Michael R. Haberman

Polynomial phase signals (PPS) are a staple of waveform design and analysis in sonar, radar, and communications fields. They also find application in the modeling of bioacoustic emissions, especially those of echolocating animals such as bats and odontocetes. This work presents a novel PPS waveform formulation that exploits some special properties of Chebyshev polynomials, such as orthogonality, recurrence relations, and equivalence to trigonometric functions. The result is the Chebyshev polynomial frequency modulation (CPSFM) family of waveforms, which prove useful in the modeling of bioacoustic signals and the approximation of non-polynomial-phase signals such as hyperbolic chirps. We demonstrate that the CPSFM model admits compact analytic expressions for fundamental continuous-time signal processing functions such as the Fourier transform, the convolution and correlation operations, and the ambiguity function. Derivations for these expressions using CPSFM are presented, along with their application to the analysis of biosonar emissions of Mexican free-tailed bats.

Mechanical behavior of synthetic materials depends on their microstructure and geometric configurations. This dependency leads to unintended performance when the material remaps its microstructures for shape reconfigurations, such as diminished rigidity in unfolded aerospace morphing structures and reduced sensitivity in twisted soft sensors. Breaking this dependency through material design to improve overall performance has been a long-standing challenge. This work develops a transformation method to design a class of grounded metamaterials that decouples mechanical behavior from microstructure and shape reconfigurations. We fabricate these metamaterials and experimentally demonstrate both configuration-mapping-invariant displacement behavior and unconventional displacement control functions that have not previously been observed. We identify two physical principles that underpin the useful, but counterintuitive behavior: (i) Mapping-invariant displacement fields are the result of body torques that automatically balance non-concurrent internal forces from microstructure reconfigurations; (ii) Tailored displacement control functions are determined by Willis springs pinned to the ground. As a result, the grounded metamaterials are shown to enable the design of highly reconfigurable material systems that demonstrate tailored deformation behavior regardless of their microscopic and geometric configurations.

The acoustic radiation force exerted by plane progressive waves with wavenumber k on a scatterer of characteristic size a is calculated in the Born approximation using Westervelt's far-field integral [J. Acoust. Soc. Am. 29, 26-29 (1957), Eq. (2)]. In the subwavelength limit ka≪1 of the Born approximation, closed-form analytical expressions for the radiation force are obtained in terms of acoustic polarizabilities, which represent the response of the scatterer to dipole order. For subwavelength scatterers whose relative compressibility and density are even functions about their centroid, Gor'kov's O[(ka)4] force [Sov. Phys. Dokl. 6, 773-775 (1962), Eq. (10)] is recovered, whereas the radiation force on scatterers characterized by odd distributions is O[(ka)6]. Radiation forces on homogeneous and inhomogeneous spheres and cubes are considered as examples, for which the analytical expressions agree with solutions based on spherical wave expansions and Fourier transforms for ka≲0.8. The present work complements the volume integral obtained by Jerome and Hamilton [J. Acoust. Soc. Am. 150, 3417-3427 (2021), Eq. (16)] for the radiation force exerted by standing waves in the subwavelength limit of the Born approximation.

Understanding and controlling the dynamic interactions between fluid flows and solid materials and structures-a field known as fluid-structure interaction-is central not only to established disciplines such as aerospace and naval engineering, but also to emerging technologies such as energy harvesting, soft robotics, and biomedical devices. In recent years, the advent of metamaterials has provided exciting opportunities to rethink and redesign fluid-structure interactions. The idea of engineering the internal structure of materials that interface with fluid flows opens a new horizon for the precise and effective manipulation and control of coupled fluidic, acoustic, and elastodynamic responses. This review focuses on this relatively unexplored interdisciplinary theme with broad technological significance. Salient potential applications, such as reduction of fuel consumption in transport systems, efficiency of renewable energy extraction, noise mitigation, and resilience against structural fatigue, depend on controlling interactions among flow, acoustic, and vibration mechanisms. Flow control, for example, which spans a wealth of regimes such as laminar, transitional, turbulent, and unsteady separated flows, is strongly influenced by fluid-structure interaction. This review surveys and discusses conceptual frameworks that describe the interplay between fluids and elastic solids, with a focus on contemporary and emerging concepts. The paper is organised into three main sections: fluid-structure and flow-phonon interactions, flow-induced acoustic interactions with metamaterials, and exotic metamaterial concepts with potential impact on fluid-structure interaction. It concludes with perspectives on current challenges and future directions in this rapidly expanding area of research.

Understanding and controlling the dynamic interactions between fluid flows and solid materials and structures-a field known as fluid-structure interaction-is central not only to established disciplines such as aerospace and naval engineering, but also to emerging technologies such as energy harvesting, soft robotics, and biomedical devices. In recent years, the advent of metamaterials has provided exciting opportunities to rethink and redesign fluid-structure interactions. The idea of engineering the internal structure of materials that interface with fluid flows opens a new horizon for the precise and effective manipulation and control of coupled fluidic, acoustic, and elastodynamic responses. This review focuses on this relatively unexplored interdisciplinary theme with broad technological significance. Salient potential applications, such as reduction of fuel consumption in transport systems, efficiency of renewable energy extraction, noise mitigation, and resilience against structural fatigue, depend on controlling interactions among flow, acoustic, and vibration mechanisms. Flow control, for example, which spans a wealth of regimes such as laminar, transitional, turbulent, and unsteady separated flows, is strongly influenced by fluid-structure interaction. This review surveys and discusses conceptual frameworks that describe the interplay between fluids and elastic solids, with a focus on contemporary and emerging concepts. The paper is organised into three main sections: fluid-structure and flow-phonon interactions, flow-induced acoustic interactions with metamaterials, and exotic metamaterial concepts with potential impact on fluid-structure interaction. It concludes with perspectives on current challenges and future directions in this rapidly expanding area of research.

Polynomial phase signals (PPS) are a staple of waveform design and analysis in sonar, radar, and communications fields. They also find application in the modeling of bioacoustic emissions, especially those of echolocating animals such as bats and odontocetes. This work presents a novel PPS waveform formulation that exploits some special properties of Chebyshev polynomials, such as orthogonality, recurrence relations, and equivalence to trigonometric functions. The result is the Chebyshev Polynomial Frequency Modulation (CPSFM) family of waveforms, which prove useful in the modeling of bioacoustic signals and the approximation of non-polynomial-phase signals such as hyperbolic chirps. We demonstrate that the CPSFM model admits compact analytic expressions for fundamental continuous-time signal processing functions such as the Fourier transform, the convolution and correlation operations, and the ambiguity function. Derivations for these expressions using CPSFM are presented, along with their application to the analysis of biosonar emissions of Mexican free-tailed bats.

Polynomial phase signals (PPS) are a staple of waveform design and analysis in sonar, radar, and communications fields. They also find application in the modeling of bioacoustic emissions, especially those of echolocating animals such as bats and odontocetes. This work presents a novel PPS waveform formulation that exploits some special properties of Chebyshev polynomials, such as orthogonality, recurrence relations, and equivalence to trigonometric functions. The result is the Chebyshev Polynomial Frequency Modulation (CPSFM) family of waveforms, which prove useful in the modeling of bioacoustic signals and the approximation of non-polynomial-phase signals such as hyperbolic chirps. We demonstrate that the CPSFM model admits compact analytic expressions for fundamental continuous-time signal processing functions such as the Fourier transform, the convolution and correlation operations, and the ambiguity function. Derivations for these expressions using CPSFM are presented, along with their application to the analysis of biosonar emissions of Mexican free-tailed bats.

Acoustic metamaterials are a class of architected materials with dynamic properties that are designed at the sub-wavelength scale to achieve exotic or unique macroscopic response. Although early concepts of acoustic metamaterials relied on static configurations, recent research has further expanded the limits of acoustic customization by incorporating active or tunable responses. This article provides an introduction to the special issues of The Journal of the Acoustical Society of America and JASA Express Letters on active and tunable acoustic metamaterials and begins with a brief description of the general categories of active control and tunable response included in the contributions to the special issue and, then, provides a brief description of the articles in this special issue, grouped by general category, and how the research presented in these works contribute to the advancement of acoustic metamaterial research.

Lithium-ion batteries (LIBs) are the leading technology used in consumer electronics, electric vehicles, and grid-level electrochemical energy storage applications. The ever-increasing use of LIBs has highlighted a gap in understanding of their behavior throughout their life cycle. Current monitoring systems rely on electrical and sometimes temperature measurements to assess the internal state which limits information about complex electrochemical processes. In response, ultrasonic testing (UT) has shown promise for non-invasive assessment due to its ease of use and sensitivity to mechanical changes which are correlated with electrochemical changes within the battery. We summarize the research in UT methods applied to LIBs throughout their life cycle. We also discuss physics-based and data-driven modeling approaches used to interpret ultrasonic signals in the context of LIBs, with an emphasis on the existing challenge of establishing rigorous links between electrochemical behavior and elastic and poroelastic wave physics to gain insight regarding physical changes in the LIB that can be directly measured using UT. Finally, we discuss the challenges of implementing UT across the LIB life cycle and identify opportunities for further research. This review aims to provide helpful guidance to researchers and practitioners of UT in the growing field of UT for electrochemical battery systems.

Lithium-ion batteries (LIBs) are the leading technology used in consumer electronics, electric vehicles, and grid-level electrochemical energy storage applications. The ever-increasing use of LIBs has highlighted a gap in understanding of their behavior throughout their life cycle. Current monitoring systems rely on electrical and sometimes temperature measurements to assess the internal state which limits information about complex electrochemical processes. In response, ultrasonic testing (UT) has shown promise for non-invasive assessment due to its ease of use and sensitivity to mechanical changes which are correlated with electrochemical changes within the battery. We summarize the research in UT methods applied to LIBs throughout their life cycle. We also discuss physics-based and data-driven modeling approaches used to interpret ultrasonic signals in the context of LIBs, with an emphasis on the existing challenge of establishing rigorous links between electrochemical behavior and elastic and poroelastic wave physics to gain insight regarding physical changes in the LIB that can be directly measured using UT. Finally, we discuss the challenges of implementing UT across the LIB life cycle and identify opportunities for further research. This review aims to provide helpful guidance to researchers and practitioners of UT in the growing field of UT for electrochemical battery systems.

Phonons are quasiparticles associated with mechanical vibrations in materials. They are at the root of the propagation of sound and elastic waves, as well as of thermal phenomena, which are pervasive in our everyday life and in many technologies. The fundamental understanding and control of phonon responses in natural and artificial media are key in the context of communications, isolation, energy harvesting and control, sensing and imaging. It has recently been realized that controlling different symmetry classes at the microscopic and mesoscopic scales in synthetic media offers a powerful tool to precisely tailor phononic responses for advanced acoustic and elastodynamic wave control. In this Review, we survey the recent progress in the design and synthesis of artificial phononic media, namely phononic crystals and metamaterials, guided by symmetry principles. Starting from tailored broken spatial symmetries, we discuss their interplay with time symmetries for non-reciprocal and non-conservative phenomena. We also address broader concepts that combine multiple symmetry classes to induce exotic phononic wave transport. We conclude with an outlook on future research directions based on symmetry engineering for the advanced control of phononic waves. Broken and tailored symmetries have a fundamental role in wave phenomena and their applications. This Review surveys the recent progress in the domain of artificial phononic media with an emphasis on the role of symmetry breaking, in both space and time, for advanced wave phenomena.

Spatiotemporal modulation (STM) has recently been used to improve diffusion from finite apertures of conventional acoustic diffuser profiles by introducing STM of the termination impedance of the diffuser wells and to scatter acoustic energy at frequencies that are up- and down-shifted from the incident wave frequency by integer multiples of the modulation frequencies. The present work employs a semi-analytical model of acoustic scattering from an STM acoustic metasurface to investigate the tunability of scattering from a flat metasurface with STM admittance by demonstrating nonreciprocal and diffuse scattering of sound via a parametric study on the modulation frequency and admittance amplitude. The results provide insight into the use of STM of input admittance to control acoustic scattering from acoustic metasurfaces.

Elastic plates support a spectrum of guided-wave modes known as Rayleigh-Lamb waves. Euler-Bernoulli and Timoshenko beam theory are well-known approximate models that are often employed to describe wave motion of the lowest order symmetric and antisymmetric modes. However, these theories make simplifying assumptions that can yield non-physical interpretation of experimental observations in structured plates that are the subject of elastic metamaterials [Lee and Kim, Smart Mater. Struct., 32 123001 (2023)]. This work investigates direction-dependent coupling between modes in elastic plates containing resonant asymmetric scatterers and discusses the limitations of approximate theories. We first discuss restrictions imposed by reciprocity for direction-dependent scattering in passive multi-mode elastic wave systems generalized to Lamb modes of arbitrary order. We then present a finite element model case study of an elastic beam containing a resonant asymmetric scatterer yielding direction-dependent coupling of symmetric and antisymmetric modes. Constitutive relationships of the Willis form are then proposed and implemented in Euler-Bernoulli and Timoshenko beam theories in order to consider coupling between strain and momentum fields using analytical models. Discrepancies between these two theories are discussed based on constraints imposed by reciprocity, and we show that Timoshenko theory is required to capture direction-dependent mode coupling.

Polarizabilities represent the response of scatterers in the long-wavelength limit. The present work employs polarizabilities to calculate the radiation force exerted on a scatterer of length a and dimensionless mass density μ(x) by 1-D progressive waves on a string. The radiation force density equals 〈∂S/∂x〉according to momentum conservation at quadratic order, where the radiation stress S is obtained in the Born approximation in terms of the polarizabilities α 0 = ∫ a μ(x) dx and α 1 = 2k ∫ a μ(x) x dx, where k is the wavenumber. The radiation force equals 〈S(a/2)–S(–a/2)〉= k 4 ξ 0 2 τα 1 2/8, where ξ 0 is the incident wave amplitude and τ is the string’s tension. The force agrees with solutions based on Fourier transforms for ka « 1 [Morse and Ingard, Theoretical Acoustics (McGraw-Hill, 1968), Eq. (4.5.17)]. To the order of the present approximation, scatterers with μ(x) = μ(–x) do not experience radiation forces due to progressive waves on a string, while scatterers with μ(x) = –μ(–x) experience forces on the order of (ka)6. The results elucidate the approximations underlying the more involved calculation of radiation force exerted by progressive acoustic waves [Gokani et al., JASA 157 (2025); doi: 10.1121/10.0037572].

Recent research on wave propagation and scattering in materials with spatiotemporal modulation (STM) of bulk properties or boundary conditions has gained interest in order to improve control of wave energy in both time and space. This work employs coupled mode theory (CMT) that was derived to study acoustic waves incident from a half-space and reflected from a fluid waveguide that has a STM boundary impedance. CMT for this system shows that coupling between propagating and evanescent modes exists at frequency–wavenumber combinations related to the modulation frequency and wavenumber that cannot be achieved without boundary modulation. We investigate the case of waveguide excitation by evanescent fields on the non-modulated boundary between a fluid waveguide and a fluid half-space while the opposite boundary is assumed to be an elastic plate with STM stiffness. The “incident” evanescent wave mimics the case of acoustic forcing from turbulent flow, which can generate waves that propagate within the waveguide and plate. We show that STM of the plate stiffness can be used to couple incident evanescent energy into modes at different frequencies and wavenumbers, which can be used to further control the generated waves from turbulence such as nonreciprocal redirection and absorption of the acoustic energy.

Bats use active sonar to navigate and forage. Performance of an active sonar, be it biological or man-made, degrades rapidly in the presence of competing (jamming) transmissions. It is in this environment that bats flying in dense swarms, such as an evening emergence from a large roost, nevertheless avoid colliding with conspecifics and other obstacles. We have previously investigated the hypothesis that Brazilian free-tailed bats (Tadarida brasiliensis) use variations spectro-temporal “shape” to facilitate successful echolocation in dense groups [J. Acoust. Soc. Am. 154, A48 (2023)]. The present work employs a compact analytical waveform model based on low-order Chebyshev polynomial series—Chebyshev Polynomial Series Frequency Modulation (CPSFM)—to represent frequency modulation functions observed in bat echolocation signals. Following this approach, we fit isolated calls from swarm recordings to the CPSFM model and show that diversity in model parameters facilitates call distinguishability. Standard signal detection methods, such as cross correlation, enable quantitative estimation of detection performance, including rejection of interfering emissions and echoes. Results demonstrate that subtle but specific variation in spectro-temporal shape, captured in CPSFM parameters, can enable rejection of acoustic signals from conspecifics in dense swarms which may aid in jamming avoidance by bats.

Recent research in wave propagation and vibration behavior in materials with spatiotemporal modulation of bulk properties or boundary conditions has gained interest in order to control both the wavenumber and frequency characteristics of waves. In this work, a coupled mode theory is derived for acoustic systems for which the bulk properties or boundary conditions are modulated as a function of space and time. The approach expresses the dynamics of the modulated system as a function of coupled modes of the unmodulated system, which are determined using with standard analytical or numerical techniques. The spatiotemporal modulation of material properties or boundary impedances gives rise to coupling between the set of modes with unique shapes and differing discrete frequencies. The modulation therefore enables control over the spatial and temporal response of an acoustic system, including resonances, that cannot be achieved with unmodulated systems. A perturbation approach is then used to investigate the effects of mode coupling near modal resonances. We apply the theory for illustrative cases to demonstrate the use of spatiotemporal modulation to couple modes, with applications focused on propagating to evanescent mode conversion and resonance control. [Work supported by ONR.]

Electrification of transportation and grid-scale renewable energy storage are driving an unprecedented demand for energy storage solutions. Next-generation (next-gen) battery technologies, including the use of alternatives to commercial graphite anode materials and solid-state electrolytes, offer the potential for enhanced performance compared to conventional lithium-ion batteries (LIBs). Recent research has shown that ultrasonic inspection methods provide insightful understanding of mechanical property changes that occur in lithium-ion batteries with different lithiation and aging states. This work presents preliminary research that extends the use of ultrasonic methods for next-gen batteries and compares the observations with those in conventional LIBs. We investigate contact and immersion ultrasonic testing methods to monitor the evolution of time-domain characteristics (e.g., time of flight, amplitude) and frequency-domain metrics (e.g., spectral content, attenuation) under various cycling conditions and thermal loading. By tracking these metrics, we intend to get insights into changes in mechanical properties associated with electrochemical behavior unique to next-gen cells. Ultrasonic immersion imaging provides insights into spatial heterogeneities of the inspected cells subjected to the same loading processes. These experiments, paired with physical modeling of wave phenomena in these systems, provide a framework for comparing next-gen batteries to traditional LIBs and provide insight into their unique chemistries.

Nonlinear elastic metamaterials (NLEMs) leverage complex subwavelength geometries to achieve superior energy dissipation and redistribution. The resulting geometric scales of interest are often unfeasible for direct numerical simulation at full resolution, especially for NLEMs undergoing complex deformation behaviors such as history- and rate-dependent plasticity, contact, and buckling. Therefore, low-order effective medium models based on mass-spring lattices have been proposed for the simulation of nonlinear wave propagation in NLEMs [Wallen et al., In Press, https://doi.org/10.1016/j.jmps.2025.106276]. However, the empirical constitutive relations of the effective discrete-element unit cells require significant effort to obtain. In this work, using the results of fine-scale, large-deformation finite-element simulations, deep neural networks are trained to represent the relationships between loading and elasto-plastic deformation of NLEM unit cells. The trained neural networks are then incorporated into the differential-algebraic equations of motion for simulation of wave propagation. The present study considers various steps in the implementation of the machine-learning model, such as sampling of training data, constraints on network architecture to ensure physical consistency, and application of automatic differentiation, to maximize the accuracy of the approach.

Ensembles of asymmetric piezoelectric scatterers embedded in a background medium have been predicted to couple acceleration to electric displacement. Previous models of this so-called electromomentum coupling are based on electrostatics. However, energy conservation involving time-varying electric fields requires considering the magnetic field. This work employs an acousto-electromagnetic polarizability matrix to calculate the fields scattered by a one-dimensional lattice of asymmetric piezoelectric scatterers. The effective constitutive relations couple acoustics and electromagnetism and satisfy passivity and reciprocity.

The study of radiation from baffled circular pistons often begins with the Rayleigh integral. The present letter offers an alternative derivation of the Rayleigh integral by solving the Helmholtz equation for a baffled circular piston in an infinitely large cylindrical waveguide. While the Rayleigh integral is typically interpreted as a sum of simple sources, the present derivation shows that the Rayleigh integral can also be cast as a sum of Bessel beams. The alternative formulation is used to recover the axial pressure radiated by a baffled circular piston and solve the Helmholtz equation numerically for a vortex beam.

Abstract A noncontact laser ultrasonics method for determining the onset temperature and the early stage sintering state is studied. Because this technique measures properties near the surface in selected regions on the sample, it is particularly well‐suited to parts produced by additive manufacturing routes such as selective laser flash sintering, where local variations in sintering state along one dimension result from the laser scan pattern. We demonstrate the ability to measure very small changes in interparticle neck size by measuring Rayleigh wave speeds. The changes in wave speed result initially from rapid changes in Young's modulus that occur at the onset and in the early stages of sintering, before significant densification is observed. This measurement method is demonstrated using alumina pellets that were partially sintered at different temperatures to produce parts with a range of neck sizes and relative densities. Using the laser ultrasonics technique, the onset of sintering is detected at temperatures between 520°C and 650°C, which is significantly below the onset sintering temperatures detectable using traditional methods.

Willis materials are metamaterials whose subwavelength asymmetry couples the macroscopic pressure-strain and momentum-velocity relations1. Recently, the design space of these metamaterials has been expanded to consider additional field coupling such as poroelasticity 2 and piezoelectricity. Of interest in this work is the case of subwavelength asymmetric piezoelectric scatterers in a background material which has been shown to couple the electric field-electric displacement relation to the constitutive equations in the Willis form 3,4. The existence of this so-called electro-momentum coupling was first predicted using dynamic homogenization of heterogeneous piezoelectric media1-3 but it can also be understood through a generalized polarizability tensor 𝛂 that calculates the electro-acoustic field scattered from a single asymmetric piezoelectric inhomogeneity as a function of local fields. We present a multiple-scattering dynamic homogenization method that extends the work of Sieck et al.5 using the generalized polarizability tensor6,7. The model considers the microscale scattered pressure, velocity, and electric fields in a one-dimensional periodic lattice of identical scatterers to find analytical expressions for the effective macroscale fields. The macroscale fields are then used to find the effective electro-momentum coupling constants in terms of the polarizability of the individual scatterers and the concentration of scatterers in a background medium. The resulting expressions for the effective properties obey constraints imposed by reciprocity and passivity and demonstrate an emergent magneto-momentum coupling even in absence of piezomagnetic coupling or electromagnetic bianisotropy at the microscale.

The forced time harmonic response of a spatio-temporally modulated elastic beam of finite length with light damping is derived using a novel Green’s function approach. Closed-form solutions are found that highlight unique mode coupling effects that are induced by spatio-temporal modulation, such as split resonances that are tunable with the modulation parameters. These effects of order unity are caused by spatio-temporal modulation with a small amplitude appropriately scaled to the magnitude of the light damping. The scalings identified here between the modulation amplitude, the damping and the inner frequency range near the modified resonances, translate over to more complicated and higher dimensional elastic systems.

Lithium-ion batteries are crucial for portable electronics, electromobility, and stationary energy storage, playing a critical role in global decarbonization goals. Tracking battery performance during their lifetime ensures reliability, as various degradation mechanisms affect their operation. These changes may alter mechanical properties and thus understanding the complex relationship between electrochemistry, heat transfer, and mechanical properties therefore remains a key research challenge. Elastodynamic inspection methods, such as ultrasonic and vibrational analysis, have shown promise in detecting mechanical changes under varying states of charge (SOC) and state of health (SOH). Recent research has demonstrated the shift in the fundamental resonance frequency is a reliable metric of the SOC and SOH of Nickel-Manganese-Cobalt (NMC) pouch cells. This study presents an analysis of flexural modes for NMC cells at 0% and 100% SOC over 80 charge–discharge cycles. We employ spatial filtering to extract and enhance the response of the first three modes. We observe a correlation between the resonance frequency and the SOC/SOH for all the modes explored. The trends in resonance frequency and quality factor versus cycle from the data are explored and we propose model-based methods to extract insights regarding the evolution of mechanical properties that exploit higher modes as a function of charge level and aging.

Acoustic vortex beams are quasiplanar waves with helical wavefronts characterized by the orbital number ℓ. Although Gaussian amplitude distributions result in closed-form analytical solutions for the entire paraxial field [Gokani et al., J. Acoust. Soc. Am. 155, 2707–2723 (2024)], acoustic vortex beams are usually radiated by sources with a uniform circular amplitude distribution. In this talk, analytical solutions for the field radiated by unfocused and focused uniform circular vortex sources of radius a are derived. Evaluation of the Fresnel diffraction integral in the far field of an unfocused source and in the focal plane of a focused source leads to a solution in terms of an infinite series of Bessel functions for ℓ>−2. By calculating the first local maximum of this solution, it is found that the vortex ring radius is rℓ = ξ ℓ z/ ka in the far field of an unfocused source and rℓ = ξ ℓ d/ka in the focal plane of a focused source with focal distance d, where ξ ℓ = 1.23ℓ + 1.49 and k is the wavenumber. The solution given by the infinite series is reduced to closed forms for 0 ≤ ℓ ≤ 4, corresponding to orbital numbers commonly used in experiments. [CAG supported by the ARL:UT McKinney Fellowship in Acoustics.]

Nonlinear elastic metamaterials (NLEMs) support a variety of dynamic phenomena that enable the manipulation of large-deformation elastic waves. Full-scale dynamic simulation of NLEMs is often prohibitively expensive due to the importance of complex, sub-wavelength geometry. Low-order effective medium models based on mass-spring lattices [Wallen et al., arXiv:2407.20434 (2024)] have recently been developed to capture history-dependent effects of plasticity for 1-D simulation of nonlinear wave propagation in NLEMs. However, the model developed therein requires significant preparatory effort to obtain empirical constitutive relations and their derivatives via a complex, ad-hoc curve-fitting procedure. Here, an alternative method is proposed whereby trained deep neural networks provide the constitutive relations, allowing for application of automatic differentiation methods to obtain derivatives for implicit solution of the differential-algebraicequations of motion. The networks are trained using cyclical force–displacement data from a finite-element model of a unit cell of interest, which exhibits buckling under elasto-plastic deformation. The trained neural networks are then incorporated into the discrete-element framework of Wallen et al. to simulate wave propagation in a chain of unit cells.

Gor’kov’s result for radiation force on a subwavelength homogeneous sphere in the direction of an incident progressive plane wave with time-averaged intensity〈I〉[Sov. Phys. Dokl. 6, 773–775 (1962)] is generalized to arbitrarily shaped inhomogeneous scatterers. Westervelt's surface integral in the far field [JASA 29, 26–29 (1957)] reduces by energy conservation to F ∥ =〈I/c 0〉∮ |Φ|2 (1 − e i •e r ) dΩ, where Φ is the scattered wave directivity, e i and e r are the incident and radial unit vectors, respectively, and dΩ is the differential solid angle. Since the scatterer size a is much smaller than the wavelength λ=2π/k, Φ can be calculated in terms of the acoustic polarizabilities α m = − ∫ f 1 dV, α d = ∫ 3f 2/(2+f 2) dV, and α c = k [3e i •e r ∫ r f 2/(2+f 2) dV − ∫ r f 1 dV], where f 1 and f 2 are Gor’kov’s contrast factors. For scatterers whose material properties are symmetric about the centroid r ≡ 0, α c vanishes, recovering Gor’kov’s O[(ka)4] force, while material asymmetry contributes at O[(ka)6]. The forces are verified by comparison to solutions based on partial wave expansions and Fourier transforms. [C.A.G. was supported by the ARL:UT McKinney Fellowship in Acoustics.]

Recent research in optical, electromagnetic, and acoustical metamaterials has shown that spatiotemporal modulation (STM) of bulk material properties and interfaces between materials can increase the control of propagating waves and wave scattering at boundaries. Specifically, STM of bulk properties has been used to enable nonreciprocal wave propagation in unbounded systems and to couple modes at different frequencies in bounded systems through frequency and wavenumber conversion. This work considers the case of mode coupling in an acoustic waveguide using STM boundaries. As a first step in the design of STM boundaries, we investigate the effect of STM on one boundary of a two-dimensional acoustic waveguide that is coupled to a fluid half-space on its other boundary. The analysis first considers guided wave modes when the waveguide has spatially varying boundaries using coupled-mode theory. Temporal modulation is then introduced by expanding the solution for propagating and leaky modes using Fourier series expansion to consider scattering into harmonics of the modulation frequency and wavenumber. An analysis of mode conversion efficiency based on the modulation amplitude and frequency is presented and discussed.

Traditional analysis of flexural wave scattering assumes that the scatter properties are time invariant and therefore the scattered wave field is at the same frequency as the incident wave and only depends on the local impedance contrast. Recent interest in time-modulated systems enables unprecedented control over wave behavior, offering opportunities for frequency and wavenumber conversions that are not possible in passive media. The control of scattered flexural waves in beams and plates with time-varying boundary conditions is of particular interest for vibration control. In this work, we present a semi-analytical model to study flexural wave reflections from time-varying boundary conditions. This model is based on Euler–Bernoulli beam theory in which expressions for reflected flexural waves are derived for various beam boundary conditions. The time dependence of the boundary conditions is incorporated by representing the solution as a Fourier series expansion to consider scattering into harmonics related to the modulation frequency and wavenumber. The semi-analytical model is compared to a realistic implementation that utilizes resonator termination with PZT patches. Numerical and experimental work is carried out to validate the model.

The manipulation of mechanical waves is a long-standing challenge for scientists and engineers, as numerous devices require their control. The current forefront of research in the control of classical waves has emerged from a seemingly unrelated field, namely, non-Hermitian quantum mechanics. By drawing analogies between this theory and those of classical systems, researchers have discovered phenomena that defy conventional intuition and have exploited them to control light, sound, and elastic waves. Here, we provide a brief perspective on recent developments, challenges, and intricacies that distinguish non-Hermitian elastodynamics from optics and acoustics. We close this perspective with an outlook on potential directions such as topological phases in non-Hermitian elastodynamics and broken Hermitian symmetry in materials with electromomentum couplings.

Analytical solutions for acoustic vortex beams radiated by sources with uniform circular amplitude distributions are derived in the paraxial approximation. Evaluation of the Fresnel diffraction integral in the far field of an unfocused source and in the focal plane of a focused source leads to solutions in terms of an infinite series of Bessel functions for orbital numbers ℓ>-2. These solutions are reduced to closed forms for 0≤ℓ≤4, which correspond to orbital numbers commonly used in experiments. A scaling law for the vortex ring radius is derived, and its relevance is characterized using ray theory.

Elastic materials with time and space varying properties are interesting candidates to control bulk and guided waves in unprecedented ways which include nonreciprocal transmission, unidirectional mode conversion, mode coupling, and frequency conversion. Previous work on elastic waves in spatiotemporally modulated (STM) media have focused on nonreciprocal vibrations of finite domains with modulated stiffness. Less attention has been given to the modulation of impedance boundary conditions of finite structures or at interfaces between domains. This work investigates elastic wave behavior at boundaries with modulated impedances. The boundary impedance is represented using a lumped parameter mass spring damper system with a spring having a temporally modulated stiffness. The effective input impedance is modeled using direct numerical simulation and a semi-analytical Fourier series expansion model. The models are compared to experiments on a base-excited cantilevered Euler-Bernoulli beam with modulated effective stiffness via piezoelectric patches with temporally varying electric shunting circuits. [Work supported by the ARL:UT Chester M. McKinney Graduate Fellowship in Acoustics and by the Office of Naval Research under Award N00014-23-1-2660.]

Acoustic and elastic metamaterials with material properties that vary in time and space have received significant attention recently as a means to realize systems that induce nonreciprocal propagating waves in unbounded systems and coupling modes at different frequencies in bounded systems. These unique behaviors are the result of frequency- and wavenumber-conversion resulting from spatiotemporal modulation. In this work, we investigate the case of acoustic scattering from a fluid inhomogeneity in which the compressibility is a general function of space and time. A two-dimensional annular geometry is considered, which allows for unknown scattered field to be decomposed into simple mode shapes. Computations of the far field directivity pattern are then carried out as a function of the modulation parameters to determine cases that yield a large degree of control over the scattered field directivity pattern for each generated frequency.

The forced time harmonic response of a spatiotemporally-modulated elastic beam of finite length with light damping is derived using a novel Green's function approach. Closed-form solutions are found that highlight unique mode coupling effects that are induced by spatiotemporal modulation, such as split resonances that are tunable with the modulation parameters. These effects of order unity are caused by spatiotemporal modulation with small amplitude appropriately scaled to the magnitude of the light damping. The scalings identified here between the modulation amplitude, the damping, and the inner range of frequency near the modified resonances, translate over to more complicated and higher dimensional elastic systems.

Nonlinear elastic metamaterials are known to support a variety of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, full-scale dynamic simulations are often prohibitively expensive at scales of interest. Prior studies have therefore utilized low-order effective medium models, such as discrete mass-spring lattices, to capture essential properties in the long-wavelength limit. While models of this type have been successfully implemented for a wide variety of nonlinear elastic systems, they have predominantly considered dynamics depending only on the instantaneous kinematics of the lattice, neglecting history-dependent effects, such as wear and plasticity. To address this limitation, the present study develops a lattice-based modeling framework for nonlinear elastic metamaterials undergoing plastic deformation. Due to the history- and rate-dependent nature of plasticity, the framework generally yields a system of differential-algebraic equations whose computational cost is significantly greater than an elastic system of comparable size. We demonstrate the method using several models inspired by classical lattice dynamics and continuum plasticity theory, and explore means to obtain empirical plasticity models for general geometries.