Download or read book Finite Element Investigation of Tunable and Non-reciprocal Elastic Wave Metamaterials written by Benjamin Michael Goldsberry and published by . This book was released on 2019 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation studies elastic wave propagation in metamaterials subjected to an externally-applied static or spatiotemporally-varying pre-strain. Elastic metamaterials are media with subwavelength structure that behave as effective materials displaying atypical effective dynamic properties that are used to directly control the propagation of macroscopic waves. One major design limitation of most metamaterial structures is that the dynamic response cannot be altered once the microstructure is manufactured. However, the ability to modify, or tune, wave propagation in the metamaterial with an external pre-strain that induces geometric nonlinearity is highly desirable for numerous applications. Acoustic and elastic metamaterials with time- and space-dependent effective material properties have also recently received significant attention as a means to induce non-reciprocal wave propagation. However, the modulation of effective material properties in space and time using mechanical deformation has been unexplored. Tunable elastic metamaterials that exhibit large effective material property changes under a varying external pre-strain are therefore strong candidates for a non-reciprocal medium. The complex geometry present in unit cells that exhibit large geometric nonlinearity necessitates the development of a numerical technique. In this dissertation, a finite element approach is derived and implemented to study elastic wave propagation in a static pre-strained metamaterial, then generalized to include the effects of a spatiotemporally-varying pre-strain. A honeycomb structure composed of a doubly-periodic array of curved beams, known as a negative stiffness honeycomb (NSH), is analyzed as a tunable and non-reciprocal elastic metamaterial. It is shown that NSH exhibits significant tunability and a high degree of anisotropic wave behavior when a static pre-strain is imposed. This behavior can be used to guide wave energy in different directions depending on static pre-strain levels. In addition, it is shown that partial band gaps exist where only longitudinal waves propagate. The NSH therefore behaves as a meta-fluid, or pentamode metamaterial, which may be of use for applications of transformation elastodynamics such as cloaking and gradient index lens devices. A negative stiffness chain, a quasi-one-dimensional representation of NSH, is also shown as a case example of a non-reciprocal medium. It is shown in this work that this structure displays a high degree of non-reciprocity for a small amount of modulation pre-strain. The utility of the finite element approach is further demonstrated by investigating the effects of chiral geometric asymmetry to enhance the non-reciprocal behavior of elastic wave propagation in NSH