Andrew N Norris - US grants

This research is focused to resolve fundamental dynamic problems in porous solids and fluid-porous interfaces. The applicability of ultrasonic phenomena will be analyzed for a fluid-porous interface and scattering problems related to pore-fluid resonance effects will be determined. Wave propagation in a fluid-filled porous rock will be studied to determine the effect of porosity on velocity and attenuation of guided waves. Scattering in porous media will be considered by placing cylindrical and spherical inhomogenities in the body. The results of this research will help to assess the feasibility of using poroelastic phenomena to analyze the role of microstructure on effective elastic moduli of porous structures such as rocks and composite materials containing microcracks.

The project explores cloaking of sound and vibration. A cloak surrounds an object so that it causes waves of sound or vibration to bypass the object. Cloaking appeared on the scene in 2006 with the first demonstration of a device that can cloak electromagnetic microwaves. Acoustic cloaking is in its infancy, and it is not even clear whether cloaking of elastic waves is possible. This project will address these questions through theory and simulation. The first goal is a thorough understanding of acoustic cloaks, focusing on so-called pentamode metamaterials. These are easily sheared, like rubber or water, but have the unusual property that they support a biaxial state of stress, as compared with hydrostatic. The main objective, elastodynamic cloaking, will first consider a metamaterial layer capable of emulating the wave properties of a thicker layer of normal solid. Mathematical relations involving coordinate and gauge transformations will be used, and more complicated cylindrical and spherical structures will be studied. The final goal is a realistic model of Rayleigh wave cloaking.

Longer term societal benefits will be enhanced technology for reducing vibration and noise, and methods to channel destructive mechanical wave energy around sensitive areas and objects, such as shielding buildings from earthquake ground motion. The project will include a seminar for honors engineering freshmen on the subject of metamaterials, cloaking, and futuristic technology. Undergraduates will be explicitly involved in the research, building on a current project for seniors. A web-page explaining cloaking in layperson terms will be enhanced.

Two of the most fundamental concepts in wave propagation and signal transmission are the closely related principles of reciprocity and time-reversal symmetry. Reciprocity requires that a wave traveling in one direction can just as well travel in the opposite direction, while time-reversal symmetry provides the same relationship when time is reversed. Recent advances in engineering have shown that either or both principles can be violated under special conditions, for instance in the presence of moving fluid and solid elements. This award supports fundamental research to demonstrate novel methods for realizing non-reciprocal behavior through the design of heterogeneous acoustic, elastic, and electro-mechanical systems. Technology that violates these fundamental rules opens the possibility of changing the standard operating procedures for measuring and utilizing acoustic and elastic waves. The work pairs these new concepts with robust materials design methodologies and additive manufacturing expertise to help redirect the nation?s technological advances in acoustics, structural vibration, ultrasonic inspection, seismic protection, and biomedical imaging. Research efforts supported in this award specifically provide opportunities for underrepresented undergraduate students to participate in knowledge acquisition and exploration via multidisciplinary projects conducted in parallel at the collaborating institutions.

One approach to breaking time-reversal symmetry in linear systems to be considered is based on the dynamic coupling of momentum and strain using excitation on fast and slow time scales for acoustic and elastic media with spatially asymmetric microstructure. Oscillations from a pump excitation provide a quasi-static momentum bias that enables non-reciprocal signal propagation. Other routes to achieving non-reciprocal response include elastically nonlinear up-conversion from the drive frequency to higher harmonics. Optimal damping and absorption in elastic waveguides, using an unexplored powerful relation between exceptional points and damping, will be examined. Other areas to be investigated include active control via shunted piezoelectric elements and hybrid time-varying circuits. Materials design is at the center of the DEPARTED project with a view towards efficient design space exploration and employing state-of-the art additive manufacturing techniques to develop optimal microstructural topology of these structures.