Joint Inversion of Rayleigh and Love Dispersion Curves Extracted from Ambient Seismic Noise Based on Secular Function

Traditional multi-mode dispersion curve inversion requires correct mode discrimination. However, when the stratum contains complex structures such as low-speed soft interlayer or high-speed hard interlayer, the dispersion curve may show phenomena such as “mode kissing” and “mode jumping”, which can easily cause mode misjudgment and lead to erroneous inversion results. Based on the “secular function”, this paper constructs a new type of objective function applied to the inversion of dispersion curve. This objective function does not require prior mode discrimination, which effectively solves the “mode misjudgment” problem of multi-mode dispersion curve inversion. The joint inversion of Rayleigh and Love dispersion curves extracted from ambient seismic noise is used to improve the constraint of the inversion and avoid the inversion falling into a local minimum in the case of a large-scale search of parameters. Finally, a numerical simulation was performed to verify the feasibility of the new inversion method.

Quantitative and nondestructive determination of residual stress for SiO2 thin film by laser-generated surface acoustic wave technique

The laser-generated surface acoustic wave (SAW) technique is a promising method to measure the mechanical properties of thin films quickly and nondestructively. Residual stress is inevitable during the processing and manufacturing of integrated circuits, which will have a major impact on the physical and mechanical properties of the thin film materials and cause deterioration to the structural strength. In this study, the SAW technique based method is proposed for quantitative and nondestructive measuring the residual stress in the nanostructured films. The method is verified by the experiment measuring the SiO2 films in the thickness range of 100 to 2000 nm. The experimental procedures, including signal excitation, reception and processing, are described in detail. By matching the SAW experimental dispersion curve with the calculated theoretical dispersion curve containing the residual stress, the residual stress of the SiO2 films along [110] and [100] crystallographic orientation of the Si wafer is successfully quantified. The determination results are ranged from -65.5 to 421.1 MPa and the stress value increases as the film thickness decreases, revealing the residual stress of the SiO2 film is compressive. Meanwhile, the conventional substrate curvature method as a comparison is used to verify the correctness and feasibility of the proposed SAW method for the residual stress determination.

A Robust Workflow for Acquiring and Preprocessing Ambient Vibration Data from Small Aperture Ocean Bottom Seismometer Arrays to Extract Scholte and Love Waves Phase-Velocity Dispersion Curves

The phase-velocity dispersion curve (DC) is an important characteristic of the propagation of surface waves in sedimentary environments. Although the procedure for DC estimation in onshore environments using ambient vibration recordings is well established, the DC estimation in offshore environments using Ocean Bottom Seismometers (OBS) array recordings of ambient vibrations presents three additional challenges: (1) the localization of sensors, (2) the orientation of the OBS horizontal components, and (3) the clock error. Here, we address these challenges in an inherent preprocessing workflow to ultimately extract the Love and Scholte wave DC from small aperture OBS array measurements performed between 2018 and 2020 in Lake Lucerne (Switzerland). The arrays have a maximum aperture of 679 m and a maximum deployment water depth of 81 m. The challenges related to the OBS location on the lake floor are addressed by combining the multibeam bathymetry map and the backscatter image for the investigated site with the differential GPS coordinates of the OBS at recovery. The OBS measurements are complemented by airgun surveys. Airgun data are first used to estimate the misorientation of the horizontal components of the OBS and second to estimate the clock error. To assess the robustness of the preprocessing workflow, we use two array processing methods, namely the three-component high-resolution frequency-wavenumber and the interferometric multichannel analysis of surface waves, to estimate the dispersion characteristics of the propagating Scholte and Love waves for one of the OBS array sites. The results show the effectiveness of the preprocessing workflow. We observe the phase-velocity dispersion curve branches in the frequency range between 1.2 and 3.2 Hz for both array processing techniques.

Reconstruction of Lamb Wave Dispersion Curves in Different Objects Using Signals Measured at Two Different Distances

The possibilities of an effective method of two adjacent signals are investigated for the evaluation of Lamb waves phase velocity dispersion in objects of different types, namely polyvinyl chloride (PVC) film and wind turbine blade (WTB). A new algorithm based on peaks of spectrum magnitude is presented and used for the comparison of the results. To use the presented method, the wavelength-dependent parameter is proposed to determine the optimal distance range, which is necessary in selecting two signals for analysis. It is determined that, in the range of 0.17–0.5 wavelength where δcph is not higher than 5%, it is appropriate to use in the case of an A0 mode in PVC film sample. The smallest error of 1.2%, in the distance greater than 1.5 wavelengths, is obtained in the case of the S0 mode. Using the method of two signals analysis for PVC sample, the phase velocity dispersion curve of the A0 mode is reconstructed using selected distances x1 = 70 mm and x2 = 70.5 mm between two spatial positions of a receiving transducer with a mean relative error δcph=2.8%, and for S0 mode, x1 = 61 mm and x2 = 79.7 mm with δcph=0.99%. In the case of the WTB sample, the range of 0.1–0.39 wavelength, where δcph is not higher than 3%, is determined as the optimal distance range between two adjacent signals. The phase velocity dispersion curve of the A0 mode is reconstructed in two frequency ranges: first, using selected distances x1 = 225 mm and x2 = 231 mm with mean relative error δcph=0.3%; and second, x1 = 225 mm and x2 = 237 mm with δcph=1.3%.

Numerical Solution of the Wave Propagation Problem in a Plate

In this work, we use the phase velocity method in combination with finite element method to compute the dispersion curve for phase velocity of an ultrasonic pulse traveling in a thin isotropic plate. This method is based on the numerical solution of the wave propagation equations for several selected frequencies. To solve these equations, a second order difference scheme is used to discretize the temporal variable, while spatial variables are discretized using the finite element method. The variational formulation of the problem corresponding to a fixed value of time is obtained and the existence and uniqueness of the solution is proved. A priori error estimates in the energy norm and in the [Formula: see text] norm are also obtained. The open software FreeFem++ is used with quadratic triangular elements to compute the displacements. Numerical experiments show that the velocities computed from the approximated displacements for different frequency values are in good agreement with analytical dispersion curve. This confirms that the proposed symbiosis between finite element and phase velocity method is suitable for computing dispersion curves in more general wave propagation problems, where the geometry is complex and the material is anisotropic.

(Generalized) Bloch mode synthesis for the fast dispersion curve calculation of 3D periodic metamaterials

Metamaterials, i.e. artificial structures with unconventional properties, have shown to be highly potential lightweight and compact solutions for the attenuation of noise and vibrations in targeted frequency ranges, called stop bands. In order to analyze the performance of these metamaterials, their stop band behavior is typically predicted by means of dispersion curves, which describe the wave propagation in the corresponding infinite periodic structure. The input for these calculations is usually a finite element model of the corresponding unit cell. Most common in literature are 2D plane metamaterials, which often consist of a plate host structure with periodically added masses or resonators. In recent literature, however, full 3D metamaterials are encountered which are periodic in all three directions and which enable complete, omnidirectional stop bands. Although these 3D metamaterials have favorable vibro-acoustic characteristics, the computational cost to analyze them quickly increases with unit cell model size. Model order reduction techniques are important enablers to overcome this problem. In this work, the Bloch Mode Synthesis (BMS) and generalized BMS (GBMS) reduction techniques are extended from 2D to 3D periodic structures. Through several verifications, it is demonstrated that dispersion curve calculation times can be strongly reduced, while accurate stop band predictions are maintained.

Design of a metamaterial-based muffler for a target frequency range

This work proposes an acoustic metamaterial-based muffler that effectively blocks a transmission noise for a target frequency range. Since the acoustic metamaterial-based muffler consists of arrayed unit cells, its noise attenuation performance is strongly affected by the internal layout of the unit cell. The wave transmission characteristics of an acoustic metamaterial is explained by the effective bulk modulus and dispersion curve of an unit cell. Therefore, the internal layout of the unit cell should be optimally designed so that its band gap should include the target frequency range of a muffler. To the end, an acoustical size optimization problem is formulated to design a unit cell of the muffler and is solved for a given design requirement. The noise blocking frequency range of the unit cell is characterized by the bandgap in its dispersion curve during the optimization process. The wave transmission characteristics of the metamaterial muffler is validated experimentally.

Impact of the unit cell choice on the efficiency of dispersion curve calculations using GBMS

Recently, the potential of metamaterials and phononic crystals to cope with conflicting requirements of obtaining lightweight structures with desirable noise and vibration properties has been demonstrated. These, often periodic, structures are commonly studied based on their representative unit cell of which the vibro-acoustic performance is examined by means of their wave propagation, visualized by dispersion curves. Typically, the unit cell is discretized using a finite element technique to capture the possibly complex geometry. This leads to a high computation cost for the dispersion curve calculation which can be strongly reduced by applying modal based model order reduction techniques such as the (generalized) Bloch mode synthesis. In this paper, the choice of the unit cell is shown to have an impact on the dispersion curve calculation time. Moreover, the efficiency of (generalized) Bloch mode synthesis strongly depends on the unit cell choice. The highest reduction in computation time is accomplished when the number of boundary degrees-of-freedom is limited.