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Acoustic metamaterial for noise reduction with negative effective mass density and bulk modulus
Keywords: Acoustic metamaterial, Sound noise reduction, packaging metarial
In the harsh acoustical environment, the high power sound (over 120 dB) at medium-high frequencies (3 kHz -20 kHz) due to engine noises, aeroacoustic vibrations, explosions and so on is one of the fetal issues to most electronic devices. The reason such devices are susceptible to acoustic noises is simple. The sound wave can go through thin structure made of conventional materials very easily and causes vibration at resonant frequencies, especially for the compact micro substructures and their corresponding packages. Experiments have proven true that high power noises in a specific frequency range are detrimental to the functional reliability and durability of devices, for instance to most MEMS gyroscopes and other sensors. Much thicker and heavier conventional materials are needed in order to diminish the noise, but most devices cannot afford them under tightly circumscribed space and weight requirements. As a kind of package, the acoustic attenuation package itself should satisfy some practical needs such as wideband noise reduction, reliability, low cost, and ease of fabrication.Therefore, researchers cast their attention on acoustic metamaterials to facilitate better solutions for such demands in acoustic attenuation. Since 2006, the interests in metamaterials have been increasing, including the acoustic area. Considerable research has proposed fascinating artificial acoustic metamaterials which perform desired properties that is impossible in nature. The idea of the metamaterial can be traced back to the postulation of Veselago who proposed an artificial material with both negative permeability and permittivity for electromagnetic waves. Extensive research has verified Veselago's concept experimentally by proposing designs of artificial metamaterial within a variety of frequency ranges. The similarity between electromagnetic and acoustic waves mathematically provides the possibility of an analogy to construct metamaterials that interact with effective mass density and bulk modulus. Researchers have performed acoustic attenuation and simultaneously obtained negative values of these two properties. To this date, many kinds of acoustic metamaterial have achieved the double negative properties by the following strategies: phononic crystals, intrinsic and inertial acoustic metamaterials. Phononic crystals require the material particle spacing artificially matching the same order as the wavelength, and create the Bragg scattering effect to reflect the sound waves. The ability to manufacture and cost highly restrain this approach from being practical in the packaging industry. The intrinsic acoustic metamaterials commonly utilize elastic materials by means of soft spheres to slow down the phase velocity. The inertial acoustic metamaterials apply elastic membrane or Helmholtz resonator to achieve a spring-mass-damper system for specific frequencies. Due to highly relying on elastic materials, both the intrinsic and inertial have to face the disadvantages in dimension, durability, tunability, and convection for heat dissipation. Considering all the factors above, this paper proposed a novel design of metamaterial in the form of microscale open-through chamber (ODC) substructures. The ODC element is designed embedded into a rigid thin substrate with two open ends on both sides of the substrate, no elastic material needed. Combinations of tubes in micrometer-scale and chambers in millimeter-scale constitute the configuration ensuring small dimension. The air can freely pass through the ODC structure to the atmosphere for the purpose of convection. According to the thermoacoustic theory, the viscous friction effect on the rigid inner boundary cannot be overlooked due to such small scales and variations in wavelength. The particle velocity of sound in the air is dragged from the maximum in the center to zero at the rigid wall by viscous force. Consequently, this significantly influences the acoustic impedance, and contributes to high attenuations continuously in a wide frequency band as well as the effect on mass density and bulk modulus. Theoretical models based on the analogous acoustic circuit predicted that high attenuations in wide frequency band could be achieved by very thin ODC elements.Meanwhile, the models also reveal that the ODC element exhibits the potential of combining the properties of both the intrinsic and inertial metamaterials. To readily test the performance of the ODC metamaterial, samples were designed in the form of a packaging box with one side open and the same inner dimensions. ODC elements were built in the walls of the box as a substructural lattice in arrays. Wall thicknesses varied with corresponding lengths of tubes and chambers. The volume ratio ϕ of the chamber to the tube V_c/V_t is denoted for the convenience of inspecting the attenuation performance. The corresponding control samples consisted of solid walls instead of the ODC substructure. The incident sound was projected perpendicularly to the wall of testing samples with a frequency range from 0 Hz to 8.2 kHz. The transmission loss results were highly identical to the corresponding predictions. The ODC metamaterials showed dominating attenuations starting from 2.5 kHz with 25.3 dB transmission loss and kept overwhelming to corresponding control samples over the rest frequencies. The effective mass density and bulk modulus can be obtained. Along with increasing frequency, the negative effective mass density and bulk modulus showed up from 4.7 kHz and 5.3 kHz respectively. The prediction and experimental results demonstrated that the transmission loss levels up and the gross curve shifts to the left along with the increasing volume ratio ϕ. Comparable demonstrations can also be observed for the start frequency of the negativity of the effective mass density and bulk modulus. Analyses of all six sets of results indicated that the acoustical characteristics of the ODC metamaterial is highly related to the volume ratio. Samples with similar volume ratio but different in other configurations (such as radii and lengths of tubes and chambers) demonstrated almost identical results. An assumption can be proposed that by properly selecting the volume ratio the thickness of the ODC metamaterial package would be controlled to a desired value, which provided a possibility of making noise reduction packages considerably thin by precision manufacturing technology.
Fuxi Zhang, Ph.D student
Auburn University
Auburn University, Alabama
United States

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