axial and flexural vibrations.

Main Results:

  • Configurational forces disrupt the band gap structure for longitudinal vibrations, allowing axial propagation within previously forbidden frequency ranges.
  • Flexural oscillations can induce axial resonance, leading to unbounded longitudinal vibrations.
  • The study highlights the significant influence of configurational forces on vibrational characteristics.

Conclusions:

  • Configurational forces are pivotal in altering vibration propagation in structured media.
  • The findings suggest opportunities for designing mechanical devices that achieve longitudinal actuation through controlled flexural vibrations.
  • This research contributes to the modeling of dynamic phenomena in structured media.