By A. B. Movchan, M. Brun, N. V. Movchan (auth.), Francesco Romeo, Massimo Ruzzene (eds.)

Waves and illness modes in constructions media.- Piezoelectric superlattices and shunted periodic arrays as tunable periodic buildings and metamaterials.- Topology optimization.- Map-based techniques for periodic structures.- Methodologies for nonlinear periodic media.

The contributions during this quantity current either the theoretical historical past and an outline of the state-of-the paintings in wave propagation in linear and nonlinear periodic media in a constant layout. They mix the cloth issued from various engineering functions, spanning quite a lot of size scale, characterised via buildings and fabrics, either man-made and of course happening, that includes geometry, micro-structural and/or fabrics homes that change periodically in area, together with periodically stiffened plates, shells and beam-like in addition to bladed disc assemblies, phononic metamaterials, photonic crystals and ordered granular media. besides linear versions and purposes, analytical methodologies for studying and exploiting advanced dynamical phenomena bobbing up in nonlinear periodic structures also are presented.

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**Example text**

2003). In fact, many proposed concepts for acoustic metamaterials consider conﬁgurations that derive their unique properties from resonators contained within each unit cell. Typical designs are characterized by inclusions with a phase velocity much lower than that of the matrix (Kushwaha and Djafari-Rouhani, 1998). This allows producing attenuation bands at frequencies which are unrelated to scattering phenomena (Bragg scattering) which occur at wavelengths of the order of the unit cell size.

One of the outstanding challenges in metamaterial development is the ability to tune their properties in response to changing operating conditions. , 2003), which operate on the basis of strong changes in material properties around a pre-deﬁned tuning frequency. One of the concepts illustrated in this chapter involves the use of piezoelectric 34 L. Airoldi, M. Senesi and M. Ruzzene materials for the conversion of elastic into electrical energy, and the use of shunting circuits to generate an equivalent resonant system in parallel to the mechanical waveguide.

Airoldi, M. Senesi and M. Ruzzene (see Figures 13). The behavior of the dispersion properties around the frequency of internal resonance is typical of periodic systems with internal resonating properties as discussed in the introduction to this chapter. Of note is the fact that the case of open circuits does not lead to an absolute zero for the attenuation constant, which may be aﬀected by other sources of dissipation which are inevitably present in an experimental setup. 4 Equivalent properties: a metamaterial perspective The analysis presented in the previous sections can be further elaborated by seeking for analytical expressions which provide insight in the behavior of the system when undergoing internal resonance through the shunting circuits.