Attenuation of low frequency turbofan engine noise has been a challenging task in an industry that requires low weight and tightly-packed solutions. Without innovative advancements, the technology currently used will not be able to keep up with the increasingly stringent requirements on aircraft noise reduction. A need exists for novel technologies that will pave the way for the future of quiet aircraft. This thesis investigates acoustic metamaterials and their ability to achieve superior transmission loss characteristics not found in traditional honeycomb liners. The acoustic metamaterials investigated are an array of Helmholtz resonators with and without coupled cavities periodically-spaced along a duct wall. Analytical, numerical, and experimental developments of these acoustic metamaterial systems are used herein to study the effects of this technology on the transmission loss. Particularly focusing on analytical modeling will aid in understanding the underlying physics that governs their interesting transmission loss behavior. A deeper understanding of the physics will be used to aid in future acoustic metamaterial liner design. A parameter study is performed to understand the effects of the geometry, spacing, and number of resonators, as well as resonator cavity coupling on performance. Increased broadband transmission loss, particularly in low frequencies, is achieved through intelligent manipulation of these parameters. Acoustic metamaterials are shown to have appealing noise cancellation characteristics that prove to be effective for aircraft engine liner applications. / Master of Science / Aircraft noise reduction is an ongoing challenge for the aerospace industry. Without innovative advancements, the next generation of aircraft will not be able to keep up with increasingly stringent noise regulations; novel acoustic technology is needed to pave the way for a future of quieter aircraft. This thesis investigates acoustic metamaterials and their ability to achieve superior noise reduction over traditional methods. Modeling techniques were developed, and experimental tests were conducted to quantitatively evaluate the effectiveness of a new acoustic metamaterial system. The acoustic metamaterial design explored herein was proven to reduce noise effectively and shows promise for a world of quieter aircraft.

Mechanics of structure genome (MSG) is a unified homogenization theory that provides constitutive modeling of three-dimensional (3D) continua, beams and plates. In present work, the author extends the MSG to study the buckling of structures such as stiffened and sandwich panels. Such structures are usually slender or flat and easily buckle under compressive loads or bending moments which may result in catastrophic failure.<div><br><div>Buckling studies of stiffened and sandwich panels are found to be scattered. Most of the existed theories employ unnecessary assumptions or only apply to certain types of structures. There are few unified approaches that are capable of studying the buckling of different kinds of structures altogether. The main improvements of current approach compared with other methods in the literature are avoiding unnecessary assumptions, the capability of predicting all possible buckling modes including the global and local buckling modes, and the potential in studying the buckling of various types of structures.<br></div><div><br></div><div>For global buckling that features small local rotations, MSG mathematically decouples the 3D geometrical nonlinear problem into a linear constitutive modeling using structure genome (SG) and a geometrical nonlinear problem defined in a macroscopic structure. As a result, the original structures are simplified as macroscopic structures such as beams, plates or continua with effective properties, and the global buckling modes are predicted on macroscopic structures. For local buckling that features finite local rotations, Green strain is introduced into the MSG theory to achieve geometrically nonlinear constitutive modeling. Newton’s method is used to solve the nonlinear equilibrium equations for fluctuating functions. To find the bifurcated fluctuating functions, the fluctuating functions are then perturbed under the Bloch-periodic boundary conditions. The bifurcation is found when the tangent stiffness associated with the perturbed fluctuating functions becomes singular. Moreover, the arc-length method is introduced to solve the nonlinear equilibrium equations for post-local-buckling predictions because of its robustness. The imperfection is included in the form of geometrical imperfection by superimposing the scaled buckling modes in linear perturbation analysis on mesh.<br></div><div><br></div><div>Extensive validation case studies are carried out to assess the accuracy of the MSG theory in global buckling analysis and post-global-buckling analysis, and assess the accuracy of the extended MSG theory in local buckling and post-local-buckling analysis. Results using MSG theory and extended MSG theory in buckling analysis are compared with direct numerical solutions such as 3D FEA results and results in literature. Parametric studies are performed to reveal the relative influence of selective geometric parameters on buckling behaviors. The extended MSG theory is also compared with representative volume element (RVE) analysis with Bloch-periodic boundary conditions using commercial finite element packages such as Abaqus to assess the efficiency and accuracy of the present approach.<br></div></div>