Wave Propagation In Multilayered Media Research Articles

Impact of initial stress and voids on love wave propagation in multilayered media

This paper investigates Love-type wave propagation in a multilayered, elastic, prestressed solid half-space with voids. Using the Haskell matrix method, the dispersion relation is derived for a stress-free boundary surface. Two distinct dispersive fronts of Love-type waves, propagating at different speeds, are identified. One behaves like waves in a prestressed elastic half-space, while the other is novel due to voids. Analytical expressions for three-layered and two-layered models are provided. Graphical representations compare the dispersion curves, highlighting differences and dependencies. The study explores how void parameters, initial stress, and layer thickness influence phase velocity, with applications in various engineering fields.

Ground-Penetrating Radar Full-Wave Inversion for Soil Moisture Mapping in Trench-Hill Potato Fields for Precise Irrigation

In this paper, we analysed the effect of trench-hill soil surface on ground-penetrating radar (GPR) full-wave inversion for soil moisture measurement. We conducted numerical experiments by modelling the trench-hill surface using finite-difference time–domain (FDTD) simulations. The FDTD simulations were carried out with the open-source software gprMax, using different centre frequencies, namely, 150 MHz, 250 MHz and 450 MHz. The gprMax source/receiver for each centre frequency was calibrated, respectively, to transform the FDTD radar signal to normalized Green’s functions for wave propagation in multilayered media. The radar signals and inversion results of the three different frequency ranges are compared. The FDTD Green’s functions of the trench-hill surface with a flat surface are also compared. The results show that the trench-hill surface only slightly affects the inversion when frequency is lower than 190 MHz, which agrees with Rayleigh’s criterion. Field measurements were performed as well, using a prototype radar mounted on an irrigation robot. The low-frequency antenna was calibrated over a large water plane. The optimal operating frequency range was set to 130–190 MHz. TDR measurements were performed as well for comparison. The results demonstrated promising perspectives for automated and real-time determination of the root–zone soil moisture in potato fields, and thereby for precise and automatic irrigation.

Evaluating resonances in PCSEL structures based on modal indices

The frequently sought after combination of characteristics in semiconductor lasers of high power together with narrow beam divergence and monochromatic output is usually difficult to attain. The photonic crystal surface emitting laser (PCSEL) is one category of device, however, which tends to provide the above-mentioned desirable output features. The PCSEL uses a large area optically active surface but with a two-dimensional periodic structure that enables it to generate high power in a narrow vertically emitted beam yet maintaining single wavelength operation. A primary requirement to model PCSELs is to obtain the optical field resonances that identify the lasing mode. This study presents an alternative method for evaluating the resonances, based essentially on the transfer-matrix technique and wave propagation in multilayer medium, which is relatively easy to formulate, and has quite modest demands on computing requirements.

Ultrasonic pulse signal resonance features in layered CFRP within voids

The ultrasonic pulse signal resonance features in layered carbon fiber reinforced plastic (CFRP) within voids were researched. The frequency domain model of acoustic wave propagation in multilayered medium was established. Then the reflection coefficient of multilayered CFRP within voids was numerically calculated. The results are as follows. When the CFRP laminate is tested by ultrasonic whose center frequency is close to the CFRP inherent resonant frequency, the ultrasonic may generate resonance phenomenon in CFRP. If CFRP contains evenly distributed voids, the frequency of resonant signal and its amplitude all decrease with the increase of porosity. For the thick section CFRP within local concentrated voids, the local concentrated voids near testing surface will cause signal frequency reduction and the decrease of its amplitude. But the voids which exist in layers far away from testing surface almost have no influence on signal resonance. The ultrasonic pulse echo testing was conducted for thick section CFRP specimen. The analysis results of testing signals were in accordance with the results of the numerical calculation, showing that the reflection coefficient frequency response model can effectively explain the ultrasonic resonance phenomenon in layered CFRP within voids.

An improved model for nanosecond pulsed laser ablation of metals

A model is presented for the ablation of metals by nanosecond laser pulses, based on one-dimensional heat flow with temperature dependent material properties. A numerical optical calculation is introduced to account for laser beam absorption in the target, utilizing established matrix methods for electromagnetic plane wave propagation in multi-layered media. By including the effects of reflection from the dielectric-metal interface, the fall in reflectivity of aluminum during nanosecond laser pulses above the phase explosion threshold is found to be approximately twice that calculated in previous works. A simulated shielding coefficient is introduced to account for reflection and absorption of the incident laser beam by the ablation products. With these additions to foregoing models, good agreement between calculated and published experimental ablation data is attained for aluminum, both in terms of ablation threshold and depth. An investigation is subsequently carried out into the effects of laser wavelength, pulse duration and target thickness on the phase explosion threshold of aluminum.

An asymptotic decoupling method for waves in layered media

This paper presents a technique, asymptotic decoup- ling, for analysing wave propagation in multi-layered media. The technique leads to a hierarchy of approximations to the exact dispersion relation, obtained from finite-product approximations to low-order dispersion relations appearing as factors in the asymptotically decoupled limits. Levels of refinement may be added or removed according to the frequency range of interest, the degree of accuracy required, and the material and geometrical parameters of the different layers. This is shown to be particularly useful in stiff problems, because unlimited accuracy is obtainable without redundancy even when Young's moduli and the thicknesses of the layers differ by many orders of magnitude, for example in a stiff sandwich plate with a very soft core. Full details are presented for a non-trivial example, that of antisymmetric waves in a three-layered planar elastic waveguide. Comparisons are made with two widely used approximations, Tiersten's thin-skin approximation and the composite Timoshenko approximation. The mathematical basis of the paper is the asymptotic decoupling of the wave motion in different layers in the limit of indefinitely large or small density ratio.

다중 접착계면의 초음파 전달 모델 연구

본 연구는 다중 접착계면에서의 초음파 전달 현상을 시스템 응답함수의 일반식을 사용하여 시뮬레이션을 수행하였고, 추진기관의 모의결함시편을 제작하여 모델링의 결과를 검증하였다. 실험 결과 추진제-라이너 미접착 결함을 초음파 펄스 반사법으로 검출할 수 있었으며, 시뮬레이션 결과와 측정된 초음파 파형이 잘 일치함을 알 수 있었다. This research simulates the ultrasonic wave propagation in multi-layered media using generalized formular of system response function. We made the artificial defect specimen of a rocket motor and compared with experimental wave forms. The simulation results are coincide with measured waves and we found that the pulse echo method is able to detect unbond defect at liner-propellant interface.

The Investigation of Effective Material Concept for the Transient Wave Propagation in Multilayered Media

AbstractIn this article, the dynamic response in a multilayered medium is analyzed by Laplace transform technique. The thickness and material constant in each layer are different. The medium is subjected an uniformly distributed loading at the upper surface, and the bottom surface is assumed to be traction-free. The analytical solutions are presented in the transform domain and the numerical Laplace inversion (Durbin's formula) is performed to obtain the transient response in time domain. The effective material concept is usually used to simplify multilayered media in static analysis. The numerical calculations of the transient responses for randomly distributed, periodically distributed, and continuously distributed multilayered media are performed to investigate if the effective material concept is suitable for dynamic analysis.

An efficient approach for simulating seismoacoustic scattering due to an irregular fluid-solid interface in multilayered media

SUMMARY The seismoacoustic scattering due to an irregular fluid–solid interface must be considered when we model the seismic wave propagation in oceanic regions or gulf areas. In this paper, an efficient approach will be presented to treat this kind of problem. The approach can be viewed as an extension of the method originally developed for seismogram synthesis in multilayered solid media with irregular interfaces. In this method, we use the traditional boundary element method to discretize the boundary integral equation in each layer; then define the global matrix propagators by the boundary and continuity conditions in such way that they propagate the information of the element displacements and tractions ‘downwards’ for layers above the source while ‘upwards’ for layers below the source, finally solve the problem in the source layer. The main idea of the method is to use the global matrix propagators to suppress the tremendous increase in the memory requirement appearing in the traditional boundary element method when modelling wave propagation in multilayered media. As for the fluid–solid interface, the direct application of the above method is difficult since the global matrix propagators in fluid layers are much different from those defined in solid layers. By using the pressure as the variable inside the fluid layer, we can treat the acoustic wave propagation as a Helmoltz problem. The global matrix propagators can then be extended into the same size as those defined for solid layers by using the standard boundary conditions at the fluid–solid interface (i.e. normal traction continuity, zero tangential traction and normal displacement continuity). By the extended global matrix propagators we can thus propagate the information of the acoustic wave into the elastic wavefield and further obtain the results of the elastic wave propagation in arbitrary solid layers. To demonstrate the validity and feasibility of our method, we should compare our numerical results with the existing solutions. For problems of irregularly layered structures, however, we do not have exact (analytic) solutions. Therefore, it is important to compare the results calculated by completely different numerical methods to ensure validity. For such purpose, we calculate the cases of a plane P wave vertically incident onto two basin-like fluid–solid structures and an SV wave source located below a basin-like fluid–solid interface, of which the synthetic seismograms are accessible from the existing publications. Our results show almost complete agreement with those calculated by the reflection/transmission matrix method and those calculated by the discrete wavenumber method. Second, we calculate the synthetic time domain waveforms for a model with and without a basin-like fluid layer. Comparison observation clearly shows the effects of the fluid layer on the seismic ground motion at land in which seismologists or geophysicists may be of great and practical interests. Furthermore, we take into account the case when an explosive source is located in a fluid layer and illustrate that the method can simulate the water reverberation in the sea. That makes significant sense to deep ocean acoustic experiments.

Generalized Reverberation Matrix Formulation for Wave Propagation in Multilayered Medium

Generalized reverberation matrix (GRM) formulation is presented to investigate elastic wave propagation in a complex multilayered solid by the combination of reverberation-ray matrix (RRM) method and stiffness matrix (SM) method. RRM method formulates a reverberation matrix, which reflects the reflection or refraction of the elastic waves in the multilayered solid. However, the dimension of RRM increases as the sublayer number increases, which may result in lower calculation efficiency of the generalized rays. SM formulation yields a system matrix of the constant dimension to promise higher calculation efficiency, but it is difficult to identify the generalized rays. In order to calculate the generalized rays in the complex multi-layered solid efficiently, the RRM formulation is applied to the interested sublayer for the evaluation of the generalized rays and SM formulation to the other sublayers, to construct a generalized reverberation matrix of the constant dimension, which is independent of the sublayer number. Numerical examples show that GRM formulation has higher calculation efficiency for the generalized rays in the complex multilayered-solid configuration compared with RRM formulation.

MRFD method for numerical solution of wave propagationin layered media with general boundary condition

A fast adaptive wavelet-based method, called multiresolution finite difference (MRFD), is proposed to simulate the wave propagation in multilayered media with general boundary. It is a promising method for complex media because of its robustness and small computational burden. Numerical results derived from geophysics exploration show the effectiveness and potential of the method.

SIMULATION OF ACOUSTIC WAVE PROPAGATION IN COMPLEX MEDIA USING MRFD METHOD

This paper is devoted to the simulation of acoustic wave propagation in complex media, applying the finite difference scheme and the orthonormal compactly supported wavelet transform approximation,to the time and the space dimension of the wave equation, respectively. A new method, which is a fast adaptive arithmetic, named Multiresolution Finite Difference (MRFD) is first proposed to solve the problem of the wave propagation in multi-layered medium with nonperiodic boundary condition. Thus the problem is solved in the wavelet domain rather than in the traditional Euclidian space. Due to adaptive and vanishing-moment property of the wavelet basis, the difference operator and solution vector have sparseness in the wavelet domain. MRFD is a promising method because of some advantages such as lighter computational burden, efficiency of convergence and robustness. Numerical results in geophysics exploration show the effectiveness and potential of the method.

Wave propagation in multilayered media

Wave propagation in multilayered media

Ultrasonic study of adhesive bond quality at a steel-to-rubber interface by using quadrature phase detection techniques

The quadrature phase detection technique was used to simultaneously monitor the phase and amplitude of a toneburst signal normally reflected from an adhesively bonded steel-to-rubber interface. The measured phase was found to show a positive shift for all bonded samples with respect to the disbonded state - the phase shift being larger for samples with weaker bonds, as manifested by smaller values of applied tensile loads at failure. A model calculation, which incorporates the concept of interfacial strength into the usual problem of wave propagation in multilayered media, was used to deduce a bond-quality parameter from an experimentally measured phase shift. This bond-quality parameter was found to be correlated with the tensile strength of the adhesive bonds at failure loads.

Ultrasonic study of adhesive bond quality at a steel-to-rubber interface by using quadrature phase detection techniques: Materials evaluation, vol. 47, no. 12, pp. 1396–1400 (Dec. 1989)

The quadrature phase detection technique was used to simultaneously monitor the phase and amplitude of a toneburst signal normally reflected from an adhesively bonded steel-to-rubber interface. The measured phase was found to show a positive shift for all bonded samples with respect to the disbonded state - the phase shift being larger for samples with weaker bonds, as manifested by smaller values of applied tensile loads at failure. A model calculation, which incorporates the concept of interfacial strength into the usual problem of wave propagation in multilayered media, was used to deduce a bond-quality parameter from an experimentally measured phase shift. This bond-quality parameter was found to be correlated with the tensile strength of the adhesive bonds at failure loads.

A boundary integral equation‐discrete wavenumber representation method to study wave propagation in multilayered media having irregular interfaces

We present a method which combines boundary‐integral equation techniques with the discrete wavenumber Green’s function representation to study wave propagation in multilayered media having irregular interfaces. The approach is based on the representation of the interfaces by distributions of body forces, the radiation from which is equivalent to the scattered wave field produced by the diffracting boundaries. The Green’s functions are evaluated by the discrete wavenumber method. Propagator matrices are introduced to relate force distributions on neighboring interfaces. The solution then requires the inversion of a matrix at each interface. The dimensions of the linear system are independent of the number of layers considered, and the computation time varies linearly with the number of interfaces. We apply the method to calculate surface and vertical seismic profiles in the presence of synclinal or anticlinal structures.

Analysis of electromagnetic wave propagation in multilayered media using dyadic Green's functions

The propagation of electromagnetic waves in media with various horizontal layers has been analyzed. The electromagnetic fields outside the source region were obtained from the dyadic Green's functions for the case of media with three and four layers and for horizontal and vertical electric dipoles. These results agree with those obtained using Hertz potentials. One of the major results is a generalization of the dyadic Green's functions for solving the problem of media with N horizontal layers.

Numerical solution of stress waves in layered media.

A numerical study is made of the transient elastic stress distribution in cylindrical and spherical bodies subjected to a radially symmetric transient normal pressure (or velocity) at an internal or external surface. The numerical procedure employs the characteristic relations on boundaries and on interfaces between media with different material properties while using an explicit finite difference scheme at all other points. In addition, as an option, the procedure can incorporate the exact jump conditions across discontinuous wave fronts. Problems with and without external boundaries are solved, and results are shown which clearly indicate the propagation of discontinuities in stress due to a step loading on the boundary. Comparison of these results with those available from other investigators yields excellent agreement. Results are also given for stress wave propagation in multilayered media consisting of two layers with different material properties.

A matrix method for elastic wave problems

abstract The solution to problems of elastic wave propagation in multilayered media, in which each layer is homogeneous and where the ensemble of layers has physical properties that vary only with one coordinate, may be given as the quotient of products of matrices. In the case of SH waves, the matrices are of order two; in the case of P-SV waves the matrices are of order four. The individual matrix elements are themselves determinants of order two or four in the two cases. The solution is obtained by means of Laplace's development by minors.