Sound attenuation characteristics of cellular metamaterials

Satya Surya Srinivas Varanasi, Purdue University

Abstract

The objectives of this work were to develop lightweight barrier and compact absorbing material systems for controlling low frequency noise (say below 2 kHz). The solutions explored fell into the broad category of segmented cellular materials in which local resonances are built-in attributes. The body of the work was divided into four parts. First, a cellular metamaterial concept for lightweight barrier materials was proposed, then, secondly, the concept was experimentally verified by testing application-scale designs in a diffuse sound field setup. In the remaining two parts of the work, the idea of shifting sound energy emporally and spatially was explored as a means of improving the performance of metamaterial-based barrier solutions and of compact sound absorbers, respectively. The high sound transmission loss (STL) metamaterials described to-date commonly require the introduction of relatively heavy resonating or constraining components which runs counter to the desire to create lightweight barrier solutions. It was proposed here that a cellular panel comprising a periodic arrangement of unit cells consisting of plates held in a grid-like frame, which itself is unsupported, can possess a high STL within a specified frequency range without an undue mass penalty. It was numerically demonstrated that such a cellular panel can yield enhanced STL if the unit cell mass is apportioned appropriately between the unit cell plate and the surrounding grid-like frame. The concept of planar cellular metamaterials was verified through diffuse field experiments on application-scale specimens by using intensity methods. Two cellular panel designs were tested and their behavior was compared with that of a reference limp panel. It was found that the predicted benefit of the cellular panels could be realized by increasing the mass contrast in the designs, and that the benefit was reduced with increasing diffuseness of the sound field. It was also found that the loss in performance could be mitigated by the addition of appropriate treatments such as a lightweight grid that modified the incident sound field to be normally directed. Although the performance of the metamaterial-based barrier solutions was better compared to the conventional ones, the performance can be poor at the system eigenfrequencies. The possibility of shifting energy from the deficit bands to other regions where the barriers are more efficient was numerically explored for embodiments of segmented cellular materials having non-linear stiffness characteristics. The acoustical behavior of such materials was probed through representative two-dimensional models of a segmented plate with a contact interface. Super-harmonic response peaks were observed for pure harmonic excitations, the strength of which were found to strongly depend on the degree of non-linearity or bilinear stiffness ratio. The closer an excitation frequency was to the characteristic eigenfrequencies of the structure, the stronger was the super-harmonic response, which supported the idea of transferring energy from problematic frequency bands to higher frequencies. Finally, the possibility of a spatial-shift of energy from longitudinal to lateral direction was explored with the idea of eliminating the design constraints associated with conventional absorbing materials, and with the hope of realizing a compact sound absorber. The embodiment was a two-phase chiral composite made using a Topologically Interlocked Material (TIM) with its unit cell being a tetrahedron consisting of two helicoid dissections. A comparative study was conducted with standard microstructures inspired by the Voigt and Reuss models. The twist mode of the chiral composites was found to be excited by an incident sound field normal to the plane of the TIM assembly. Although this behavior is not unique to a chiral microstructure, many other microstructures do not exhibit this behavior. The excitation of the twist mode by the incident sound field offers a new avenue for realizing a compact sound absorber.

Degree

Ph.D.

Advisors

Bolton, Purdue University.

Subject Area

Mechanical engineering|Acoustics

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