Acoustic measurement and statistical characterization of direct-printed, variable-porosity aluminum foams.

Additive manufacturing has expanded greatly in recent years with the promise of being able to create complex and custom structures at will. Enhanced control over the microstructure properties, such as percent porosity, is valuable to the acoustic design of materials. In this work, aluminum foams are fabricated using a modified powder bed fusion method, which enables voxel-by-voxel printing of structures ranging from fully dense to approximately 50% porosity. To understand the acoustic response, samples are measured in an acoustic impedance tube and characterized with the Johnson-Champoux-Allard-Lafarge model for rigid-frame foams. Bayesian statistical inversion of the model parameters is performed to assess the applicability of commonly employed measurement and modeling methods for traditional foams to the additively manufactured, low porosity aluminum foams. This preliminary characterization provides insights into how emerging voxel-by-voxel additive manufacturing approaches could be used to fabricate acoustic metal foams and what could be learned about the microstructure using traditional measurement and analysis techniques.

Elastic bandgap widening and switching via spatially varying materials and buckling instabilities.

Efficient control over elastic wave transmission is often critical in the design of architected materials. In this work, lattices that achieve buckling induced band gaps are designed with spatially varying material properties to leverage both effects for enhanced wave control. Each unit cell exhibits a large shape change when subjected to an external activation. Unit cells with discrete material properties are then arranged in different spatial configurations. Numerical simulations for transmission through the example structures demonstrate both bandgap widening due to different material properties in adjacent unit cells and switching at different deformation states.

Acoustic response for nonlinear, coupled multiscale model containing subwavelength designed microstructure instabilities.

Nonperiodic arrangements of inclusions with incremental linear negative stiffness embedded within a host material offer the ability to achieve unique and useful material properties on the macroscale. In an effort to study such types of inclusions, the present paper develops a time-domain model to capture the nonlinear dynamic response of a heterogeneous medium containing a dilute concentration of subwavelength nonlinear inclusions embedded in a lossy, nearly incompressible medium. Each length scale is modeled via a modified Rayleigh-Plesset equation, which differs from the standard form used in bubble dynamics by accounting for inertial and viscoelastic effects of the oscillating spherical element and includes constitutive equations formulated with incremental deformations. The two length scales are coupled through the constitutive relations and viscoelastic loss for the effective medium, both dependent on the inclusion and matrix properties. The model is then applied to an example nonlinear inclusion with incremental negative linear stiffness stemming from microscale elastic instabilities embedded in a lossy, nearly incompressible host medium. The macroscopic damping performance is shown to be tunable via an externally applied hydrostatic pressure with the example system displaying over two orders of magnitude change in energy dissipation due to changes in prestrain. The numerical results for radial oscillations versus time, frequency spectra, and energy dissipation obtained from the coupled dynamic model captures the expected response for quasistatic and dynamic regimes for an example buckling inclusion for both constrained and unconstrained negative stiffness inclusions.

Frequency-dependent behavior of media containing pre-strained nonlinear inclusions: Application to nonlinear acoustic metamaterials.

One emerging research area within the fields of acoustic and elastic metamaterials involves designing subwavelength structures that display elastic instabilities in order to generate an effective medium response that is strongly nonlinear. To capture the overall frequency-dependent and dispersive macroscopic response of such heterogeneous media with subwavelength heterogeneities, a theoretical framework is developed that accounts for higher-order stiffnesses of a resonant, nonlinear inclusion that varies with a macroscopic pre-strain, and the inherent inertia associated with an inclusion embedded in a nearly incompressible elastic matrix material. Such a model can be used to study varying macroscopic material properties as a function of both frequency and pre-strain and the activation of such microscale instabilities due to an external, macroscopic loading, as demonstrated with a buckling metamaterial inclusion that is of interest due to its tunable and tailorable nature. The dynamic results obtained are consistent with similar static behavior reported in the literature for structures with elastic instabilities.