Wave Propagation Control via Bandgap Panel with Negative Mass Density and Cloaking Device Composed of Embedded Cylinders with Varying Thicknesses

Abstract

Acoustic metamaterials with zero or negative material properties (effective density or modulus) open up new possibilities for the wave propagation control. Transformation of acoustics theory and highly anisotropic materials enables accurate control over the diffraction of sound or vibrational waves, which can be used to occult by frequency bandgap or cloaking objects from incident wave. This dissertation presents two types of acoustic metamaterial for the control of sound and flexural waves. For acoustic wave control, a two-dimensional flow-through and sound-proof metamaterial exhibiting tunable multi-band negative effective mass density was presented. The metamaterial is composed of periodic funnel-shaped units in a square lattice and each unit cell operates simultaneously as a Helmholtz resonator (HR) and an extended pipe chamber resonator (EPCR) to lead a negative effective mass density to create the multiple bandgaps for incident sound energy dissipation without transmission. Simultaneously, this structure allowed large flow-through the cross-sectional area of the extended pipe since the acoustic resonance is generated by elements without using solid membranes. The pipes are horizontally directed to a flow source to enable small flow resistance for cooling. Measurements of the sound reflection and transmission were performed using a two-load, four-microphone method for a unit cell and small reverberation chamber for two-dimensional panel to characterize the acoustic performance. The effective mass density showed significant frequency dependent variation exhibiting negative values at the specific bandgaps, while the effective bulk modulus was not affected by the resonator. Theoretical models incorporating negative effective material properties in the multiple resonator units were proposed to analyze the noise reduction mechanism. The designed acoustic metamaterial parameters to create broader frequency bandgaps were investigated using the theoretical model. The variation of negative effective mass density was calculated to investigate the creation of the broad bandgaps. The effects of design parameters such as length, cross-sectional area, and volume of the HR; length and cross-sectional area of the EPCR were analyzed. To maximize the frequency bandgap, the suggested acoustic metamaterial panel, small neck length, and cross-sectional area of the HR, large EPCR length was advantageous. The bandgaps became broader when the two resonant frequencies were similar. For flexural wave control, the cloaking object from multiple scattering events that are achieved by metamaterial with embedded cylinders in a thin plate are suggested. Minimization of refraction is performed using small surrounding cylinders with systemically varying thickness in radial and angular directions, respectively. The thickness variations render the effective wave speed lower in the radial direction and higher in the angular direction compared to the phase speed in the surrounding media, which results in the cloaking effect. In order to verify the feasibility of this cloaking object, fifteen-layers of cylinders were placed around the cloaked area. The multiple-scattering method was used to predict wave propagations and to take the interactions between surrounding small cylinders into account. The effects of the thickness variation on the cloaking performance were analyzed. The results demonstrated that minimal scattering was achieved when the area of interest was surrounded by the systemically thickness-varying cylinders.