Elastic wave tailoring at the macro/micro/nano- scales using intentional strongly nonlinear coupling
In acoustics, wave tailoring refers to the manipulation of the propagation of waves or energy that are generated due to some form of dynamic loading. It includes real world examples ranging from impact mitigation to sensors and communication applications and is typically accomplished through the design of material properties. There are two approaches to designing materials for wave tailoring: the first is to develop new materials by tailoring their atomic structure—for example metallic alloys, ceramic crystals and polymers. The second approach, adopted in this work, is to build “metamaterials” using the existing materials as building blocks and leveraging local architecture to develop new engineered materials with extraordinary properties. The properties of metamaterials can be controlled by treating local architecture and local material properties as optimizable design parameters to exploit their “coupled” behavior to achieve properties and behaviors that cannot be found in nature and often surpass the physical limits imposed by the atomic structure of materials. Nonlinearity, especially strong nonlinearity, introduces additional dynamics that are not accessible in the linear dynamic regime such as frequency-amplitude dependence, sudden transitions (jumps), bifurcations, saturation effects, internal resonances, and chaos. In this work we harness this nonlinear behavior in the form of nonlinear coupling in acoustic waveguides. Common methods of achieving strongly nonlinear behavior are reviewed and a novel class of nonlinear 2D materials is developed and characterized revealing that it is highly tunable and can robustly produce various nonlinear behaviors including strongly softening and strongly stiffening regimes. Importantly, the design readily lends itself to scalable manufacturing processes on both the macro and micro/nanoscales. Wave tailoring applications of nonlinear interactions are studied—for example, micro-granular contact interactions in 1D granular crystals supported by a linear substrate. The propagation of waves through this granular crystal can be tailored through tuning the substrate stiffness, that governs the formation of local clusters which is strongly associated with huge increases in effective damping of the crystal. Several studies on the use of strongly nonlinear metamaterials to passively break acoustic reciprocity—a fundamental property of linear, time-invariant acoustic systems—are performed and nonreciprocity is successfully demonstrated, both theoretically and experimentally. This is accomplished using two different schemes: first, a system involving nonlinearity and internal scale hierarchy in mass, and, second, a system consisting of two dissimilar coupled lattices. Both these systems contain the two main requirements for nonreciprocity in unbiased, time invariant systems: nonlinearity and asymmetry. In the first system, nonreciprocity stems from the nonlinear energy sink – like behavior of one of the asymmetric small-scale masses leading to targeted resonance captures. In the second system, the mechanism of nonreciprocity is the intentional mismatch of the band structures of the lattice in combination with the frequency-amplitude dependence that is characteristic of nonlinearity. In both cases, nonreciprocity is achieved in a controllable, predictable manner. Following this, we advanced into the nanoscale in which, due to scaling, there are many practical applications, e.g., NEMS/MEMS sensors and communication devices such as filters, frequency synthesizers, and temperature-compensated MEMS resonators. We consider two linear nanophononic waveguides connected by strongly nonlinear couplings. The band structures are highly tunable, and, either the nonlinear coupling, or the linear waveguides can introduce the asymmetry required for nonreciprocity. In this case the nonlinearity is due to electrostatic interactions that are readily accessible in the nanoscale. Nonlinear acoustic metamaterials signify a departure from traditional physical constraints and facilitate previously inaccessible acoustic phenomena and applications, e.g., one-way energy transmission, passive wave redirection, advanced acoustic mitigation devices, new classes of sensors with tunable transmission and receiving patterns, energy-dependent frequency-based energy partitions, and heretofore unachievable acoustic logic devices and acoustic computers.
wave tailoring, nanoscale, acoustic, nonlinearity, architectured materials, nonlinear materials, nonreciprocity
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign