With the continual challenges associated with reducing aircraft engine noise, there is need for acoustic liner configurations that target broadband performance. This thesis experimentally and analytically investigates passive noise control methods to improve broadband frequency attenuation through various acoustic liner designs. The inclusion of acoustic metamaterials within these liners is examined and optimized. The metamaterials studied consist of resonant and non-resonant materials which include porous foams, microperforated plates (MPP), and embedded aluminum masses. Through finite element analysis, the understanding of the physics behind acoustics as well as aeroacoustics inspire their design. Sensitivity studies on the overall liner shape, facesheet properties, poro-elastic material properties, MPP's, as well as size and placement of embedded masses assist in successfully achieving broadband attenuation. Within the finite element study, an optimization tool will provide additional assistance in quantifying critical system parameters within the designs by minimizing the sum of the transmitted sound intensity over the design frequency bandwidth and hence maximizing attenuation. Broadband frequency absorption and attenuation is successfully achieved within the frequency range of 400-2600 Hz through the design of a varying depth optimized acoustic liner as well as a metamaterial-inspired liner.