Search

We present a new computational method for the accurate identification of the propagation modes and polarizations of elastic waves propagating in periodic solid structures and metamaterials. The method uses the eigenvectors calculated at each propagating wave solution eigenfrequency to identify the contribution of each translational and rotational component of the total mass in motion. We use this information to identify the dominant wave propagation mode by defining a relative effective modal mass vector. Further, we associate each wave solution with its correct polarization by defining a new polarization factor that quantifies the relative orientation between the wave propagation and lattice motion directions and provides a positive numerical value between 0 (pure S-wave) and 1 (pure P-wave). Further, we suggest a graphical representational scheme for an easier visualization of the wave polarization within traditional dispersion plots. The method is validated by comparing our predictions against previously published results for various elastodynamic problems. Finally, we use the proposed method to analyze the effect of various lattice and structural parameter perturbations on the elastic wave propagation and bandgap behavior of a square planar beam lattice and show the emergence of previously unobserved dynamic characteristics, including various polarized bandgaps, fluid-like behavior, and ultralow-frequency SH- and SV-bandgaps that extend to 0 Hz. The proposed method provides an alternative computational approach to the typically employed visual mode inspection technique and provides a robust technique for analyzing the elastic wave response of periodic solid media., Comment: Paper currently under review. Corresponding author: bhisham.sharma@wichita.edu

We investigate the acoustical properties of uncompressed and compressed open-celled aluminum metal foams fabricated using a directional solidification foaming process. We compressed the fabricated foams using a hydraulic press to different compression ratios and characterized the effect of compression on the cellular microstructure using microtomography and scanning electron microscopy. The static airflow resistances of the samples are measured and related to the observed microstructural changes. We measured the normal incidence acoustical properties using two- and four-microphone impedance tube methods and show that the compression substantially improves their sound absorption and transmission loss performance. We then stack individual disks with different compression ratios to create various stepwise relative density gradient configurations and show that stepwise gradients provide a significant improvement in properties as compared to the uncompressed sample. The effect of increasing and decreasing relative density gradients on the overall absorption and transmission loss behavior is characterized. Finally, we use an experimentally informed and validated transfer matrix method to predict the effect of various layer thicknesses and stacking sequences on the global acoustical properties. Our results show that open-celled metal foams with stepwise relative density gradients can be designed to provide tailored acoustic absorption performance while reducing the overall weight of the noise reduction package., Comment: Currently under submission at Applied Acoustics *Corresponding author: Bhisham Sharma, Mechanics and Dynamics Laboratory, Department of Aerospace Engineering, Wichita State University, Wichita, KS 67270, USA. Email: bhisham.sharma@wichita.edu

We investigate the possibility of additively manufacturing fibrous sound absorbers using fused deposition modeling. Two methods for 3D printing fibers are proposed. The fiber bridging method involves extruding the filament between two points with no underlying supports. The extrude-and-pull method involves extruding a filament droplet before pulling away the extruder rapidly to generate thin fibers. Both methods can produce fibers with aspect ratios greater than 100. Optical microscopy is used to investigate the effect of various printing parameters on the fiber characteristics. The sound absorption coefficient of samples printed using the two techniques are measured using a two-microphone normal incidence impedance tube setup. Effects of printing parameters and fiber density variables are experimentally studied. The experimental studies are supported by the Johnson-Champoux-Allard semi-empirical analytical model informed using an inverse characterization approach. The analytical model is then utilized to understand the effect of fiber parameters on the acoustical transport parameters. It is observed that the two methods result in individual fibers with distinct characteristics. On average, the fiber bridging method results in thicker fibers, which results in comparatively higher sound absorption. However, the extrude-and-pull method results in fibers with hair-like characteristics (thick base with progressively decreasing thickness) and one may easily incorporate it within existing additive manufacturing routines to add fibers to a base surface, thus opening up a new route towards fiber-enhanced multifunctional structures., Comment: Paper accepted for publication in Additive Manufacturing

We study the low frequency wave propagation behavior of sandwich beams containing periodically embedded internal resonators. A closed form expression for the propagation constant is obtained using a phased array approach and verified using finite element simulations. We show that local resonance and Bragg bandgaps coexist in such a system and that the width of both bandgaps is a function of resonator parameters as well as their periodicity. The interaction between the two bandgaps is studied by varying the local resonance frequency. We find that a single combined bandgap does not exist for this system and that the Bragg bandgaps transition into sub-wavelength bandgaps when the local resonance frequency is above their associated classical Bragg frequency.

An acoustic negative bulk modulus metamaterial based on the concept of expansion chambers is proposed. It is shown that addition of a neck region to an ordinary expansion chamber improves its transmission loss characteristics at low frequencies and the resulting structure displays a negative bulk modulus behavior. Additionally, membrane based metamaterials are analyzed. Using FEM, the negative density behavior of a membrane carrying a center mass and of a tensioned membrane array is analyzed and the inherent similarity of the two designs is discussed. Further, the modified expansion chamber is combined with an array of stretched membranes and the resulting structure is analyzed for double negative behavior.