Keynote1

J.R.F. Arruda, University of Campinas.

Manipulating elastic waves aiming at reducing vibration and noise: band gaps, metamaterials, and topological modes

Abstract:

In this work, we discuss some aspects of the wave propagation approach to structural dynamics. The dispersion diagram is a powerful tool to understand dynamic phenomena, allowing a convenient representation of both passbands and stopbands (or band gaps), i.e., frequency ranges where elastic waves can propagate or not, respectively. Such relations can be obtained by considering periodic boundary conditions and, thus, can be used for both homogeneous and spatially periodic structures. Since vibration modes are a consequence of propagating waves reflected at the boundaries and discontinuities of a finite structure, their existence can be avoided by ensuring that waves do not propagate within certain frequency bands. An exception is observed for defect or topological modes, which are localized at interfaces due to a break of periodicity or symmetry. Stop bands can be achieved by (i) periodically varying geometrical or mechanical properties (passive phononic crystals), (ii) periodically attached resonators (periodic metamaterials), or (iii) periodically applied feedback using electromechanical systems (active phononic crystals). The existence of topological modes, i.e., wave modes that are topologically protected and, therefore, robust against defects in the structure periodicity which are likely to be present in manufactured structures, can also be detected using dispersion diagrams. While passive phononic crystals mainly rely on Bragg scattering effects to nucleate stopbands, metamaterials commonly make use of resonators, which can open band gaps in the sub-wavelength domain, an essential feature for practical applications. Active phononic crystals, on the other hand, produce non-reciprocal systems which may have unusual properties such as the skin mode effect, which is a topological behavior. There is currently an important research effort aiming at using stopbands as vibration attenuation mechanisms since they can avoid resonances and attenuate transmitted vibration. Understanding the physics of band gaps and how they can be used to attenuate noise and vibration and manipulate elastic waves is of key importance. Some examples of one- and two-dimensional passive and active periodic structures such as frame structures, acoustic ducts, and plate structures are presented to illustrate the possibilities of using band gaps for vibration and noise attenuation and topological modes for wave manipulation. These examples have been investigated by my research team in the last few years. The future will show if metamaterials and band gaps will become ubiquitous in structural dynamics, or if they are just another red herring.