Data-driven Identification of Parametric Governing Equations of Dynamical Systems Using the Signed Cumulative Distribution Transform.

This paper presents a novel data-driven approach to identify partial differential equation (PDE) parameters of a dynamical system. Specifically, we adopt a mathematical "transport" model for the solution of the dynamical system at specific spatial locations that allows us to accurately estimate the model parameters, including those associated with structural damage. This is accomplished by means of a newly-developed mathematical transform, the signed cumulative distribution transform (SCDT), which is shown to convert the general nonlinear parameter estimation problem into a simple linear regression. This approach has the additional practical advantage of requiring no a priori knowledge of the source of the excitation (or, alternatively, the initial conditions). By using training data, we devise a coarse regression procedure to recover different PDE parameters from the PDE solution measured at a single location. Numerical experiments show that the proposed regression procedure is capable of detecting and estimating PDE parameters with superior accuracy compared to a number of recently developed machine learning methods. Furthermore, a damage identification experiment conducted on a publicly available dataset provides strong evidence of the proposed method's effectiveness in structural health monitoring (SHM) applications. The Python implementation of the proposed system identification technique is integrated as a part of the software package PyTransKit [1].

Detecting acoustic chirality with matched metamaterial vortex wave antennas.

Acoustic communications often have limited data rates because of the intrinsically low frequencies. Exploring new spatial modes to increase data bandwidth at fixed frequency is a possible solution to this problem. Here, we demonstrate acoustic wave chirality transmission between two reciprocal metamaterial vortex wave antennas, generating and sensing transmitted acoustic wave chirality through the sub-wavelength geometry of the system. By adding an acoustic leaky wave surface to a ring resonator waveguide, acoustic vortex waves with positive or negative integer mode chirality are independently radiated and detected using a small number of microphones. Through computational simulation and experimental verification, using three-dimensional printed waveguides, we show that the vortex mode chirality can be transferred between two opposing acoustic vortex wave antennas across a small unguided air gap. We also show that emission into an external waveguide can provide long distance data transmission. This demonstrates the first use of metamaterial vortex wave antennas as chiral, mode multi-channel data transceivers.

Exact radiation boundary conditions to determine the complex wavenumber of an underwater acoustic leaky wave antenna.

Underwater elastic leaky wave antennas (LWAs) steer acoustic energy as a function of frequency by exploiting fluid-solid coupling. LWAs present a modeling challenge due to complex radiation impedance on the waveguide surface that leads to changes in dynamic response. This work presents an approach to model underwater LWAs that considers an elastic unit cell surrounded by a fluid domain and includes a radiation boundary condition to simulate an open boundary. The model solves an eigenvalue problem for the complex-valued wavenumber given a specified frequency, forming an accurate representation for the free response of an elastic LWA in an underwater environment.

Characterizing the acoustic response of Thalassia testudinum leaves using resonator measurements and finite element modeling.

Seagrasses play an important role in coastal ecosystems and serve as important marine carbon stores. Acoustic monitoring techniques exploit the sensitivity of underwater sound to bubbles, which are produced as a byproduct of photosynthesis and present within the seagrass tissue. To make accurate assessments of seagrass biomass and productivity, a model is needed to describe acoustic propagation through the seagrass meadow that includes the effects of gas contained within the seagrass leaves. For this purpose, a new seagrass leaf model is described for Thalassia testudinum that consists of a comparatively rigid epidermis that composes the outer shell of the leaf and comparatively compliant aerenchyma that surrounds the gas channels on the interior of the leaf. With the bulk modulus and density of the seagrass tissue determined by previous work, this study focused on characterizing the shear moduli of the epidermis and aerenchyma. These properties were determined through a combination of dynamic mechanical analysis and acoustic resonator measurements coupled with microscopic imagery and finite element modeling. The shear moduli varied as a function of length along the leaves with values of 100 and 1.8 MPa at the basal end and 900 and 3.7 MPa at the apical end for the epidermis and aerenchyma, respectively.

Introduction to the special issue on Additive Manufacturing and Acoustics.

Additive manufacturing (AM) has expanded to a wide range of applications over the last few years, and acoustic applications are no exception. This article is an introduction to the special issue of the Journal of the Acoustical Society of America on AM and acoustics. To provide background to the reader, a brief introduction to the manufacturing approach of AM is included. The ways in which the articles in this special issue advance the field of acoustics are described for a range of applications.

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.

Evaluation of the resolution of a metamaterial acoustic leaky wave antenna.

Acoustic antennas have long been utilized to directionally steer acoustic waves in both air and water. Typically, these antennas are comprised of arrays of active acoustic elements, which are electronically phased to steer the acoustic profile in the desired direction. A new technology, known as an acoustic leaky wave antenna (LWA), has recently been shown to achieve directional steering of acoustic waves using a single active transducer coupled to a transmission line passive aperture. The LWA steers acoustic energy by preferential coupling to an input frequency and can be designed to steer from backfire to endfire, including broadside. This paper provides an analysis of resolution as a function of both input frequency and antenna length. Additionally, the resolution is compared to that achieved using an array of active acoustic elements.

Experimental Demonstration of Underwater Acoustic Scattering Cancellation.

We explore an acoustic scattering cancellation shell for buoyant hollow cylinders submersed in a water background. A thin, low-shear, elastic coating is used to cancel the monopole scattering from an air-filled, neutrally buoyant steel shell for all frequencies where the wavelength is larger than the object diameter. By design, the uncoated shell also has an effective density close to the aqueous background, independently canceling its dipole scattering. Due to the significantly reduced monopole and dipole scattering, the compliant coating results in a hollow cylindrical inclusion that is simultaneously impedance and sound speed matched to the water background. We demonstrate the proposed cancellation method with a specific case, using an array of hollow steel cylinders coated with thin silicone rubber shells. These experimental results are matched to finite element modeling predictions, confirming the scattering reduction. Additional calculations explore the optimization of the silicone coating properties. Using this approach, it is found that scattering cross-sections can be reduced by 20 dB for all wavelengths up to k0a = 0.85.

Highly anisotropic elements for acoustic pentamode applications.

Pentamode metamaterials are a class of acoustic metafluids that are characterized by a divergence free modified stress tensor. Such materials have an unconventional anisotropic stiffness and isotropic mass density, which allow themselves to mimic other fluid domains. Here we present a pentamode design formed by an oblique honeycomb lattice and producing customizable anisotropic properties. It is shown that anisotropy in the stiffness can exceed 3 orders of magnitude, and that it can be realistically tailored for transformation acoustic applications.

Scaling of membrane-type locally resonant acoustic metamaterial arrays.

Metamaterials have emerged as promising solutions for manipulation of sound waves in a variety of applications. Locally resonant acoustic materials (LRAM) decrease sound transmission by 500% over acoustic mass law predictions at peak transmission loss (TL) frequencies with minimal added mass, making them appealing for weight-critical applications such as aerospace structures. In this study, potential issues associated with scale-up of the structure are addressed. TL of single-celled and multi-celled LRAM was measured using an impedance tube setup with systematic variation in geometric parameters to understand the effects of each parameter on acoustic response. Finite element analysis was performed to predict TL as a function of frequency for structures with varying complexity, including stacked structures and multi-celled arrays. Dynamic response of the array structures under discrete frequency excitation was investigated using laser vibrometry to verify negative dynamic mass behavior.