Wave Propagation in Linear and Nonlinear Periodic Media: Analysis and Applications

June 21, 2010 — June 25, 2010


  • Francesco Romeo (Università "La Sapienza", Roma, Italy)
  • Massimo Ruzzene (Georgia Institute of Technology, Atlanta, USA)

Periodic structural configurations are ubiquitous: many heterogeneous structures and materials, both man-made and naturally occurring, feature geometry, micro-structural and/or materials properties that vary periodically in space. The classes of periodic materials and structures span a wide range of length scales, and a broad range of applications.
Periodic trusses, periodically stiffened plates, shells and beam-like assemblies can be found for example in many civil, aerospace, mechanical and ship constructions. Their introduction is mostly motivated by structural strength and weight requirements. However recent studies have shown how the periodicity can be exploited to attenuate, isolate and localize vibrations. Such studies explore the unique ability of periodic assemblies to impede the propagation of elastic waves over specified frequency bands, within which strong attenuation of vibration and radiated noise can be achieved. The attenuation levels that can be obtained through tailored structural periodicity far exceed the performance of most energy dissipation and damping mechanisms. For this reason, passive, active and hybrid periodic structural configurations are being proposed for the reduction of vibration transmission and structure-born, as well as airborne noise. In addition, the understanding of the dynamics of periodic structures is essential for the analysis of bladed disc assemblies which are found in turbo machinery and in turbines for energy generation, where failure mechanisms due to localization phenomena may occur.
At much smaller scales, extensive research is being devoted to the analysis and design of phononic metamaterials for a variety of applications. Phononic metamaterials are essentially periodic structural configurations obtained through composite design, featuring periodic modulations of mass and stiffness properties, or elastic lattice structures. Gigahertz communication devices, such as mobile phones, use phononic-based systems for their low-power filtering characteristics. Many sensing devices based on resonators, acoustic logic ports, and surface acoustic wave-based filters rely on the unique band gap characteristics of periodic phononic materials. These properties are associated with the destructive and constructive interference of acoustic waves originating at the periodic interfaces, which produce frequency band of strong attenuation of acoustic waves (band gaps). Depending on the inclusions, geometry, and elastic properties, one can design for specific band gaps.
In photonic crystals, periodic modulations of the dielectric properties of a medium allow guiding, focusing and steering of electromagnetic waves. Properties modulations and engineered anisotropy in heterogeneous media can also produce negative refractive indexes, both in photonics as well as in phononic metamaterials, which lead to super-lensing or super-focusing characteristics. Other potential implications of the “acoustic wave guiding” technology include active sensing of structural integrity, smart sensing of environment, dissipation of high frequency modes of vibration to enhance vehicle performance or stealth, as well as applications to the medical field for sensing or diagnostic applications.
The aim of the course is to present both the theoretical background and an overview of the state-of-the art in wave propagation in linear and nonlinear periodic media in a consistent lecture format.
The course is intended for doctoral and postdoctoral researchers in civil and mechanical engineering, applied mathematics and physics, academic and industrial researchers, which are interested in conducting research in the topic.

Keywords: Wave Motions in Solids, Vibrations of Solids and Structures, Computational Mechanics, Diagnosis of Structural Damages by Inverse Analysis


See also