Nonlinear Acoustic Metamaterials Research Articles

Novel energy exchange behaviors and mechanisms in nonlinear acoustic metamaterials with multiple nonlinear resonators

Wave-wave interactions in a nonlinear metamaterial or structure with two propagating waves can induce energy exchange within the nonlinear systems. The effects of nonlinear resonators on these interactions and energy exchanges in a nonlinear acoustic metamaterial have not been extensively studied in the literature. In this paper, a nonlinear monatomic acoustic metamaterial with multiple nonlinear resonators (NMAM-MNR) is constructed to investigate the new behaviors and mechanisms introduced by these nonlinear resonators. Stability analyses reveal that stability can be tuned by adjusting the number of nonlinear resonators and by selecting different intensities or masses of the resonators and the chain. Additionally, direct numerical simulations are performed to study the novel energy exchange behaviors and mechanisms in NMAM-MNR systems. The results demonstrate that the degree and frequency of energy exchange can be tuned by altering the mass ratios, stiffness ratios, intensities, and natural frequencies of the nonlinear resonators and the chain. The influence of mass and stiffness ratios on the time taken for the B-wave magnitude to first reach its maximum value in NMAM-MNR systems is also studied, showing that the rate of energy exchange induced by wave-wave interactions can be tuned by changing the stiffness and mass ratios of multiple nonlinear resonators. These properties have potential applications in the fields of energy harvesters, waveguides, and resonant energy transfer mechanisms.

Nonlinear metamaterial enabled aeroelastic vibration reduction of a supersonic cantilever wing plate

The violent vibration of supersonic wings threatens aircraft safety. This paper proposes the strongly nonlinear acoustic metamaterial (NAM) method to mitigate aeroelastic vibration in supersonic wing plates. We employ the cantilever plate to simulate the practical behavior of a wing. An aeroelastic vibration model of the NAM cantilever plate is established based on the mode superposition method and a modified third-order piston theory. The aerodynamic properties are systematically studied using both the timedomain integration and frequency-domain harmonic balance methods. While presenting the flutter and post-flutter behaviors of the NAM wing, we emphasize more on the pre-flutter broadband vibration that is prevalent in aircraft. The results show that the NAM method can reduce the low-frequency and broadband pre-flutter steady vibration by 50%–90%, while the post-flutter vibration is reduced by over 95%, and the critical flutter velocity is also slightly delayed. As clarified, the significant reduction arises from the bandgap, chaotic band, and nonlinear resonances of the NAM plate. The reduction effect is robust across a broad range of parameters, with optimal performance achieved with only 10% attached mass. This work offers a novel approach for reducing aeroelastic vibration in aircraft, and it expands the study of nonlinear acoustic/elastic metamaterials.

Effectively reduce transient vibration of 2D wing with bi-stable metamaterial

Unsteady time-varying flow during flight may causes transient vibrations of wings, limiting aircraft safety and requiring effective suppression methods. Nonlinear acoustic metamaterials have recently attracted extensive attention owing to their superior capability for low-frequency and broadband vibration suppression. However, most existing nonlinear metamaterials consist of mono-stable nonlinear resonators, whose transient vibration reduction capability requires significant improvement. This paper proposes a 2D metamaterial wing model consisting of bi-stable nonlinear resonators. Based on CFD simulation, we establish an equivalent model surrounded by a fluid-like medium and systematically investigate its transient dynamics and energy dissipation. Results indicate that the bi-stable metamaterial can quickly dissipate the transient vibrations of the wing with an efficiency much higher than the linear and mono-stable nonlinear counterparts. An energy dissipation rate of over 75 % is achievable with an added mass ratio of 4 %–8 %, while the energy dissipation rate of the linear counterpart is below 60 %. The subharmonic nonlinear beatings and subharmonic resonance capture, such as 1:2 or 2:3 resonances between multiple modes, are essential mechanisms for the improvement. The reduction is robust to varying amplitudes and the distance between the two stable states. These findings provide new ways to reduce the fluid-structure interaction transient vibrations of structures.

Learning from failure: An analysis of a flawed nonlinear acoustic metamaterial design

Acoustic metamaterials (AMMs) are structured systems designed to exhibit specific, often exotic, effective material properties for acoustic wave motion. Most research on AMMs prioritize linear wave behavior, but a growing body of work has focused on nonlinear phenomena. While the primary approach to enhancing the nonlinear response of a system has been to place highly nonlinear inclusions in the system (such as bubbles, cracks, or buckling beams), an alternative approach is to control the linear material properties to enhance the relative strength of the nonlinearity. For example, one may reduce the shock formation distance of a system by reducing the effective mass density and wave speed even if the coefficient of nonlinearity is left unchanged. However, due to the nature of nonlinear waves, developing a practical design to accomplish this control can be challenging. We recently designed and built an experimental nonlinear AMM and found it to be fundamentally flawed. In this paper we discuss the thought process that led to the flawed design and present the lessons learned from an unsuccessful experiment.

Application of acoustic metamaterials to phase computing

We review the notion of “phase bit” or “phi-bit” in externally driven nonlinear acoustic metamaterials. Phi-bits are classical analogues of quantum bits, which open pathways to promising and validated modes of initializing, operating, and measuring information. Acoustic metamaterials offer ways to compute information using phase that should compare favorably with state-of-the-art quantum systems without suffering from quantum fragility.

Impact of viscothermal loss on modulation instability and rogue waves in left-handed nonlinear diffractive acoustic transmission line metamaterials

In this study, the transmission line approach is used to describe the studied acoustic metamaterial model. Through Kirchoff’s pressure and volume-velocity laws and using multiple scales method, nonlinear coupled Schrödinger equations are obtained. Then, the amplitude disturbance method is applied to these equations to obtain and plot the modulational instability gain curves. Analytically, the impact of viscothermal loss on the modulational instability gain is studied. The similarity technique is used to derive integrable Manakov’s equations. First and second-order rational rogue wavelike solutions of coupled nonlinear Schrödinger are deduced. The results indicate that the modulational instability gain and Rogue wave intensities depend on the viscothermal parameter. This parameter can be considered in the design of nonlinear acoustic metamaterials to minimize the damage caused by the dynamics of freak waves.

Research on new wave behavior and mechanisms in nonlinear diatomic acoustic metamaterials with linear damping

Research on new wave behavior and mechanisms in nonlinear diatomic acoustic metamaterials with linear damping

Rogue waves as modulational instability result in one-dimensional nonlinear triatomic acoustic metamaterials

In this study, a triatomic acoustic nonlinear metamaterial was modelled. It is a network of identical periodic unit cells made up of three different masses. These masses interact with connections modelled by springs whose stiffnesses are linear and nonlinear. Handling the motion equations of nth unit cell, the semidiscrete approximation method is used to extract the three-component coupled nonlinear Schrödinger equations. The dispersion relationship was determined. The results showed that the dispersion relation of the one-dimensional triatomic chain contained an acoustic branch and two optical branches. The dispersion curves show that the proposed acoustic metamaterial exhibits two local resonance bandgaps independent of spatial periodicity. The spectral range and frequency bandgap are related to the mass of the three atoms in the original cell. Based on the theory of linear stability analysis, modulation instability is the condition for the existence of rogue waves. Analytically, it is shown that modulational instability and rogue wave phenomena are strongly influenced by variations in the nonlinearity, dispersion, and diffraction terms, which contain the values of the masses and stiffnesses.

Breaking the mass law for broadband sound insulation through strongly nonlinear interactions

Sound transmission through panels is governed by the well-known mass law in the mid-frequency range. This paper reveals a possibility of breaking this density-dominant law through strongly nonlinear interaction, while broadening the bandwidth for effective sound insulation. For this purpose, a basic model is established, and corresponding exact analytical methods for bifurcation and stability analyses are proposed. Influences of four typical types of nonlinear interactions on the wave insulation are analytically and numerically investigated. We find that, by introducing strongly nonlinear interactions at appropriate locations, the nonlinear model can not only break the barrier imposed by the mass law, but also entails broadband sound insulation by 2–3 times relative to the optimal linear model. Meanwhile, the sound insulation valley due to the coincident effects can also be eliminated. With bifurcation and effective mass, we clarify that the enhanced wave insulation of the strongly nonlinear models arises from the broader band of super mass induced by strongly nonlinear local resonances, which depends on the bifurcation of periodic solutions. The proposed models and the findings provide a solid basis and new possibilities for wave insulation in complex nonlinear structures and nonlinear acoustic metamaterials.

A Nonlinear Gradient-Coiling Metamaterial for Enhanced Acoustic Signal Sensing

Acoustic sensing systems play a critical role in identifying and determining weak sound sources in various fields. In many fault warning and environmental monitoring processes, sound-based sensing techniques are highly valued for their information-rich and non-contact advantages. However, noise signals from the environment reduce the signal-to-noise ratio (SNR) of conventional acoustic sensing systems. Therefore, we proposed novel nonlinear gradient-coiling metamaterials (NGCMs) to sense weak effective signals from complex environments using the strong wave compression effect coupled with the equivalent medium mechanism. Theoretical derivations and finite element simulations of NGCMs were executed to verify the properties of the designed metamaterials. Compared with nonlinear gradient acoustic metamaterials (Nonlinear-GAMs) without coiling structures, NGCMs exhibit far superior performance in terms of acoustic enhancement, and the structures capture lower frequencies and possess a wider angle acoustic response. Additionally, experiments were constructed and conducted using set Gaussian pulse and harmonic acoustic signals as emission sources to simulate real application scenarios. It is unanimously shown that NGCMs have unique advantages and broad application prospects in the application of weak acoustic signal sensing, enhancement and localization.

Modulation instability in nonlinear acoustic metamaterials with coupling coefficients

Modulation instability in nonlinear acoustic metamaterials with coupling coefficients

A nonlinear acoustic metamaterial beam with tunable flexural wave band gaps

Although linear acoustic metamaterials (LAMs) have been widely studied, the design and analyses of nonlinear acoustic metamaterials (NAMs) are relatively immature. In this paper, a new NAM beam is designed, which is composed of a homogeneous beam with periodic resonant units attached on its top surface. Each resonant unit consists of two Duffing oscillators connected in series. First, an analytical model is developed based on the harmonic balance method, from which the amplitude-frequency response and dispersion of flexural wave are derived, and the position and width of the band gaps produced by this novel structure are quantitatively evaluated. Then, the effects of the linear and nonlinear stiffness, as well as the arrangement of the series-connected resonators on the frequency band structure are discussed. A finite element (FE) simulation is conducted to obtain the transmission of a finite NAM beam. The numerical results show that the frequency range of vibration suppression is consistent with the analytically predicted band gap, which validate the developed analytical model. Our study demonstrates that comparing with the corresponding linear counterpart, the system nonlinearity effectively enhances the tunability of the band gap of the flexural wave. It’s worth mentioning that an ultra-wide band gap starting from 0Hz can be achieved via introducing softening nonlinearity, which is quite attractive in engineering applications requiring low-frequency vibration suppression.

Nonlinear wave propagation in acoustic metamaterials with bilinear nonlinearity

Nonlinear phononic crystals have attracted great interest because of their unique properties absent in linear phononic crystals. However, few researches have considered the bilinear nonlinearity as well as its consequences in acoustic metamaterials. Hence, we introduce bilinear nonlinearity into acoustic metamaterials, and investigate the propagation behaviors of the fundamental and the second harmonic waves in the nonlinear acoustic metamaterials by discretization method, revealing the influence of the system parameters. Furthermore, we investigate the influence of partially periodic nonlinear acoustic metamaterials on the second harmonic wave propagation, and the results suggest that pass-band and band-gap can be transformed into each other under certain conditions. Our findings could be beneficial to the band gap control in nonlinear acoustic metamaterials.

Graduate acoustics education in the Cockrell School of Engineering at The University of Texas at Austin

While graduate study in acoustics takes place in several colleges and schools at The University of Texas at Austin (UT Austin), including Communication, Fine Arts, Geosciences, and Natural Sciences, this poster focuses on the acoustics program in Engineering. The core of this program resides in the Departments of Mechanical Engineering (ME) and Electrical and Computer Engineering (ECE). Acoustics faculty in each department supervise graduate students in both departments. One undergraduate and nine graduate acoustics courses are taught in ME and ECE. Instructors for these courses include staff at Applied Research Laboratories at UT Austin, where many of the graduate students have research assistantships. The undergraduate course, taught every fall, begins with basic physical acoustics and proceeds to draw examples from different areas of engineering acoustics. Three of the graduate courses are taught every year: a two course sequence on physical acoustics, and a transducers course. The remaining six graduate acoustics courses, taught in alternate years, are on nonlinear acoustics, underwater acoustics, ultrasonics, architectural acoustics, wave phenomena, and acoustic metamaterials. An acoustics seminar is held most Fridays during the long semesters, averaging over ten per semester since 1984. The ME and ECE departments both offer Ph.D. qualifying exams in acoustics.

Synthetical vibration reduction of the nonlinear acoustic metamaterial honeycomb sandwich plate

Light-weight and high-stiffness honeycomb sandwich plates are widely used in high- speed vehicles. Suppressing their low-frequency and broadband vibration is significant for improving safety and reducing noise, but remains challenging with limited mass cost. Bandgaps and chaotic band in nonlinear acoustic metamaterials (NAMs) offer an effective way for vibration reduction. This paper conceives a NAM sandwich plate and studies its vibration reduction properties based on numerical and experimental methods. We establish its nonlinear finite element model based on the equivalent homogeneous model and experiments. The influences of the resonator distribution, nonlinear stiffness, resonant frequencies, mass, amplitude and structural plate parameters on its vibration are thoroughly analyzed to achieve the best performance. Then, we manufacture an optimized NAM plate and experimentally demonstrate that all resonances of the high-stiffness NAM plate below 800 Hz are greatly reduced with only 17.7 % attached mass; particularly, the first low-frequency resonance at 93 Hz is reduced by 20 dB. This shows that the NAM strategy can robustly and effectively suppress the low-frequency and broadband vibration of the light-weight and high-stiffness plates with small mass cost, a synthetical performance desired for broad potential applications. The models, regularities, designs and experiments can also enlighten more studies on relate topics.

A nonlinear metamaterial plate for suppressing vibration and sound radiation

Nonlinear acoustic metamaterials (NAMs) exhibit extraordinary properties for low-frequency and broadband vibration mitigation. Despite the increasing attention received, exotic properties and the physical mechanisms underpinning NAM-enabled functionalities have not been fully understood. Moreover, investigations on the sound radiation of NAM structures have not been reported. Here we systematically investigate the vibration of a NAM plate and its sound radiation using experimental and theoretical methods. We experimentally demonstrate that the NAM plate can entail significant vibration and sound radiation reduction in an ultra- low and broad frequency band, typically from 20 to 1800 Hz, without any artificial damping element. This is attributed to the nonlinear coupling among multiple local resonances, and the nonlinear collision-friction damping. This understanding allows the proposal of two design strategies to achieve ultra- low and broadband vibration and sound radiation suppression with NAMs. Moreover, we clarify the mechanisms governing the ultra- low and broadband features, including bandgaps, output saturation of nonlinear resonances, efficient energy pumping due to high-order harmonics and chaos, and modulation of nonlinear resonance modal amplitudes and shapes. These mechanisms and diverse wave behaviors are inter-related and occur concurrently. The reported study provides answers to several key questions of paramount importance in designs, mechanics and applications of nonlinear metamaterials.

Mechanism of the low-frequency wide-band within a nonlinear acoustic metamaterial

In this paper, the formation and broadening mechanism of the low-frequency bandgap are revealed by designing a type of nonlinear acoustic metamaterial (NAM) with gaps. The mechanism of the chaotic evolution through the harmonic coupling for the NAM structure is revealed in detail, which can effectively change spectral characteristics in the bifurcation sequence, and finally, lead to a low frequency and chaos. Then, a low-frequency broadband within the NAM structures with gaps is obtained by the finite element method (FEM) due to the mechanism of chaos. Most importantly, the width of the bandgap can be successfully enlarged by adjusting the small gap, because the energy of the elastic wave can be greatly decreased or redistributed with the system going from periodic motion to doubling bifurcation. This mechanism for achieving a low-frequency bandgap overcomes the shortcomings both in the traditional local resonance with too large additional mass and in the inertial amplification structures with narrow bandgaps. Therefore, this idea of achieving a low-frequency bandgap has great theoretical significance for controlling low-frequency sound waves.

Harnessing rotational geometry to design reconfigurable dispersion and refractive index in nonlinear acoustic metamaterials

We investigate 1D and 2D monatomic lattice structures composed of in-plane rotators coupled by angled elastic linkages and explore their reconfigurable dispersion, negative refraction, amplitude-dependent dynamics, and acoustoelastic effect. At small amplitude, the linear band structure can be configured to be either acoustic or optical in nature by changing the connecting locations on the rotators, which corresponds to positive and negative refractive index. An interface problem between two rotator lattices with opposite dispersion type is modeled, and illustrates negative refraction in numerical simulations—experimental measurements are in progress. Its frequency–transmission relation matches the linear theory. At higher amplitude, the hardening nonlinearity shifts the dispersion and induces amplitude-dependent transmission. A novel nonlinear phenomenon–amplitude saturation (a constant far-field transmission independent of input amplitude) is observed when the transmitted wave falls in the nonlinear stopband and simultaneously the linear passband of the receiving lattice. We analyze the nonlinear effects via perturbation methods and propose a framework for evanescent-specific nonlinear waves to explain the saturation phenomenon. Additionally, we observe a strong acoustoelastic effect in chiral-patterned rotator lattices, where a static stretch can shift the equilibrium positions of the rotators and morph the band structure from acoustic to optical.

Elastic wave propagation in nonlinear two-dimensional acoustic metamaterials

This study describes the wave propagation in a periodic lattice which is formed by a spring-mass two-dimensional structure with local Duffing nonlinear resonators. The wave propagation characteristics of the system are evaluated by using the perturbation method to determine the dispersion relationships and wave propagation characteristics in the nonlinear two-dimensional acoustic metamaterials. A quantitative study of wave amplitude is carried out to determine the maximum allowable wave amplitude for the whole structures under the assumption of small parameters. In particular, the harmonic balance method is introduced to investigate the frequency response and effective mass of the nonlinear systems. We find that the dispersion relations and group velocity of unit cell are related to wave amplitude. Furthermore, the dual-wave vector is observed in the nonlinear systems. Numerical simulations validate the dispersion analytical results. The results can be used to tune wave propagation in the nonlinear acoustic metamaterials and provide some ideas for the study of nonlinear metamaterials.

Modulational instability and rogue waves in one-dimensional nonlinear acoustic metamaterials: case of diatomic model

In this paper, by means of the expanded Taylor series and Lindstedt-Poincaré perturbation methods, the coupled nonlinear Schrödinger equations (CNLSE) modeling the propagation of acoustic waves in acoustic metamaterial is obtained. Using these equations, the Modulational Instability (MI) phenomenon is observed in disturbance mode. Manakov integrable system is derived with suitable parameters and we shown that the Rogue Waves (RWs) can propagate diatomic acoustic metamaterials.