The nonlinear S0 Lamb mode in a plate with a linearly-varying thickness

Investigation of the Zero-Frequency Component of Nonlinear Lamb Waves in a Symmetrical Undulated Plate

When an ultrasonic pulse propagates in a thin plate, nonlinear Lamb waves with higher harmonics and a zero-frequency component (ZFC) will be generated because of the nonlinearity of materials. The ZFC, also known as the static displacement or static component, has its unique application on the evaluation of early-stage damages in the elastic symmetrical undulated plate. In this study, analysis of the excitation mechanism of the ZFC and the second harmonic component (SHC) was theoretically and numerically investigated, and the material early-stage damage of a symmetrical undulated was characterized by studying the propagation of nonlinear Lamb waves. Both the ZFC and SHC can be effectively employed in monitoring the material damages of the undulated plate in its early stage. However, several factors must be considered for the propagation of the SHC in an undulated plate because of the geometric curvature and interference between the second harmonics during propagation, preventing efficient application of this technique. If the fundamental wave can propagate in the plate regardless of the plate boundary conditions, an accumulative effect always exists for the ZFC in a thin plate, indicating that the ZFC is independent of the structural geometry. This study reveals that the ZFC-based inspection technique is more efficient and powerful in characterizing the damages of a symmetrical undulated plate in the early stage of service compared to the second harmonic method.

Solution of nonlinear Lamb waves in plates with discontinuous thickness

Nonlinear Lamb waves can propagate over long distances in plate and shell structures and are sensitive to the early fatigue damage of materials. Therefore, they offer unique advantages in the fields of nondestructive testing and material health monitoring. Plate and shell structures with discontinuous thicknesses (e.g., ribs, stiffeners, or joints) will cause nonlinear Lamb wave scattering, and it is necessary to study the scattering processes of nonlinear Lamb waves at discontinuities and how these processes impact the resulting signal characteristics. Thus, nonlinear Lamb waves can be used to identify the structural characteristics and defect characteristics of signals in practical applications. In this paper, the propagating and scattering processes of the second harmonic of a Lamb wave in a discontinuous plate are studied, including the contributions of the evanescent Lamb modes near the discontinuity and the nonlinear boundary effect at the discontinuity. The scattering characteristics of the second harmonics with respect to the frequency and geometry of the plate are analyzed. In addition, the integral formula is adjusted to improve the computational stability under different numbers of Lamb wave modes. Transient finite element simulation is used to validate the proposed method.

Guided wave propagation in a double-layer plate with a nonlinear spring-interface

This article derives the solution to the guided wave fields in a double-layer plate consisting of two sublayers. It is assumed that the two sublayers are linearly elastic. They are bonded together at their interface by a nonlinear adhesive layer of infinitesimal thickness. This allows us to propose a nonlinear spring-interface model. Based on such an idealized model for the double-layer plate, guided wave fields in the plate are solved using the modified normal mode expansion method. It is found that the nonlinearity of the spring-interface can generate resonant guided waves in the double-layer plate. Specifically, when certain conditions are met, mixing of two primary guided waves will generate resonant guided waves whose frequencies are either the sum or difference of those of the two primary waves. Amplitudes of such resonant mixed waves are proportional to the compliance of the nonlinear spring-interface. As a special case, if the two primary waves have the same frequency, a resonant second harmonic guided wave may be generated. In addition, the conditions that generate resonant mixed waves are identified. We believe that the results of this work provide the theoretical foundation on which nondestructive evaluation techniques using nonlinear guided waves can be developed to nondestructively evaluate, for example, the bond strength of thin coating on a substrate.

Binary acoustic metasurfaces for dynamic focusing of transcranial ultrasound

Transcranial focused ultrasound (tFUS) is a promising technique for non-invasive and spatially targeted neuromodulation and treatment of brain diseases. Acoustic lenses were designed to correct the skull-induced beam aberration, but these designs could only generate static focused ultrasound beams inside the brain. Here, we designed and 3D printed binary acoustic metasurfaces (BAMs) for skull aberration correction and dynamic ultrasound beam focusing. BAMs were designed by binarizing the phase distribution at the surface of the metasurfaces. The phase distribution was calculated based on time reversal to correct the skull-induced phase aberration. The binarization enabled the ultrasound beam to be dynamically steered along wave propagation direction by adjusting the operation frequency of the incident ultrasound wave. The designed BAMs were manufactured by 3D printing with two coding bits, a polylactic acid unit for bit "1" and a water unit for bit "0." BAMs for single- and multi-point focusing through the human skull were designed, 3D printed, and validated numerically and experimentally. The proposed BAMs with subwavelength scale in thickness are simple to design, easy to fabric, and capable of correcting skull aberration and achieving dynamic beam steering.

Airy Beam-enabled Binary Acoustic Metasurfaces for Underwater Ultrasound Beam Manipulation

Airy beams are peculiar beams that are non-diffracting, self-accelerating, and self-healing, and they have offered great opportunities for ultrasound beam manipulation. However, one critical barrier that limits the broad applications of Airy beams in ultrasound is the lack of simply built device to generate Airy beams in water. This work presents a family of Airy beam-enabled binary acoustic metasurfaces (AB-BAMs) to generate Airy beams for underwater ultrasound beam manipulation. AB-BAMs are designed and fabricated by 3D printing with two coding bits: a polylactic acid (which is the commonly used 3D printing material) unit acting as a bit "1" and a water unit acting as a bit "0". The distribution of the binary units on the metasurface is determined by the pattern of Airy beam. To showcase the wavefront engineering capability of the AB-BAMs, several examples of AB-BAMs are designed, 3D printed, and coupled with a planar single-element ultrasound transducer for experimental validation. We demonstrate the capability of AB-BAMs in flexibly tuning the focal region size and beam focusing in 3D space by changing the design of the AB-BAMs. The focal depth of AB-BAMs can be continuous and electronical tuned by adjusting the operating frequency of the planar transducer without replacing the AB-BAMs. The superimposing method is leveraged to enable the generation of complex acoustic fields, e.g., multi-foci and letter patterns (e.g., "W" and "U"). The more complex focal patterns are shown to be also continuously steerable by simply adjusting the operating frequency. Furthermore, the proposed 3D-printed AB-BAMs are simple to design, easy to fabricate, and low-cost to produce with the capabilities to achieve tunable focal size, flexible 3D beam focusing, arbitrary multipoint focusing, and continuous steerability, which creates unprecedented potential for ultrasound beam manipulation.

Error analysis and reliability of zero-order Lamb mode inversion for waveguide characterization

In recent years, several fitting techniques have been presented to reconstruct the parameters of a plate from its Lamb wave dispersion curves. Published studies show that these techniques can yield high accuracy results and have the potential of reconstructing several parameters at once. The precision with which parameters can be reconstructed by inverting Lamb wave dispersion curves, however, remains an open question of fundamental importance to many applications. In this work, we introduce a method of analyzing dispersion curves that yields quantitative information on the precision with which the parameters can be extracted. In our method, rather than employing error minimization algorithms, we compare a target dispersion curve to a database of theoretical ones that covers a given parameter space. By calculating a measure of dissimilarity (error) for every point in the parameter space, we reconstruct the distribution of the error in that space, beside the location of its minimum. We then introduce dimensionless quantities that describe the distribution of this error, thus yielding information about the spread of similar curves in the parameter space. We demonstrate our approach by considering both idealized and realistic scenarios, analyzing the dispersion curves obtained numerically for a plate and experimentally for a pipe. Our results show that the precision with which each parameter is reconstructed depends on the mode used, as well as the frequency range in which it is considered.

Hypersonic magnetoelastic waves in inhomogeneous structures

This work focuses on the propagation of surface magnetoelastic waves in a inhomogeneous structure containing ferromagnetic layer of smooth and slowly variable thickness. The dispersion relation of magnetoelastic waves and the wave attenuation due to the thickness variation in the studied structure were analytically obtained. We found that the magnetoelastic resonance frequency is changed at different positions in this structure. Then proposed the idea of modifying the magnetic field to control the magnetoelastic resonance region, and finally considered the possible applications of this structure for signal processing.