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This paper describes the concept of natural attenuation and its role as a remediation method. It contains examples illustrating the various modalities via which natural attenuation may assist in dealing with environmental contamination.

The purpose of this study is to investigate the reflection of plane waves in a double-porosity (DP) thermoelastic medium.

To derive the theoretical formulas for elastic wave propagation velocities through the potential decomposition of wave-governing equations. The boundary conditions have been designed to incorporate the unique characteristics of the surface pores, whether they are open or sealed. This approach provides a more accurate and realistic mathematical interpretation of the situation that would be encountered in the field. The reflection coefficients are obtained through a linear system of equations, which is solved using the Gauss elimination method.

The solutions obtained from the governing equations reveal the presence of five inhomogeneous plane waves, consisting of four coupled longitudinal waves and a single transverse wave. The energy ratios of reflected waves are determined for both open and sealed pores on the stress-free, the thermally insulated surface of DP thermoelastic medium. In addition, the energy ratios are compared for the cases of a DP medium and a DP thermoelastic medium.

A numerical example is considered to investigate the effect of fluid type in inclusions, temperature and inhomogeneity on phase velocities and attenuation coefficients as a function of frequency. Finally, a sensitivity analysis is performed graphically to observe the effect of the various parameters on propagation characteristics, such as propagation/attenuation directions, phase shifts and energy ratios as a function of incident direction in double-porosity thermoelasticity medium.

A simple interaction‐potential model has been established to calculate the higher order elastic constants of intermetallic YbAl2 in the temperature range from 10‐300K. Temperature dependent second and third order elastic constants are used for the determination of the ultrasonic attenuation, velocity, Grüneisen numbers, Acoustic‐coupling constants, and thermal relaxation time at the different temperatures. Temperature dependency of the ultrasonic properties of YbAl2 is similar at low temperatures to that of pure metals and the low carrier heavy fermion systems ‐ LaSb, YbAs and YbP having simple NaCl‐type structures. Thermal energy density makes significant contribution to the total attenuation in the compound at the higher temperatures from 100‐300K. Effect of the magnetic field on the ultrasonic attenuation is also evaluated using the magneto resistance data. At 100K, the effect of the magnetic field becomes insignificant. The attenuation decreases with the field at 3K to 50K.

This mathematical analysis has been accomplished for the purpose of understanding the propagation behaviour like phase velocity and attenuation of Love-type waves through visco-micropolar composite Earth’s structure.

The considered geometry of this problem involves a micropolar Voigt-type viscoelastic stratum imperfectly bonded to a heterogeneous Voigt-type viscoelastic substratum. With the aid of governing equations of motion of each individual medium and method of separation of variable, the components of micro-rotation and displacement have been obtained.

The boundary conditions of the presumed geometry at the free surface and at the interface, together with the obtained components of micro-rotation, displacement and mechanical stresses give rise to the determinant form of the dispersion relation. Moreover, some noteworthy cases have also been extrapolated in detail. Graphical interpretation irradiating the impact of viscoelasticity, micropolarity, heterogeneity and imperfectness on the phase velocity and attenuation of Love-type waves is the principal highlight of the present study.

In this study, the influence of the considered parameters such as micropolarity, viscoelasticity, heterogeneity, and imperfectness has been elucidated graphically on the phase velocity and attenuation of Love-type waves. It has been noticed from the graphs that with the rising magnitude of micropolarity and heterogeneity, the attenuation curves shift upwards, that is the loss of energy of these waves takes place in a rapid way. Hence, from the outcomes of the present analysis, it can be concluded that heterogeneous micropolar stratified media can serve as a helpful tool in increasing the attenuation or in other words, loss of energy of Love-type waves, thus reducing the devastating behaviour of these waves.

Till date, the mathematical modelling as well as vibrational analysis of Love-type waves in a viscoelastic substrate overloaded by visco-micropolar composite Earth’s structure with mechanical interfacial imperfection remain unattempted by researchers round the globe. The current analysis is an approach for studying the traversal traits of surface waves (here, Love-type waves) in a realistic stratified model of the Earth’s crust and may thus, serves as a dynamic paraphernalia in various domains like earthquake and geotechnical engineering; exploration geology and soil mechanics and many more, both in a conceptual as well as pragmatic manner.

The purpose of this article is to investigate the propagation characteristics (such as particle motion, attenuation and phase velocity) of a Rayleigh wave in a nonlocal generalized thermoelastic media.

The bulk waves are represented with Helmholtz potentials. The stress-free insulated and isothermal plane surfaces are taken into account. Rayleigh wave dispersion relation has been established and is found to be complex. Due to the presence of radicals, the dispersion equation is continuously computed as a complicated irrational expression. The dispersion equation is then converted into a polynomial equation that can be solved numerically for precise complex roots. The extra zeros in this polynomial equation are eliminated to yield the dispersion equation’s roots. These routes are then filtered for inhomogeneous wave propagation that decays with depth. To perform numerical computations, MATLAB software is used.

In this medium, only one mode of Rayleigh wave exists at both isothermal and insulated boundaries. The thermal factors of nonlocal generalized thermoelastic materials significantly influence the particle motion, attenuation and phase velocity of the Rayleigh wave.

Numerical examples are taken to examine how the thermal characteristics of materials affect the existing Rayleigh wave’s propagation characteristics. Graphical analysis is used to evaluate the behavior of particle motion (such as elliptical) both inside and at the isothermal (or insulated) flat surface of the medium under consideration.

This study aimed to determine the peak impact force and force attenuation capacity of weft-knitted spacer fabrics intended for padding that can be used for human body protection against impact.

A total of five weft-knitted spacer fabrics were fabricated with four different diameters of nylon monofilament yarns and one doubled monofilament yarns, respectively. The impact performances of the weft-knitted spacer fabrics were tested using a drop test method with a customized test rig to simulate falling. Impact tests were conducted on single- and multilayered experimental spacer fabrics to investigate the peak impact force and force attenuation capacity.

It was found that weft-knitted spacer fabric with a coarser or larger diameter of monofilament spacer yarn generated lower impact force and higher force attenuation capacity, thus resulting in better impact performance. Greater force attenuation can be achieved by utilizing a higher number of spacer fabric layers. However, the increase in thickness must be considered with the spacer fabric end use.

This study employed relatively coarse nylon monofilament yarn as spacer yarns to gain knowledge on the impact performance of weft-knitted spacer fabrics compared to warp-knitted spacer fabrics which are more common. The results showed that the diameter of spacer yarn significantly influenced the impact performance of the experimental weft-knitted spacer fabrics. These results could be useful for designing and engineering textile-based impact protectors.

The purpose of this paper is to numerically investigate time-harmonic elastic wave propagation with the analysis of effective wave velocities and attenuation coefficients in a three-dimensional elastic composite consisting of infinite matrix and uniformly distributed soft, low-contrast and absolutely rigid disc-shaped micro-inclusions.

Within the assumptions of longitudinal mode of a propagating wave as well as dilute concentration and parallel orientation of inclusions in an infinite elastic matrix, Foldy’s dispersion relation is applied for introducing a complex and frequency-dependent wavenumber of homogenized structure. Then, the effective wave velocities and attenuation coefficients are directly defined from the real and imaginary parts of wavenumber, respectively. Included there a far-field forward scattering amplitude by a single low-contrast inclusion given in an analytical form, while for the other types of single scatterers it is determined from the numerical solution of boundary integral equations relative to the displacement jumps across the surfaces of soft inclusion and the stress jumps across the surfaces of rigid inclusion.

On the frequency dependencies, characteristic extremes of the effective wave velocities and attenuation coefficients are revealed and analyzed for different combinations of the filling ratios of involved types of inclusions. Anisotropic dynamic behavior of composite is demonstrated by the consideration of wave propagation in perpendicular and tangential directions relatively to the plane of inclusions. Specific frequencies are revealed for the first case of wave propagation, at which inclusion rigidities do not affect the effective wave parameters.

This paper develops a micromechanical study that provides a deeper understanding of the effect of thin-walled inclusions of diversified rigidities on elastic wave propagation in a three-dimensional composite. Described wave dispersion and attenuation regularities are important for the non-destructive testing of composite materials by ultrasonics.

The acousto-ultrasonic approach is used for propagating stress waves through different configurations of CORTEN steel specimens. The propagated waves are recorded and analysed by piezoelectric sensors. The purpose of the study is to study the characteristics of the CORTEN steel by analysing the propagated waves.

To investigate the attenuation in acoustic wave propagation due to the corrosion formation in CORTEN steel specimens and to train a neural network model to classify the attenuated acoustic waves automatically.

Due to the corrosion formation in CORTEN steel specimens, attenuation is observed in amplitude, energy, counts and duration of the propagated waves. When the waves are analysed in their time-frequency characteristics, attenuation is observed in their frequency and spectral energy.

The corrosion formation in CORTEN steel can automatically be analysed by using the acousto-ultrasonic approach and the trained deep learning neural network.

The purpose of the present study is to investigate the dispersion and damping behaviors of Love-type waves propagating in an irregular fluid-saturated fissured porous stratum coated by a sandy layer.

Two cases are analyzed in this study. In case-I, the irregular fissured porous stratum is covered by a dry sandy layer, whereas in case-II, the sandy layer is considered to be viscous in nature. The method of separation of variables is incorporated in this study to acquire the displacement components of the considered media.

With the help of the suitable boundary conditions, the complex frequency relation is established in each case leading to two distinct equations. The real and imaginary parts of the complex frequency relation define the dispersion and attenuation properties of Love-type waves, respectively. Using the MATHEMATICA software, several graphical implementations are executed to illustrate the influence of the sandiness parameter, total porosity, volume fraction of fissures, fluctuation parameter, flatness parameters and ratio of widths of layers on the phase velocity and attenuation coefficient. Furthermore, comparison between the two cases is clearly framed through the variation of aforementioned parameters. Some particular cases in the presence and absence of irregular interfaces are also analyzed.

To the best of the authors' knowledge, although many articles regarding the surface wave propagation in different crustal layers have been published, the propagation of Love-type waves in a sandwiched fissured porous stratum with irregular boundaries is still undiscovered. Results accomplished in this analytical study can be employed in different practical areas, such as earthquake engineering, material science, carbon sequestration and seismology.

Attenuation characteristics of microstrip transmission lines on alumina substrates up to 50GHz are discussed. The lines under test came from three different manufacturers, each of whom used different processes to realise the transmission lines. Two of the manufacturers used silver (Ag) paste, whereas the process of one of the manufacturers was copper (Cu) based. Each manufacturer used identical alumina substrates and identical test pattern files so that the measured attenuation properties reflected manufacturer’s capability to fabricate microstrips and the quality of the metal system used. Measurements showed that the attenuation of copper microstrips was slightly lower than that of the silver microstrips, but the difference was small. Measured attenuation (S21) of about 50Ω microstrips was approximately 0.5db/cm at 30GHz and 0.8dB/cm at 50GHz, respectively. The loss coefficient, α_t, of about 0.035dB/mm at 40GHz was obtained for the Cu microstrips. Such an attenuation is reasonable for many practical applications in the microwave and millimetre wave regions.