arXiv subjects

Kathryn H. Matlack

Publications and source records attributed to Kathryn H. Matlack.

15 recordsLinked to original sources

arXiv2026

Quantifying the effect of resonant amplitude and frequency of phononic material vibrations on the coupled fluid-structure interaction dynamics in separated aerodynamic flows

Phononic materials (PMs) with engineered resonances have been leveraged for fluid-structure interaction (FSI) with fluid flow instabilities, yielding beneficial outcomes such as transition delay, stabilized hypersonic boundary layers, and increased aerodynamic lift. Prior PM-FSI studies primarily identify spatio-temporal flow scales of interest and choose PM structural parameters producing structural dynamics conducive for FSI. However, a fully-coupled FSI system generally produces complex coupled dynamics that is not accurately captured by studying either physical system in isolation. In this context, our prior work established behavioral parameters that govern the coupled PM-FSI dynamics in a separated aerodynamic flow over a limited parameter range. Adopting this framework, this paper explores strongly-coupled high-fidelity PM-FSI simulations over a broader range of two behavioral parameters---truncation resonance frequency and displacement amplitude---to establish their quantitative (linear/cubic) relations to the coupled frequency, lift force, and circulation in the coupled system response. In addition, the results indicate the presence of distinct FSI regimes, depending on the proximity of the truncation resonance frequency or its sub-/super-harmonics to the vortex-shedding frequency. FSI dynamics ranging from multi-/single-frequency dynamics, downshifted coupling frequency due to fluid-added mass effects, generation of non-linear harmonics to convergence of FSI dynamics to the rigid plate case are observed. These results reiterate the importance of the PM frequency and amplitude in determining the coupled FSI dynamics, and the proposed quantitative relations provide a new pathway for designing PMs for aerodynamic flow control to achieve beneficial outcomes, e.g., lift force enhancement.

physics.flu-dyn↗

arXiv2026

Weakly coupled fluid-structure interaction between wall-bounded turbulent flows and defect-embedded phononic subsurfaces

We investigate the interaction between wall-bounded turbulence and defect-embedded phononic subsurface (D-Psub) using a weakly coupled fluid--structure framework, in which the flow and structure are advanced sequentially without sub-iterations. The D-Psub subsurface is modeled as a dynamic wall with a resonance introduced via a localized structural defect, driven by spatially averaged wall-pressure fluctuations from a turbulent channel flow. This configuration enables a controlled study of how a narrow-band structural response interacts with the broadband forcing of near-wall turbulence. Despite broadband turbulent forcing, the D-Psub exhibits a narrow-band response that modifies near-wall dynamics, with representative cases showing suppression of velocity fluctuations, increased coherence of streamwise streaks, and a measurable reduction in turbulent drag. Crucially, the coupled system displays behavior that cannot be replicated by prescribed wall motion: the dominant oscillation frequency shifts away from the designed resonance due to fluid--structure interaction. Additionally, the phase between panels is shown to be governed by the convection of turbulent structures. These results reveal a mechanism by which phononic subsurfaces filter and reorganize turbulent energy through frequency-selective coupling, distinct from conventional compliant or actively forced walls. The findings provide a physical basis for designing passive resonant surfaces that exploit turbulence-structure coupling for flow control.

physics.flu-dyn↗

arXiv2025

A Framework to Systematically Study the Nonlinear Fluid-Structure Interaction of Phononic Materials with Aerodynamic Flows

Phononic materials (PMs) are periodic media that exhibit novel elastodynamic responses. While PMs have made progress in vibration-mitigation applications, recent studies have demonstrated the potential of PMs to passively and adaptively modulate flow behavior through fluid-structure interaction (FSI). For example, PMs have been shown to delay laminar-to-turbulent transition and mitigate unsteadiness in shock-boundary layer interactions. However, a systematic framework to relate the effect of specific PM behaviors to the FSI dynamics is lacking. Such a framework is essential to systematically investigate the complex and nonlinear coupled dynamics of the FSI. Further, parameters that are not typically considered in PM models become critical, such as the vibration amplitude. This article addresses this gap by proposing FSI-relevant ``behavioral'' parameters, distinct from the structural parameters of the PM, but with a clear mapping provided to them. We use high-fidelity, strongly coupled simulations to quantify the FSI between a novel configuration of laminar flow past a flat plate, equipped with a PM. Our study proposes four critical PM behavioral parameters -- effective stiffness, truncation resonance frequency, a quantity representing the dynamic displacement amplitude, and unit cell mass -- that influence the spectral characteristics of the vortex-shedding process inherent to the flat plate system. Results show connections between each parameter and distinct behavior in the lift coefficient in FSI. While the focus of this work is on the PM-FSI dynamics in an aerodynamic flow, we argue that identifying these behavioral parameters is key to unlocking scientific study and design with phononic materials in fluid flows more broadly.

physics.flu-dyn↗

arXiv2025

On the effective magnetostrictive properties of anisotropic magneto-active elastomers in the small-deformation limit

Magneto-active elastomers (MAEs) are composite materials comprising an elastomer matrix with embedded magnetic particles, endowing the composite with coupled effective magneto-mechanical responses. It is widely reported that anisotropic MAEs exhibit much stronger magneto-mechanical coupling than isotropic MAEs. However, most efforts to model effective magneto-mechanical properties of MAEs via homogenization focused on isotropic microstructures or those with large separations between particles, to use analytical solutions. In this work, we introduce a periodic homogenization approach to compute effective magneto-mechanical properties of anisotropic MAEs, and analyze microstructural features that enhance the magneto-mechanical coupling. Using the finite element method, we numerically determine the effect of particle shape, gap, and voids on the effective stiffness, permeability, and magneto-mechanical coupling tensors for chain-like periodic microstructures. Using insights gained from the full-field simulations, we derive an analytical expression for the magneto-mechanical coupling in the chain direction, in terms of the volume fraction, gap size, and properties of the matrix and particles. Results show that the overall magnetostriction of anisotropic MAEs is most sensitive to the gap between particles and the waviness of the particle chains, with smaller gap sizes and straighter chains yielding higher overall magnetostriction. Simulations also show that while isotropic MAEs elongate in a uniform magnetic field, anisotropic MAEs contract with much larger strain amplitudes, a result of the attractive forces between particles being much stronger in anisotropic MAEs than in isotropic MAEs. Results provide fundamental insights into the mechanisms that govern magneto-mechanical coupling in anisotropic MAEs, and constitute a toolbox of homogenized MAE material properties.

cond-mat.mtrl-sci↗

arXiv2025

A Quantitative Study of Energy Localization Characteristics in Defect-embedded Phononic Crystals

Phononic crystals (PnCs) are periodic engineered media that can customize the spatio-temporal characteristics of mechanical energy propagation. PnCs that additionally leverage precisely embedded defects can achieve robust energy localization with desirable spatio-temporal characteristics, opening avenues for critical engineering applications, e.g., energy harvesting, waveguiding, and fluid flow control. Numerous studies have qualitatively explored the localized dynamics via simulations and experiments, investigating the defect resonance frequency as the primary feature. However, the frequency represents only a subset of the relevant characteristics and a systematic approach to quantify the full scope of the defect dynamics remains elusive. This article establishes the frequency, mode shape, and localized velocity (or displacement) amplitude envelope as three significant factors governing the defect resonance dynamics, and quantitatively examines these characteristics using a modified version of the perturbed tridiagonal n-Toeplitz method. The proposed method accurately estimates the resonance characteristics in 1D and 2D defect-embedded PnC lattices with single and multiple defects and elucidates the effects of damping. The method is used to highlight how the key characteristics of defect modes depend on system parameters. Finally, we demonstrate the benefits of defect modes through two defect-based PnCs that can accommodate -- (i) a virtual ground, and (ii) achieve customized acoustic interaction and absorption, and use the proposed method to analyze these scenarios. The proposed strategy can be readily extended to more elaborate PnCs and augments the design space for defect-based PnCs.

physics.app-ph↗

arXiv2024

Subwavelength topological interface modes in a multilayered vibroacoustic metamaterial

We present a systematic and rigorous analytical approach, based on the transfer matrix methodology, to study the existence, evolution, and robustness of subwavelength topological interface states in practical multilayered vibroacoustic phononic lattices. These lattices, composed of membrane-air cavity unit cells, exhibit complex band structures with various bandgaps, including Bragg, band-splitting induced, local resonance, and plasma bandgaps. Focusing on the challenging low-frequency range and assuming axisymmetric modes, we show that topological interface states are confined to Bragg-like band-splitting induced bandgaps. Unlike the Su-Schrieffer-Heeger model, the vibroacoustic lattice exhibits diverse topological phase transitions across infinite bands, enabling broadband, multi-frequency vibroacoustics in the subwavelength regime. We establish three criteria for the existence of these states: the Zak phase, surface impedance, and a new reflection coefficient concept, all derived from transfer matrix components. Notably, we provide an explicit expression for the exact location of topological interface states within the band structure, offering insight for their predictive implementation. We confirm the robustness of these states against structural variations and identify delocalization as bandgaps narrow. Our work provides a complete and exact analytical characterization of topological interface states, demonstrating the effectiveness of the transfer matrix method. Beyond its analytical depth, our approach provides a useful framework and design tool for topological phononic lattices, advancing applications such as efficient sound filters, waveguides, noise control, and acoustic sensors in the subwavelength regime. Its versatility extends beyond the vibroacoustic systems, encompassing a broader range of phononic and photonic crystals with repetitive inversion-symmetric unit cells.

physics.app-ph↗

arXiv2024

Sub-Bragg Phenomena in Multilayered Vibroacoustic Phononic Metamaterials

Beyond classical Bragg diffraction, we report on new sub-Bragg phenomena to achieve enhanced sound wave tunability in the low-frequency range in a multilayered acoustic metamaterial system. Remarkably, we reveal and study the formation of genuinely sub-wavelength Bragg-like band-splitting induced bandgaps, generalizing the band-folding induced bandgaps in the literature. Additionally, we propose a methodology to widen sub-wavelength local resonance bandgaps by simultaneously hosting two local resonances within the same bandgap. These sub-Bragg bandgaps are realized in an axisymmetric vibroacoustic phononic metamaterial consisting of repetitive multilayered unit cells, each composed of two layers of membrane-cavity resonators. The resulting coupled sound-structure interaction system is analytically solved in closed form. Furthermore, the studied multilayered vibroacoustic metamaterial exhibits sub-wavelength acoustical transparency, akin to electromagnetically induced transparency, and an acoustic analogue of low-frequency plasma oscillations, resulting in a plasma bandgap where wave propagation is entirely prohibited below the plasma frequency. These sub-wavelength phenomena, achieved predictively and well below the ubiquitous first-order Bragg diffraction range, provide broadband attenuation and superior wave manipulation capabilities for low-frequency sound. This highlights the potential of utilizing sound-structure interaction across diverse physical applications. Moreover, our findings can be extrapolated to wave propagation in broader classes of physical systems where sub-wavelength phenomena are crucial, including phononic and photonic crystals of more general configurations.

physics.app-ph↗

arXiv2024

Analytical Study of a Monolayered Vibroacoustic Metamaterial

This study investigates a vibroacoustic phononic metamaterial system composed of repeated monolayered membrane-air cavity unit-cells to assess its efficacy in controlling sound waves. Assuming low-frequency axisymmetric modes, the coupled membrane-cavity vibroacoustic system for a representative unit-cell is solved entirely analytically. Unlike previous research that relied on an infinite series of eigenfunctions, our analysis offers a single-term exact solution for the membrane's displacement field, fully accounting for coupling with the acoustic cavities. Utilizing the transfer matrix method and the Bloch-Floquet theorem, we offer a comprehensive analytical characterization of the band structure, including closed-form analytical expressions for determining the bounding frequencies of the bandgaps and the dispersion branches. Interaction between Bragg and local resonance bandgaps is examined by adjusting Bragg bandgap positions, with detailed mathematical descriptions provided for their overlapping and transition. Additionally, a "plasma bandgap" analogous to metallic plasma oscillations is identified, with a derived analytical expression for its frequency. First two passbands remain robust against cavity depth variations, limiting wave manipulation capabilities. Analysis of the finite phononic system involves constructing the global transfer matrix to study natural frequencies and scattering coefficients. Interaction between Bragg and local resonance bandgaps in finite systems results in ultra-narrow passbands, creating transparency windows analogous to electromagnetically induced transparency by quantum interference. This theoretical framework enables precise characterization and engineering of bandgaps in the monolayered vibroacoustic phononic metamaterial, highlighting its potential for controlling low-frequency sound wave propagation across multiple frequencies.

physics.app-ph↗

arXiv2024

Physics-Informed Machine Learning for the Inverse Design of Wave Scattering Clusters

Clusters of wave-scattering oscillators offer the ability to passively control wave energy in elastic continua. However, designing such clusters to achieve a desired wave energy pattern is a highly nontrivial task. While the forward scattering problem may be readily analyzed, the inverse problem is very challenging as it is ill-posed, high-dimensional, and known to admit non-unique solutions. Therefore, the inverse design of multiple scattering fields and remote sensing of scattering elements remains a topic of great interest. Motivated by recent advances in physics-informed machine learning, we develop a deep neural network that is capable of predicting the locations of scatterers by evaluating the patterns of a target wavefield. We present a modeling and training formulation to optimize the multi-functional nature of our network in the context of inverse design, remote sensing, and wavefield engineering. Namely, we develop a multi-stage training routine with customized physics-based loss functions to optimize models to detect the locations of scatterers and predict cluster configurations that are physically consistent with the target wavefield. We demonstrate the efficacy of our model as a remote sensing and inverse design tool for three scattering problem types, and we subsequently applicability for designing clusters that direct waves along preferred paths or localize wave energy. Hence, we present an effective model for multiple scattering inverse design which may have diverse applications such as wavefield imaging or passive wave energy control.

eess.SP↗

arXiv2023

Wavenumber Scattering and Inter-band Targeted Energy Transfer in Phononic Lattices with Local Vibro-Impact Nonlinearities

We propose a method for manipulating wave propagation in phononic lattices by employing local vibro-impact (VI) nonlinearities to \textit{scatter} energy across the underling linear band structure of the lattice, and \textit{transfer} energy from lower to higher optical bands.Inspired by recent developments in the field of nonlinear targeted energy transfer (TET) using \textit{non-resonant} energy exchanges, we achieve this using spatially localized VI forces that redistribute energy across the linear spectrum of the lattice in a non-resonant fashion.First, a 1-dimensional (1D), 2-band phononic lattice with embedded VI unit cells is computationally studied to demonstrate that energy is scattered in the wavenumber domain, and this nonlinear scattering mechanism depends on the energy of the propagating wave. Next, a 4-band lattice is studied with a similar technique to demonstrate the concept of inter-band targeted energy transfer (IBTET) and to establish analogous scaling relations with respect to energy. To interpret the results of IBTET, we study the nonlinear normal modes (NNMs) of a reduced order model (ROM) of the VI unit cell in the 4-band lattice, using the method of numerical continuation. Interestingly, the slope of the frequency-energy branches of the ROM corresponding to the 1:1 resonance NNM matches remarkably well with the dependence of IBTET to input energy in the 4-band lattice. Moreover, relations between the dynamics of the VI lattice and the NNMs of the underlying Hamiltonian system provide physical interpretations for the relative energy transfers.

physics.app-ph↗

arXiv2022

In situ nonlinear Rayleigh wave technique to characterize the tensile plastic deformation of stainless steel 316L

The acoustic nonlinearity parameter(beta) is sensitive to dislocation parameters, which continuously change during plastic deformation. Dislocation-based damage in structures/components is the source of the failure; thus, beta has been studied as a metric for non-destructive evaluation. This work consists of two parts: the development of an in situ experimental setup for nonlinear Rayleigh wave measurements, and characterization of the dependence of beta on applied stress at different levels of initial plastic strain. First, we introduce an experimental setup and methods for repeatable in situ nonlinear ultrasonic measurements. Details on design considerations and measurement schemes are provided. In the second part, beta was measured in situ during an incremental monotonic tensile test. The measured βmonotonically decreases with plastic strain, but it is relatively insensitive to the applied stress during elastic deformation. This result highlights three aspects of the evolution of beta, which have not been sufficiently emphasized in prior work: the apparent insensitivity of beta to the applied stress during elastic deformation, decreasing beta with plastic deformation, and the saturation of beta. We attribute the trend of decreasing beta to a scaling of beta with monopole loop length during plastic deformation, which depends on initial microstructure. The saturation of beta at 1.8% coincides with a planar-to-wavy transition of dislocation structures. The in situ nonlinear ultrasonic experimental method presented in this work is significant as the in situ results can provide broader insights on beta and dislocation-based damage evolution than ex situ measurements alone.

cond-mat.mtrl-sci↗

arXiv2021

Topological Protection in a Strongly Nonlinear Interface Lattice

Mechanical topological insulators are well understood for linear and weakly nonlinear systems, however traditional analysis methods break down for strongly nonlinear systems since linear methods can not be applied in that case. We study one such system in the form of a one-dimensional mechanical analog of the Su-Schrieffer-Heeger interface model with strong nonlinearity of the cubic form. The frequency-energy dependence of the nonlinear bulk modes and topologically insulated mode is explored using Numerical continuation of the system's nonlinear normal modes (NNMs), and the linear stability of the NNMs are investigated using Floquet Multipliers (FMs) and Krein signature analysis. We find that the nonlinear topological lattice supports a family of topologically insulated NNMs that are parameterized by the total energy of the system and are stable within a range of frequencies. Next, it is shown that empirical calculations of the geometric Zak Phase can define an energy threshold to predict the excitability of the nonlinear topological mode, and that this threshold coincides with the energy that the topological NNM intersects the linear bulk-spectrum. These predictions are validated with numerical simulations of the nonlinear topological system. These results are also tested for parametric perturbations which preserve and break chirality in the system. Thus, we provide a new method for analyzing and predicting the existence of topologically insulated modes in a strongly nonlinear lattice based on the physical observable of band topology.

physics.app-ph↗

arXiv2020

Effective Phononic Crystals for Non-Cartesian Elastic Wave Propagation

We introduce the concept of effective phononic crystals, which combine periodicity with varying isotropic material properties to force periodic coefficients in the elastic equations of motion in a non-Cartesian basis. Periodic coefficients allow for band structure calculation using Bloch theorem. Using the band structure, we demonstrate band gaps and topologically protected interface modes can be obtained in cylindrically propagating waves. Through effective phononic crystals, we show how behaviors of Cartesian phononic crystals can be realized in regions close to sources, where near field effects are non-negligible.

physics.app-ph↗

arXiv2016

Designing Perturbative Metamaterials from Discrete Models: From Veselago lenses to topological insulators

Discrete models provide concise descriptions of complex physical phenomena, such as negative refraction, topological insulators, and Anderson localization. While there are multiple tools to obtain discrete models that demonstrate particular phenomena, it remains a challenge to find metamaterial designs that replicate the behavior of desired nontrivial discrete models. Here we solve this problem by introducing a new class of metamaterial, which we term 'perturbative metamaterial', consisting of weakly interacting unit cells. The weak interaction allows us to associate each element of the discrete model (individual masses and springs) to individual geometric features of the metamaterial, thereby enabling a systematic design process. We demonstrate our approach by designing 2D mechanical metamaterials that realize Veselago lenses, zero-dispersion bands, and topological insulators. While our selected examples are within the mechanical domain, the same design principle can be applied to acoustic, thermal, and photonic metamaterials composed of weakly interacting unit cells.

cond-mat.mtrl-sci↗

arXiv2015

Composite 3D-printed meta-structures for low frequency and broadband vibration absorption

Architected materials that control elastic wave propagation are essential in vibration mitigation and sound attenuation. Phononic crystals and acoustic metamaterials use band gap engineering to forbid certain frequencies from propagating through a material. However, existing solutions are limited in the low frequency regimes and in their bandwidth of operation because they require impractical sizes and masses. Here, we present a class of materials (labeled elastic meta-structures) that supports the formation of wide and low frequency band gaps, while simultaneously reducing their global mass. To achieve these properties, the meta-structures combine local resonances with structural modes of a periodic architected lattice. While the band gaps in these meta-structures are induced by Bragg scattering mechanisms, their key feature is that the band gap size and frequency range can be controlled and broadened through local resonances, which is linked to changes in the lattice geometry. We demonstrate these principles experimentally, using novel additive manufacturing methods, and inform our designs using finite element simulations. This design strategy has a broad range of applications, including control of structural vibrations, noise and shock mitigation.

cond-mat.mtrl-sci↗