[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] "Metamaterials have been extensively developed in many areas over the past two decades, a great deal of research has been conducted on acoustic/elastic metamaterials exhibiting unusual dynamic effective material properties produced by artificially engineered microstructures. While most of the studies are still scattered, superficial delineations and lack of effective practical application. To promote the application of metamaterials, we designed the structures to explore the metamaterials application in elastic wave mitigation, elastic cloaking, and acoustic wave modulation, where all these techniques can be used to mitigate the wave inside the structure and ensure the safety of the target. For wave mitigation, vibration suppression at subwavelength scales is of great interest in acoustic and/or elastic metamaterial engineering, which has a wide range of potential applications requiring dynamic stabilities by using light-weight structures and materials. Thus, we propose the concept of bio-inspired metamaterials with hierarchically organized local resonators, which possess the ability to efficiently tailor elastic wave attenuation to various frequency regions through different hierarchical designs. Wave dispersion relations and bandgap behaviors of one-dimensional lumped mass-spring hierarchical metamaterials are characterized first with outward and inward hierarchical configurations. A honeycomb hierarchical lattice with embedded rubber coated lead cylinders is then designed to demonstrate the vibration suppression at subwavelength scales in two separate frequency regions, where the first-order outward hierarchy is selected. Good agreement between experimental and numerical results is observed in the frequency response functions of a metamaterial sample. The hierarchical metamaterials are proposed to be efficient solutions in elastic wave bandgap engineering at subwavelength scales, which will benefit light-weight passive structures for low-frequency vibration and/or elastic wave mitigation. To further improve the wave mitigation performance of designed metamaterials, a nonlinear elastic metamaterial (NEM) is presented for broadband wave attenuation by incorporating strongly nonlinear elements in a triatomic microstructural design. The nonlinear elements are considered between the primary and secondary orders of the triatomic model where the primary focus is the influence of damping between the secondary and lowest orders of the triatomic microstructure, respectively. The NEM with both weak and strong damping considered is investigated for efficient attenuation of transient blast waves. The fourth-order Runge-Kutta numerical method is used for obtaining the attenuation, transmission, and reflection coefficients of the NEM. It is found that the NEM can expand the bandwidth of the bandgap and enhance the absorption of elastic waves compared with a purely linear elastic metamaterial. Next, we explore an elastic cloak that can be applied to an arbitrary inclusion to make it indistinguishable from the background medium. Cloaking against elastic disturbances has been demonstrated using several designs and gauges. None tolerate the coexistence of normal and shear stresses due to a shortage of physical realization of transformation-invariant elastic materials. Here, we overcome this limitation to design and fabricate a new class of polar materials with a distribution of body torque that exhibits asymmetric stresses. A static cloak for full two-dimensional elasticity is thus constructed based on the transformation method. The proposed cloak is made of a functionally graded multi-layered lattice embedded in an isotropic continuum background. While one layer is tailored to produce a target elastic behavior, the other layers impose a set of kinematic constraints equivalent to a distribution of body torque that breaks the stress symmetry. Experimental testing under static compressive and shear loads demonstrate encouraging cloaking performance in good agreement with our theoretical prediction. The work sets a precedent in the field of transformation elasticity and should find applications in mechanical stress shielding and stealth technologies. In the last, to mitigate the acoustic wave in one direction and let free propagation in another direction, we then present the physical realization of a nonreciprocal acoustic material with space-time modulated interfacial conditions to generate acoustic topological pumping and nonreciprocal transport. The modulated material inspired by a water wheel consists of a helix rotating around a slotted tube at a controllable speed. When the helix rotates, it creates moving interfaces between the tube and the external medium at a constant speed. Experiments demonstrate acoustic nonreciprocity and topologically robust bulk-edge correspondences for this material which is in good agreement with analytical and numerical predictions. These findings provide insight into practical implications of topological modes in acoustics and the implementation of higher-dimensional topological acoustics that use time as a synthetic dimension. All the proposed work will promote the application of metamaterials in structure protection and wave mitigation."--Summary.
Analysis of a Tubular Torsionally Resonating Viscosity–Density Sensor
