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This study introduces a novel underground subwavelength seismic metamaterial (SM) designed to attenuate ultra-low-frequency surface waves. The SM comprises a three-component column featuring rubber embedded within a steel resonator. Through calculations utilizing the Bloch theorem and the sound cone method, we investigate the dispersion relations and vibration modes of three distinct SM configurations. Our proposed rubber-embedded SM exhibits a wide bandgap (BG) and effectively attenuates surface Rayleigh waves within the frequency ranges of 1.19–1.31Hz and 1.41–20Hz, respectively. We elucidate the mechanism behind BG formation by analyzing vibration modes. Additionally, through numerical simulations in both frequency and time domains, we validate the attenuation capabilities of the SM system within the BG and observe the deflection phenomena of surface waves. We further simulate seismic wave propagation within the SMs. Comparative analysis of two-dimensional building frames, with and without SM protection, under realistic seismic waves demonstrates significant vibration attenuation and structural protection provided by SMs. We explore the impact of geometric and material parameters, as well as the number of SM layers, on BG frequency range, designing an optimal SM model with the widest BG. Finally, we calculate transmission spectra for two- and three-dimensional subwavelength SMs and evaluate their efficacy in Rayleigh wave attenuation.

We have studied the influence of the methane gas (CH₄) pressure on the surface morphology, composition, structural and electrical properties of nitrogenated amorphous carbon (a-C:N) films grown by surface wave microwave plasma chemical vapor deposition (SWMP-CVD) using Scanning electron microscopy (SEM), Atomic force microscopy (AFM), Auger electron spectroscopy (AES), X-rays photoelectron spectroscopy (XPS), UV-visible spectroscopy and 4-point probe resistance measurement. We have succeeded in growing a-C:N films using a novel method of SWMP-CVD at room temperature and found that the surface morphology, bonding, optical and electrical properties of a-C:N films are strongly dependent on the CH₄ gas sources and the a-C:N films grown at higher CH₄ gas pressure have relatively high electrical conductivity.

A numerical investigation for the stability of the incompressible slip flow of normal quantum fluids (above the critical phase transition temperature) inside a microslab where surface acoustic waves propagate along the walls is presented. Governing equations and associated slip velocity and wavy interface boundary conditions for the flow of normal fluids confined between elastic wavy interfaces are obtained. The numerical approach is an extension (with a complex matrix pre-conditioning) of the spectral method. We found that the critical Reynolds number (Re_cr or the critical velocity) decreases significantly once the slip velocity and wavy interface effects are present and the latter is dominated (Re_cr mainly depends on the wavy interfaces).

Nitrogen-doped amorphous carbon (a-C:N) thin-films have been deposited on novel heat tolerant flexible plastic substrates by a newly developed microwave surface wave plasma chemical vapor deposition (MWSWP-CVD) method. Methane gas and also camphor dissolved with ethyl alcohol gas composition have been used as plasma source. Nitrogen gas has been used as a dopant material for a-C:N films. In this paper, the optical characteristics of absorption coefficients and band gaps for a-C:N are discussed. The optical band gap of a-C:N films was found to be approximately 1.7 eV, which is close to the suitable band gap for solar cell. The optical band gap of a-C:N was found to be dependent on the composition gas source pressures.

The n-type conductivity nitrogen-doped amorphous carbon (n-C) films have been grown by surface wave microwave chemical vapor deposition (SWP-CVD) on plastic and quartz substrates. The bonding, electrical and photovoltaic properties have been studied. The Tauc plot of UV-Visible measurement have shown that n-C films deposited on plastic have smaller optical band gaps compared to the films grown on quartz substrate at the same parameters. Temperature dependence and photoresponse measurements also have shown that the properties of n-C thin films deposited on plastic have higher photoelectrical response. Our experimental results have shown that the flexible polytetrafluoroethene plastic substrate is a reliable candidate for future photovoltaic applications.

Amorphous carbon nitride (a-CN_x) films were deposited on quartz substrates by newly developed surface wave microwave plasma chemical vapor deposition (SWMP-CVD) of alcohol camphoric carbon plasma source at room temperature. Then the a-CN_x films were heat-treated at various annealing temperatures (AT) in the 100–500°C range. The effects of heat treatment on the structural modifications were studied by Visible-Raman spectroscopy through the evolution of D and G peaks. The spectral evolution observed on heat-treated a-CN_x shows progressive formation of crystallites. Raman spectra have revealed the amorphous structure of as-grown a-CN_x films and the growth of nanocrystallinity upon increase of AT. These structural changes were further correlated with optical band gap and fraction of sp³ bonded carbons present, derived respectively from the UV-visible and photoelectron spectroscopy. The wide range of optical absorption coefficient characteristics is observed depending on the AT. The optical band gap of as-grown a-CN_x films is found to be approximately 2.8 eV; it gradually decreases to 2.5 eV for the films heat-treated at 300°C and then it decreases rapidly to 0.9 eV at 500°C. The results obtained are discussed and compared with the literatures.

We have studied the influence of the methane gas (CH₄) flow rate on the composition and structural and electrical properties of nitrogenated amorphous carbon (a-C:N) films grown by surface wave microwave plasma chemical vapor deposition (SWMP-CVD) using Auger electron spectroscopy, X-ray photoelectron spectroscopy, UV-visible spectroscopy, four-point probe and two-probe method resistance measurement. The photoelectrical properties of a-C:N films were also studied. We have succeeded to grow a-C:N films using a novel method of SWMP-CVD at room temperature and found that the deposition rate, bonding and optical and electrical properties of a-C:N films are strongly dependent on the CH₄ gas sources, and the a-C:N films grown at higher CH₄ gas flow rate have relatively high electrical conductivity for both cases of in dark and under illumination condition.

Nitrogen doped amorphous carbon (a-C:N) thin films were deposited on silicon and quartz substrates by microwave surface-wave plasma chemical vapor deposition (SWMP-CVD) technique at low temperatures (<100°C). We used argon (Ar), camphor dissolved in alcohol, and nitrogen (N) as carrier, source, and dopant gases, respectively. Optical band gap (E_g) decreased from 4.1 to 2.4 eV when the N gas concentration increased from 0% to 4.5%. The films were annealed at different temperatures ranging from 150°C to 450°C in Ar gas environment to investigate the optical and electrical properties of the films before and after annealing. Both E_g and electrical resistivity (ρ) decreased dramatically up to 0.95 eV and 57×10³ Ω cm at 450°C annealing. The structural modifications of the films leading them to become more graphitized as a function of the annealing temperature were confirmed by the characterization of Raman spectra.

The model of the composite symmetric waveguide consisting of self-focusing slab between defocusing nonlinear media separated by interfaces characterized by own nonlinearity response is proposed. Two new types of nonlinear surface waves propagating along it with anti-phase amplitude oscillations at interface planes are found. The frequencies of the nonlinear surface waves existing near the interfaces with the nonlinear response only are calculated analytically. The conditions of the surface wave existence are found. The frequencies and localization distances of the surface waves in dependence on nonlinearity waveguide parameters, slab width and interface characteristics are analyzed.

The nonlinear surface waves propagating along the ultra-thin-film layers with nonlinear properties separating three nonlinear media layers are considered. The model based on a stationary nonlinear Schrödinger equation with a nonlinear potential modeling the interaction of a wave with the interface in a short-range approximation is proposed. We concentrated on effects induced by the difference of characteristics of the layers and their two interfaces. The surface waves of three types exist in the system considered. The dispersion relations determining the dependence of surface waves energy on interface intensities and medium layer characteristics are obtained and analyzed. The localization energy is calculated in explicit form for many difference cases. The conditions of the wave localization on dependence of the layer and interface characteristics are derived. The surface waves with definite energies in specific cases existing only in the presence of the interface nonlinear response are found. All results are obtained in an explicit analytical form.

By introducing the concept of a graded structure to seismic metamaterials, a new type of graded seismic metamaterial assembled using four steel sections with different graded levels is proposed to investigate its attenuation performance for surface waves. The dispersion curves and vibration modes are obtained using the finite element method and the sound cone method. A comparative analysis of the band gap characteristics of the four graded seismic metamaterials shows that an increase of the graded level is beneficial for widening the total band gap to a much larger relative bandwidth in the range of 0.1–13.07 Hz. In addition, a detailed analysis of the vibration modes reveals that local resonance is the main mechanism for the generation and change of the three band gaps. Moreover, the filling materials in the cavities, material and geometric parameters of the structure play important roles in the distribution and relative bandwidth of the band gaps. Finally, frequency–domain analysis is carried out on a finite system, and the agreement with the bandgaps is verified. This study paves the way for the design of graded seismic metamaterials. This concept allows flexible manipulation of the surface wave propagation by adjusting the graded level, fillers, geometric parameters of the steel sections, and soil materials to achieve seismic wave attenuation in low-frequency broadband.

The assumption of quasi-static electric field in the problem of wave reflection in piezoelectric half-plane results in missing an independent electric wave mode at the piezoelectric boundary, which leads to oversimplified solutions of reflected waves in a strong piezoelectric medium if only elastic bulk wave boundary conditions are considered. The paper presents a novel solution to address the issue by using the inhomogeneous wave theory and introducing a virtual reflection wave mode in addition to the elastic bulk wave modes. The virtual wave is assumed to satisfy the Snell's law as well as the piezoelectric boundary condition and can be treated in the same way as the elastic bulk waves. The analysis results show that this virtual wave always propagates along the boundary for any incident angle and can be treated as a pseudo surface wave. The energy transmission analysis reveals that this surface wave transmits zero energy and does not violate the energy conservation between the incident and the reflected elastic bulk waves. In addition, the analysis also reveals an interesting result that the quasi-transverse, not the quasi-longitudinal, incident wave will be fully reflected and no quasi-longitudinal reflected wave will be generated if the incident angle is beyond a critical angle.

The isolation of surface wave-induced vibration using periodically modulated piles in soil is investigated. We demonstrate through simulations the dependence of complete bandgaps on the lattice symmetries, geometric parameters of the piles and material properties of the soil. The simulated results suggest that the piles modulated with square and hexagonal lattices are much more favorable for the formation of complete bandgaps than those modulated with honeycomb lattice. The height of the piles also plays a significant role in governing the evolution of complete bandgaps. Besides, complete bandgaps can be tuned by tailoring the volume fraction of the piles and the geometries of the pile cross section. Our results indicate that the contrast in the Young's modulus and the density is vital for the evolution of complete bandgaps and the viscosity of the soil should be considered as well. The analysis of surface wave propagation in a finite number of piles confirms the simulated complete bandgaps and also reveals that the complete bandgaps stem from Bragg interferences. This paper not only demonstrates the promising application of periodically modulated piles as wave barriers but also provides design guidelines for civil engineers.

Surface acoustic wave resonators are fabricated on a finite elastic substrate with proper mountings. In the analysis of the wave propagation of finite elastic solids with complications such as electrodes, mountings, and boundary conditions, approximate theory has to be developed based on dominant vibration modes and actual boundary conditions. In considering the effect of mountings in a finite elastic plate and vibration mode changes, we start from an elastic plate with one face rigidly fixed to examine the vibration frequency and mode changes in the vicinity of the surface acoustic wave velocity. For an isotropic elastic plate, we introduce two potential functions for the three-dimensional elasticity equations. Solutions satisfying the boundary conditions of one rigidly fixed face and one free face are obtained along with frequency equation. It is found that with the increase of the plate thickness, solutions of the velocity and displacements approach to Rayleigh wave solutions we are familiar with. We further obtain stresses of the plate with known plate thickness and wave velocity to see the overall changes in addition to the velocity itself and displacements. These results will be used in the analysis of surface acoustic waves in finite solids in conjunction of our recent work on the two-dimensional theory for the analysis of surface wave propagation in finite plates. Such analytical methods and procedures are essential in the analysis and design of surface acoustic wave resonators, which are based on finite anisotropic piezoelectric solids with structural complications.