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.

Transcranial Ultrasonic Focusing by a Phased Array Based on Micro-CT Images.

In this paper, we utilize micro-computed tomography (micro-CT) to obtain micro-CT images with a resolution of 60 µm and establish a micro-CT model based on the k-wave toolbox, which can visualize the microstructures in trabecular bone, including pores and bone layers. The transcranial ultrasound phased array focusing field characteristics in the micro-CT model are investigated. The ultrasonic waves are multiply scattered in skull and time delays calculations from the transducer to the focusing point are difficult. For this reason, we adopt the pulse compression method and the linear frequency modulation Barker code to compute the time delay and implement phased array focusing in the micro-CT model. It is shown by the simulation results that ultrasonic loss is mainly caused by scattering from the microstructures of the trabecular bone. The ratio of main and side lobes of the cross-correlation calculation is improved by 5.53 dB using the pulse compression method. The focusing quality and the calculation accuracy of time delay are improved. Meanwhile, the beamwidth at the focal point and the sound pressure amplitude decrease with the increase in the signal frequency. Focusing at different depths indicates that the beamwidth broadens with the increase in the focusing depth, and beam deflection focusing maintains good consistency in the focusing effect at a distance of 9 mm from the focal point. This indicates that the phased-array method has good focusing results and focus tunability in deep cranial brain. In addition, the sound pressure at the focal point can be increased by 8.2% through amplitude regulation, thereby enhancing focusing efficiency. The preliminary experiment verification is conducted with an ex vivo skull. It is shown by the experimental results that the phased array focusing method using pulse compression to calculate the time delay can significantly improve the sound field focusing effect and is a very effective transcranial ultrasound focusing method.

Multi Spherical Wave Imaging Method Based on Ultrasonic Array.

The imaging range of traditional plane wave imaging is usually limited by the directivity of the plane wave. In this paper, a multi spherical wave imaging method based on an ultrasonic array is proposed, which radiates both compression and shear waves in a solid medium to form the multi spherical wave. Firstly, excitation characteristics of the multi spherical wave are analyzed theoretically and the calculation method of echo delay of multi spherical wave imaging is derived. Multi spherical wave imaging is compared with conventional ultrasonic plane wave imaging by designing experiments. Compared with ultrasonic plane wave imaging, multi spherical wave imaging is not limited to the size of the transducer and can greatly improve the detection range. In addition, compared with the multi plane wave imaging method, the multi spherical wave imaging algorithm is relatively simple, fast, and has high application value.

Research on perturbation method for nonlinear elastic waves.

This paper explores the propagation of nonlinear elastic waves in a two-dimensional isotropic medium. The analytical expressions of first-order potentials corresponding to second harmonic acoustic components are obtained and discussed by using the perturbation method. Based on the careful theoretical analysis, it is shown that the first-order P wave always has a resonant term, which is proportional to the propagation distance in the condition of simultaneous excitation of the P wave. On the contrary, the first-order SV wave does not have any cumulative effect. Moreover, the nonlinear interactions between the P wave and SV are also presented.

Excitation mechanisms and dispersion characteristics of guided waves in multilayered cylindrical solid media.

This paper first reviews a method of simulating the propagation characteristics of guided waves in multilayered coaxial cylindrical elastic solid media. Secondly, this method is used to investigate the properties of the guided waves for the ultrasonic long-range non-destructive evaluation techniques for rockbolts. To do so, the special case of non-leaky guided modes in open waveguides is considered. The method explains how the complex dispersion function is converted into a real function: hence the bisection technique can be employed to search for all the real roots. The model is used to (i) characterize the low dispersion range and anomalous dispersion of normal and Stoneley modes and (ii) analyze the excitation mechanisms of guided waves from axisymmetric and non-axisymmetric acoustic sources. The results are used to select suitable excitation frequency ranges associated with dominant modes with large amplitudes, low dispersion, and distinguishable propagation velocities to reduce signal distortion. The results suggest the lowest order flexural mode, excited by a radial force source, has potential to be used in practice. Also, the highly dispersive Stoneley mode propagating along a cylindrical interface is defined and distinguished from the normal mode using two properties, velocity high-frequency asymptotes and amplitude distributions along the radial direction.

Elastic waves excited by a plane source on the surface of a multilayered medium.

Elastic waves excited by a plane piezoelectric source with an arbitrary shape on the surface of a multilayered medium have been studied for the first time in this paper. On the basis of Abzo-zena [Geophys. J. R. Astron. Soc. 58, 91-105 (1979)] and Menke [Geophys. J. R. Astron. Soc. 59, 315-323 (1979)], the propagator matrix for the elastic wave field in multilayered medium is extended from two- to three-dimensional (3D) space. 3D elastic wave field is investigated and the displacement-stress response for the boundary conditions is obtained. The propagation of elastic wave in multilayered media is analyzed in 3D space in the frequency domain. The P-SV and SH modes corresponding to the poles are studied. The excitation and propagation of the modes are analyzed further. It is found that the propagation velocities of the P-SV and SH modes do not depend on the propagation azimuth theta in the plane parallel to the free surface of the multilayered medium while the displacement amplitudes are strongly dependent on the azimuth theta. The directional distribution functions of the modes are independent of the medium parameters and the modes and dependent on the shape and excitation fashion of the source. Finally, as an example, the displacement fields of the P-SV and SH modes excited by a rectangle source are analyzed. The displacement representation and numerical results of the directivity distribution functions for the P-SV and SH modes are obtained.

In-plane P-SV waves from a piezoelectric strip actuator: exact versus effective boundary condition solutions.

A piezoelectric strip of finite width and thickness is placed on top of an isotropic elastic half space. It operates in actuator mode, and a time harmonic voltage is thus applied across it. The piezoelectric material is of type 6 mm oriented so that a two-dimensional (2-D) in-plane (P-SV) problem results. By Fourier series expansions, the problem is solved exactly, and this result is compared to the case when the piezoelectric strip is replaced by an effective boundary condition, which is derived by series expansions in the thickness coordinate in the piezoelectric strip. At low frequencies, the results agree very well, and this corresponds to the situation often met in practice. In general, the effective boundary condition should be much easier to apply, for example when a finite element method (FEM) program is used.