Flexoelectricity in solids: Progress, challenges, and perspectives

Noise pollution has become a significant global problem in recent years. Unfortunately, conventional acoustic materials cannot offer substantial improvements in noise reduction. However, acoustic metamaterials are providing new solutions for controlling sound waves, and have huge potential for mitigating noise propagation in particular. Recently, owing to the rapid development of acoustic metamaterials, metamaterials for acoustic noise reduction have drawn the attention of researchers worldwide. These metamaterials are often both light and compact, and are excellent at reducing low‐frequency noise, which is difficult to control with conventional acoustic materials. Recent progress has illustrated that acoustic metamaterials effectively control sound waves, and optimizing their structure can enable functionality based on new physical phenomena. This review introduces the development of acoustic metamaterials, and summarizes the basic classification, underlying physical mechanism, application scenarios, and emerging research trends for both passive and active noise‐reduction metamaterials. Focusing on noise reduction, the shortcomings of current technologies are discussed, and future development trends are predicted. As our knowledge in this area continues to expand, it is expected that acoustic metamaterials will continue to improve and find more practical applications in emerging fields in the future.

Acoustic Metamaterials for Noise Reduction: A Review

The concept of a metasurface opens new exciting directions to engineer the refraction properties in both optical and acoustic media. Metasurfaces are typically designed by assembling arrays of subwavelength anisotropic scatterers able to mold incoming wave fronts in rather unconventional ways. The concept of a metasurface was pioneered in photonics and later extended to acoustics while its application to the propagation of elastic waves in solids is still relatively unexplored. We investigate the design of acoustic metasurfaces to control elastic guided waves in thin-walled structural elements. These engineered discontinuities enable the anomalous refraction of guided wave modes according to the generalized Snell's law. The metasurfaces are made out of locally resonant toruslike tapers enabling an accurate phase shift of the incoming wave, which ultimately affects the refraction properties. We show that anomalous refraction can be achieved on transmitted antisymmetric modes (A_{0}) either when using a symmetric (S_{0}) or antisymmetric (A_{0}) incident wave, the former clearly involving mode conversion. The same metasurface design also allows achieving structure embedded planar focal lenses and phase masks for nonparaxial propagation.

Anomalous Refraction of Acoustic Guided Waves in Solids with Geometrically Tapered Metasurfaces.

Elastic metamaterials have been extensively investigated due to their significant effects on controlling propagation of elastic waves. One of the most interesting properties is the generation of band gaps, in which subwavelength elastic waves cannot propagate through. In the study, a new class of active elastic metamaterials with negative capacitance piezoelectric shunting is presented. We first investigated dispersion curves and band gap control of an active mass-in-mass lattice system. The unit cell of the mass-in-mass lattice system consists of the inner masses connected by active linear springs to represent negative capacitance piezoelectric shunting. It was demonstrated that the band gaps can be actively controlled and tuned by varying effective stiffness constant of the linear spring through appropriately selecting the value of negative capacitance. The promising application was then demonstrated in the active elastic metamaterial plate integrated with the negative capacitance shunted piezoelectric patches for band gap control of both the longitudinal and bending waves. It can be found that the location and the extent of the induced band gap of the elastic metamaterial can be effectively tuned by using shunted piezoelectric patch with different values of negative capacitance, especially for extremely low-frequency cases.

Band Gap Control in an Active Elastic Metamaterial With Negative Capacitance Piezoelectric Shunting

Acoustics is a classical field of study that has witnessed tremendous developments over the past 25 years. Driven by the novel acoustic effects underpinned by phononic crystals with periodic modulation of elastic building blocks in wavelength scale and acoustic metamaterials with localized resonant units in subwavelength scale, researchers in diverse disciplines of physics, mathematics, and engineering have pushed the boundary of possibilities beyond those long held as unbreakable limits. More recently, structure designs guided by the physics of graphene and topological electronic states of matter have further broadened the whole field of acoustic metamaterials by phenomena that reproduce the quantum effects classically. Use of active energy-gain components, directed by the parity-time reversal symmetry principle, has led to some previously unexpected wave characteristics. It is the intention of this review to trace historically these exciting developments, substantiated by brief accounts of the salient milestones. The latter can include, but are not limited to, zero/negative refraction, subwavelength imaging, sound cloaking, total sound absorption, metasurface and phase engineering, Dirac physics and topology-inspired acoustic engineering, non-Hermitian parity-time synthetic active metamaterials, and one-way propagation of sound waves. These developments may underpin the next generation of acoustic materials and devices, and offer new methods for sound manipulation, leading to exciting applications in noise reduction, imaging, sensing and navigation, as well as communications.

Breaking the barriers: advances in acoustic functional materials

In this letter, a class of honeycomb acoustic metamaterial possessing lightweight and yet sound-proof properties is designed, theoretically proven, and then experimentally verified. It is here reported that the proposed metamaterial having a remarkably small mass per unit area at 1.3 kg/m2 can achieve low frequency (<500 Hz) sound transmission loss (STL) consistently greater than 45 dB. Furthermore, the sandwich panel which incorporates the honeycomb metamaterial as the core material yields a STL that is consistently greater than 50 dB at low frequencies. The proposed metamaterial is promising for constructing structures that are simultaneously strong, lightweight, and sound-proof.

A lightweight yet sound-proof honeycomb acoustic metamaterial

Bonding a two-dimensional planar array of small lead discs on an aluminum plate with silicone rubber is shown numerically to focus low-frequency flexural guided waves. The “effective mass density profile” of this type of elastic metamaterials (EMMs), perpendicular to wave propagation direction, is carefully tailored and designed, which allows rays of flexural A0 mode Lamb waves to bend in succession and then focus through a 7 × 9 planar array. Numerical simulations show that Lamb waves can be focused beyond EMMs region with amplified displacement and yet largely retained narrow banded waveform, which may have potential application in structural health monitoring.

Focusing guided waves using surface bonded elastic metamaterials

A direct curvature sensing measurement based on the flexoelectricity of Ba0:64Sr0:36TiO3 (BST) material through electromechanical coupling is proposed and developed in this paper. The curvature sensing was demonstrated in four point bending tests of a beam with bonded BST curvature sensors under different applied loads with low time-harmonic frequencies from 0.5 to 3 Hz. A shear lag concept which describes the efficiency of the loading transfer from the epoxy bonding layer was taken into account in extracting the actual curvature from the sensor measurement. A finite element analysis has been performed to estimate the curvature transfer efficiency and the bonding layer thickness is found to be a critical parameter in determining the curvature transfer. Experimental results showed a good linearity of charge output dependence on curvature inputs in a limited frequency range and showed a curvature sensitivity of 30.78 pC m, in comparison with 32.48 pC m from theoretical predictions. Using the measured curvature, the bending stiffness of the beam was then obtained from the experimentally obtained moment‐curvature curve. This work demonstrated that the flexoelectric BST sensor provides a direct curvature measurement instead of using a traditional strain gage sensor through interpolation, and thus offers an important avenue for on-line and in situ structural health monitoring. (Some figures may appear in colour only in the online journal)

A sensor for the direct measurement of curvature based on flexoelectricity

Strain gradient sensing offers an alternative avenue for in-situ monitoring of onset and growth of cracks in structural health monitoring, where the strain gradient is the most sensitive measurand. In this study, flexoelectric strain gradient sensing structures using Ba0.64Sr0.36TiO3 (BST) were attached on the proximity of an open hole in an aluminum plate, to monitor strain gradient variations of the specimen under a uniaxial dynamic load. Charge outputs of the BST micro-bars showed good linearity with the average strain gradients, with a sensitivity of 88 pC m, which is in good agreement with the theoretical estimation by assuming a 30 μm bonding thickness.

Flexoelectric strain gradient detection using Ba0.64Sr0.36TiO3 for sensing

This paper presents a quantitative study of conversion of evanescent Lamb waves into propagating in isotropic plates. The conversion is substantiated by prescribing time-harmonic Lamb displacements/tractions through a narrow aperture at an edge of a semi-infinite plate. Complex-valued dispersion and group velocity curves are employed to characterize the conversion process. The amplitude coefficient of the propagating Lamb modes converted from evanescent is quantified based on the complex reciprocity theorem via a finite element analysis. The power flow generated into the plate can be separated into radiative and reactive parts made on the basis of propagating and evanescent Lamb waves, where propagating Lamb waves are theoretically proved to radiate pure real power flow, and evanescent Lamb waves carry reactive pure imaginary power flow. The propagating power conversion efficiency is then defined to quantitatively describe the conversion. The conversion efficiency is strongly frequency dependent and can be significant. With the converted propagating waves from evanescent, sensors at far-field can recapture some localized damage information that is generally possessed in evanescent waves and may have potential application in structural health monitoring.

Conversion of evanescent Lamb waves into propagating waves via a narrow aperture edge.

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