Subsonic leaky Rayleigh waves at liquid-solid interfaces

Computing leaky Lamb waves for waveguides between elastic half-spaces using spectral collocation

In non-destructive evaluation guided wave inspections, the elastic structure to be inspected is often embedded within other elastic media and the ensuing leaky waves are complex and non-trivial to compute; we consider the canonical example of an elastic waveguide surrounded by other elastic materials that demonstrates the fundamental issues with calculating the leaky waves in such systems. Due to the complex wavenumber solutions required to represent them, leaky waves pose significant challenges to existing numerical methods, with methods that spatially discretise the field to retrieve them suffering from the exponential growth of their amplitude far into the surrounding media. We present a spectral collocation method yielding an accurate and efficient identification of these modes, leaking into elastic half-spaces. We discretise the elastic domains and, depending on the exterior bulk wavespeeds, select appropriate mappings of the discretised domain to complex paths, in which the numerical solution decays and the physics of the problem are preserved. By iterating through all possible radiation cases, the full set of dispersion and attenuation curves are successfully retrieved and validated, where possible, against the commercially available software disperse. As an independent validation, dispersion curves are obtained from finite element simulations of time-dependent waves using Fourier analysis.

Identification of Stress States in Compressed Masonry Walls Using a Non-Destructive Technique (NDT)

The structure safety can be assessed, but only indirectly, by identifying material properties, geometry of structures, and values of loads. The complete and comprehensive assessment can be done only after determining internal forces acting inside structures. Ultrasonic extensometry using an acoustoelastic effect (AE) is among the most common non-destructive techniques (NDT) of determining true stresses in structures. Theoretical bases of the method were described in the mid 20th century. They were founded on the correlation between ultrasonic waves and the value and direction of stresses. This method is commonly used to determine stresses mainly in homogeneous materials without any inherent internal defects. This method is rarely applied to porous or composite materials, such as concrete or rock due to a high dispersion of results. Autoclaved aerated concrete (AAC), characterized by high homogeneity and porosity, is the popular material in the construction sector, used to produce masonry units. The discussed tests involved the acoustoelastic effect to determine stresses in the masonry wall made of AAC. This paper presents a widely theoretical background for the AE method, and then describes the author’s own research on AAC divided into two stages. At first, the empirical relationships between compressive stress and velocity of longitudinal ultrasonic wave, including humidity, were determined. In stage II, nine masonry walls were tested in axial compression. Mean compressive stresses in the masonry wall determined with the proposed method were found to produce a satisfactory confidence level up to ca. 50% of failure stresses. Results were significantly understated for stresses of the order of 75% of failure stresses.

Measurement of Rayleigh Wave Beams Using Angle Beam Wedge Transducers as the Transmitter and Receiver with Consideration of Beam Spreading

A theoretical model, along with experimental verification, is developed to describe the generation, propagation and reception of a Rayleigh wave using angle beam wedge transducers. The Rayleigh wave generation process using an angle beam wedge transducer is analyzed, and the actual Rayleigh wave sound source distributions are evaluated numerically. Based on the reciprocity theorem and considering the actual sound source, the Rayleigh wave beams are modeled using an area integral method. The leaky Rayleigh wave theory is introduced to investigate the reception of the Rayleigh wave using the angle beam wedge transducers, and the effects of the wave spreading in the wedge and transducer size are considered in the reception process. The effects of attenuations of the Rayleigh wave and leaky Rayleigh wave are discussed, and the received wave results with different sizes of receivers are compared. The experiments are conducted using two angle beam wedge transducers to measure the Rayleigh wave, and the measurement results are compared with the predictions using different theoretical models. It is shown that the proposed model which considers the wave spreading in both the sample and wedges can be used to interpret the measurements reasonably.

Dispersion analysis of leaky guided waves in fluid-loaded waveguides of generic shape

A fully coupled 2.5D formulation is proposed to compute the dispersive parameters of waveguides with arbitrary cross-section immersed in infinite inviscid fluids. The discretization of the waveguide is performed by means of a Semi-Analytical Finite Element (SAFE) approach, whereas a 2.5D BEM formulation is used to model the impedance of the surrounding infinite fluid. The kernels of the boundary integrals contain the fundamental solutions of the space Fourier-transformed Helmholtz equation, which governs the wave propagation process in the fluid domain. Numerical difficulties related to the evaluation of singular integrals are avoided by using a regularization procedure. To improve the numerical stability of the discretized boundary integral equations for the external Helmholtz problem, the so called CHIEF method is used. The discrete wave equation results in a nonlinear eigenvalue problem in the complex axial wavenumbers that is solved at the frequencies of interest by means of a contour integral algorithm. In order to separate physical from non-physical solutions and to fulfill the requirement of holomorphicity of the dynamic stiffness matrix inside the complex wavenumber contour, the phase of the radial bulk wavenumber is uniquely defined by enforcing the Snell-Descartes law at the fluid-waveguide interface. Three numerical applications are presented. The computed dispersion curves for a circular bar immersed in oil are in agreement with those extracted using the Global Matrix Method. Novel results are presented for viscoelastic steel bars of square and L-shaped cross-section immersed in water.

Rayleigh wave scattering from sessile droplets

Radiation of energy by large-amplitude leaky Rayleigh waves is regarded as one of the key physical mechanisms regulating the actuation and manipulation of droplets in surface acoustic wave (SAW) microfluidic devices. The interaction between a SAW and a droplet is highly complex and is presently the subject of extensive research. This paper investigates the existence of an additional interaction mechanism based on the propagation of quasi-Stoneley waves inside sessile droplets deposited on a solid substrate. In contrast with the leaky Rayleigh wave, the energy of the Stoneley wave is confined within a thin fluid layer in contact with the substrate. The hypothesis is confirmed by three-dimensional finite element simulations and ultrasonic scattering experiments measuring the reflection of Rayleigh waves from droplets of different diameters. Moreover, real-time monitoring of the droplet evaporation process reveals a clear correlation between the droplet contact angle and the spectral information of the reflected Rayleigh signal, thus paving the way for ultrasonic measurements of surface tension.

Study of factors affecting the magnitude and nature of ultrasound exposure with in vitro set-ups

Therapeutic ultrasound is a clinically applied method to improve fracture healing and holds great potential as a manipulator of biologic material relevant to tissue engineering approaches. Unfortunately, the cell stimulating property of ultrasound is not known, which inhibits the optimal use of this technique. Additionally, many in vitro studies in this field use ultrasound configurations that are vulnerable to errors during calibration and use. These errors arise from the structural simplicity and incomplete characterization of these configurations. In this study, pulse-echo ultrasound, laser Doppler vibrometry and Schlieren imaging were applied to noninvasively characterize common in vitro experimental configurations. Fine wire thermocouple measurements were conducted to characterize any possible temperature rise during the ultrasound exposures. The results quantified the frequency dependent sound transmission through culture wells and the standing wave effect within the cell volume. These effects can cause uncertainty of up to 700% in the actual ultrasound exposure experienced by the cell. A temperature rise of 2.7°C was measured from an ultrasound configuration commonly used in vitro ultrasound studies. Furthermore, wave mode conversion in culture wells was observed, emphasizing the complexity of these sonications. Similar type Lamb waves have been observed in bone in vivo. Thus, Lamb waves may be a mechanism for stimulating the cells.

Amplitude-modulated acoustic radiation force experienced by elastic and viscoelastic spherical shells in progressive waves

The dynamic acoustic radiation force resulting from a dual-frequency beam incident on spherical shells immersed in an inviscid fluid is examined theoretically in relation to their thickness and the contents of their interior hollow regions. The theory is modified to include a hysteresis type of absorption inside the shells' material. The results of numerical calculations are presented for stainless steel and absorbing lucite (PolyMethyMethacrylAte) shells with the hollow region filled with water or air. Significant differences occur when the interior fluid inside the hollow region is changed from water to air. It is shown that the dynamic radiation force function Yd deviates from the static radiation force function Yp when the modulation size parameter deltax = mid R:x2 - x1mid R: (x1 = k1a, x2 = k2a, k1 and k2 are the wave vectors of the incident ultrasound waves, and a is the outer radius of the shell) starts to exceed the width of the resonance peaks in the Yp curves.