Search Results (19)

In this paper, we investigate the physical mechanics of vibration wave detection in distributed acoustic sensing (DAS) systems with the aim of enhancing the interpretation of the quantitative wavefield. We investigate the nonlinear relationship of DAS gauge length and pulse width on the seismic wave response, and the result is explained by the trigonometric relationship of backscattered Rayleigh wave phases. We further demonstrate the influence of spiral winding on DAS performance and also build phase response models for P-waves and S-waves in helically wound cables. These models suggest that the winding angle controls the measurement interval spacing and the angle of wave incidence. Additionally, integration of structural reinforcement improves the amplitude response characteristics and SNR. The experimentally inspired results show, using simulations and field tests, that the same vibration sources can give helically wound cables with larger winding angles the largest phase amplitudes, which would substantially exceed that of straight cables. SNR increased significantly (approximately 10% to 30%). The efficacy of the method was also checked using experiments for different vibration amplitudes and frequencies. Such results provide evidence for the design and installation of fiber-optic cables for use in practical engineering applications involving safety monitoring. Full article

This paper presents the design, simulation, and fabrication of a horn antenna integrated with a dielectric lens for focusing RF energy at 10 GHz. The antenna system combines established electromagnetic principles with 3D printing techniques to produce a cost-effective alternative to commercial focusing antennas. The design methodology employs the lensmaker’s formula and Snell’s law to determine lens curvature for achieving a specified focal length of 100 mm. COMSOL Multiphysics simulations indicate that adding a PTFE lens increases power density concentration compared to a standard horn antenna, with a simulated focal point at approximately 100 mm. Surface roughness analysis based on the Rayleigh criterion supports 3D printing suitability for this application. Experimental validation includes radiation pattern measurements of the antenna without the lens and power density measurements versus distance with the lens, both showing good agreement with simulation results. The measured focal length was $95\pm 5$ mm, closely matching simulation predictions. This work presents an approach for implementing focused RF delivery solutions for medical treatments, wireless power transfer, and precision sensing at significantly lower costs than commercial alternatives. Full article

This study investigates the propagation of shear horizontal transverse waves in a functionally graded piezoelectric half-space (FGPHS), where the material properties vary linearly and quadratically. The analysis focuses on deriving and understanding the dispersion characteristics of such waves in in-homogeneous media. The WKB approximation method is employed to obtain the dispersion relation analytically, considering the smooth variation of material properties. To validate and study the wave behavior numerically, two advanced techniques were utilized: the Semi-Analytical Finite Element with Perfectly Matched Layer (SAFE-PML) and the Semi-Analytical Infinite Element (SAIFE) method incorporating a (1/r) decay model to simulate infinite media. The numerical implementation uses the Rayleigh–Ritz method to discretize the wave equation, and Gauss 3-point quadrature is applied for efficient numerical integration. The dispersion curves are plotted to illustrate the wave behavior in the graded piezoelectric medium. The results from SAFE-PML and SAIFE are in excellent agreement, indicating that these techniques effectively model the shear horizontal transverse wave propagation in such structures. This study also demonstrates that combining finite and infinite element approaches provides accurate and reliable simulation of wave phenomena in functionally graded piezoelectric materials, which has applications in sensors, actuators, and non-destructive testing. Full article

The nonlinear deformation and vibrations of elastic plates represent a fundamental problem in structural vibration analysis, frequently encountered in engineering applications and classical mathematical studies. In the field of studying the nonlinear phenomena of elastic plates, numerous methods and techniques have emerged to obtain approximate and exact solutions for nonlinear differential equations. A particularly powerful and flexible method, known as the extended Rayleigh–Ritz method (ERRM), has been proposed. In this approach, the temporal variable is introduced as an additional dimension in the formulation. Through expanded integration across both the physical domain and a vibration period, the temporal variable is eliminated. The ERRM builds on the traditional RRM that offers a straightforward, sophisticated, and highly effective way to approximate solutions for nonlinear vibration and deformation issues in the realm of structural dynamics and vibration. In the case of circular plates, the method incorporates the linear displacement function along with high-frequency terms. As a result, it can accurately determine the nonlinear axisymmetric vibration frequencies of circular plates. For scenarios involving smaller deformations, its accuracy is on par with other approximate solution methods. This approach provides a valuable and novel procedure for the nonlinear analysis of circular structural vibrations. Full article

Lightweight components can have structural integrity and reliability concerns, coming from dynamic airborne pressure fields. Hardly tuned numerical structural models may enter into vibro-acoustic simulations of the pressure fields radiated by vibrating plates, potentially masking the forecast of severe outputs. Instead, this paper proposes—for the direct and inverse vibro-acoustic approaches—to characterise the broad frequency band structural dynamics of radiating surfaces by means of experiment-based full-field contactless techniques, with increased spatial resolution, but without the inertia-related distortions of traditional measurement transducers. The SLDV-based mobilities bring the real-life behaviour of the component into the vibro-acoustic simulations, with the actual realisation-related complete structural dynamics and broad frequency band excitation. The paper aims at assessing the procedure for the estimation, in the whole spectrum, of the airborne force, which can be transmitted by an airborne pressure field to known structural locations. The simulation tools revisit the simple Rayleigh integral approximation of sound radiation from a vibrating surface, a real thin flat plate, describable by SLDV-based complex-valued full-field mobilities. Airborne pressure fields and excitation forces concern the early attempts of direct and pseudo-inverse vibro-acoustics. Details, examples and considerations about the whole procedures are thoroughly provided: on the simulation of the vibro-acoustic transfer matrix and of the radiated sound pressures with given excitation forces; on the retrieval of the airborne forces in restraining locations, together with the assessment of the numerical precision of the retrieving procedure. Full article

Thin sound-absorbing materials are particularly desired in space-constrained applications, such as in the automotive industry. In this study, we theoretically analyzed the structure of relatively thin glass wool or polyester wool laminated with a nonpermeable polyethylene membrane and a permeable nonwoven fabric sheet. We also measured and compared the sound-absorption coefficients of these samples between experimental and theoretical values. The sound-absorption coefficient was derived using the transfer matrix method. The Rayleigh model was applied to describe the acoustic behavior of glass wool and nonwoven sheet, while the Miki model was used for polyester wool. Mathematical formulas were employed to model an air layer without damping and a vibrating membrane. These acoustic components were integrated into a transfer matrix framework to calculate the sound-absorption coefficient. The sound-absorption coefficients of glass wool and polyester wool were progressively enhanced by sequentially adding suitable nonwoven fabric and PE membranes. A sample approximately 10 mm thick, featuring permeable and nonpermeable membranes as outer layers of porous sound-absorbing material, achieved a sound-absorption coefficient equivalent to that of a sample occupying 20 mm thickness (10 mm of porous sound-absorbing material with a 10 mm back air layer). Full article

In this paper, diffraction of scalar waves by a screen with a circular aperture is explored, considering the incidence of either a collimated beam or a focused wave, a historical review of the development of the theory is presented, and the introduction of the Fresnel approximation is described. For diffraction by a focused wave, the general case is considered for both high numerical aperture and for finite values of the Fresnel number. One aim is to develop a theory based on the use of dimensionless optical coordinates that can help to determined the general behaviour and trends of different system parameters. An important phenomenon, the focal shift effect, is discussed as well. Explicit expressions are provided for focal shift and the peak intensity for different numerical apertures and Fresnel numbers. This is one application where the Rayleigh–Sommerfeld diffraction integrals provide inaccurate results. Full article

Spatially dense operative deflection shapes and receptances, acquired in broad frequency bands, increase the detail in the spatial and frequency domains of the responses of parts in actual dynamic loading, manufacturing and mounting conditions. This work remarks the potential benefits of greater spatial resolution in the Rayleigh integral approximation of sound pressure—here reformulated to exploit the increased quality output from experiment-based optical full-field technologies in contactless structural dynamics—radiated by a vibrating surface in a broad frequency band. But in some cases the noise that is scattered over the estimated receptance maps might be heavier, or with different patterns, than expected, with potential repercussions on the sound pressure simulations that come thereof. This work covers this specific latter issue with insight over examples from experiment-based receptances of a lightweight vibrating plate. The effects of error spreading are analysed in the space and frequency domains, with special attention to the contribution of the experiment-based full-field receptance maps to the accuracy of the vibro-acoustic frequency response function maps. Full article

Proposing a matrix transform method to solve a fractional partial differential equation is the main aim of this paper. The main model can be transferred to a partial-integro differential equation (PIDE) with a weakly singular kernel. The spatial direction is approximated by a fourth-order difference scheme. Also, the temporal derivative is discretized via a second-order numerical procedure. First, the spatial derivatives are approximated by a fourth-order operator to compute the second-order derivatives. This process produces a system of differential equations related to the time variable. Then, the Crank–Nicolson idea is utilized to achieve a full-discrete scheme. The kernel of the integral term is discretized by using the Lagrange polynomials to overcome its singularity. Subsequently, we prove the convergence and stability of the new difference scheme by utilizing the Rayleigh–Ritz theorem. Finally, some numerical examples in one-dimensional and two-dimensional cases are presented to verify the theoretical results. Full article

Although the full form of the Rayleigh–Plesset (RP) equation more accurately depicts the bubble behavior in a cavitating flow than its reduced form, it finds much less application than the latter in the computational fluid dynamic (CFD) simulation due to its high stiffness. The traditional variable time-step scheme for the full form RP equation is difficult to be integrated with the CFD program since it requires a tiny time step at the singularity point for convergence and this step size may be incompatible with time marching of conservation equations. This paper presents two stable and efficient numerical solution schemes based on the finite difference method and Euler method so that the full-form RP equation can be better accepted by the CFD program. By employing a truncation bubble radius to approximate the minimum bubble size in the collapse stage, the proposed schemes solve for the bubble radius and wall velocity in an explicit way. The proposed solution schemes are more robust for a wide range of ambient pressure profiles than the traditional schemes and avoid excessive refinement on the time step at the singularity point. Since the proposed solution scheme can calculate the effects of the second-order term, liquid viscosity, and surface tension on the bubble evolution, it provides a more accurate estimation of the wall velocity for the vaporization or condensation rate, which is widely used in the cavitation model in the CFD simulation. The legitimacy of the solution schemes is manifested by the agreement between the results from these schemes and established ones from the literature. The proposed solution schemes are more robust in face of a wide range of ambient pressure profiles. Full article

The actual modern problem of developing and improving measurement and observation systems (including robotic ones) is to increase the volume and quality of the information received. Increasing the angle resolution to values significantly exceeding the Rayleigh criterion, i.e. achieving super-resolution is one of important ways to solve the problem. Angular super-resolution which makes it possible to detail images of research objects and their individual fragments, improves the quality of solutions to detection, recognition and identification problems, increases the range of such systems. In many papers methods developed by authors to achieve a super-resolution based on approximate solutions of inverse problems in the form of Fredholm integral equation of the first kind of convolution type called algebraic are presented. The methods used, as well as their varieties, make it possible to reduce solutions of inverse problems posed to solving sets of linear algebraic equations (SLAE). This paper presents results of further improvement of algebraic methods based on intelligent analysis of received signals. It is shown that their use in systems based on digital antenna arrays makes it possible to increase the achieved degree of exceeding the Rayleigh criterion. In the course of numerical experiments with a mathematical model, the stability of the solutions obtained and their adequacy were confirmed. The numerical results obtained open the following possibilities: (1) obtaining images of studied objects with a resolution exceeding the Rayleigh criterion by 4 to 10 times, (2) determining the angular coordinates of individual small-sized objects as part of multi-element complex objects (group targets), (3) clarifying boundaries of extended objects and their individual elements, (4) localizing individual bright objects on a smoothly inhomogeneous reflective background. Applying presented new methods does not require a significant computing power, what allows you to work in a real time mode using relatively simple and inexpensive computing devices. The ways of further improvement of presented algebraic methods for solving applied inverse problems are described. Full article

This paper analyzes the sound radiation behavior of a clamped thin, functionally graded material plate using the classical plate theory and Rayleigh Integral with the elemental radiator approach. The material properties of the plate are assumed to vary according to the power-law distribution of the constituent materials in the transverse direction. The functionally graded material is modeled using a physical neutral surface instead of a geometric middle surface. The effects of the power-law index, elastic modulus ratio, different constituent materials, and damping loss factor on the sound radiation of functionally graded plate are analyzed. It was found that, for the considered plate, the power-law index significantly influences sound power level and radiation efficiency. There exists a critical value of the power-law index for which the corresponding peak of sound power level is minimum. In a wide operating frequency range, approximately 500–1500 Hz, this research suggests that the radiation efficiency is lower for the power-law index equal to 0 and 1. However, for very low frequencies (less than 250 Hz), the power-law index does not affect radiation efficiency significantly. Further, as the modulus ratio increases, the sound power peak decreases for a given power-law index. For the given material constituents of the functionally graded plate, the different values of damping loss factors do not significantly influence radiation efficiency. However, the selection of material constituents affects the radiation efficiency peak. Full article

In this research work, our aim is to use the fast algorithm to solve the Rayleigh–Stokes problem for heated generalized second-grade fluid (RSP-HGSGF) involving Riemann–Liouville time fractional derivative. We suggest the modified implicit scheme formulated in the Riemann–Liouville integral sense and the scheme can be applied to the fractional RSP-HGSGF. Numerical experiments will be conducted, to show that the scheme is stress-free to implement, and the outcomes reveal the ideal execution of the suggested technique. The Fourier series will be used to examine the proposed scheme stability and convergence. The technique is stable, and the approximation solution converges to the exact result. To demonstrate the applicability and viability of the suggested strategy, a numerical demonstration will be provided. Full article

We have developed a simple method of fabricating liquid metal nanowire (NW) arrays of eutectic GaIn (EGaIn). When an EGaIn droplet anchored on a flat substrate is pulled perpendicular to the substrate surface at room temperature, an hourglass shaped EGaIn is formed. At the neck of the shape, based on the Plateau–Rayleigh instability, the EGaIn bridge with periodically varying thicknesses is formed. Finally, the bridge is broken down by additional pulling. Then, EGaIn NW is formed at the surface of the breakpoint. In addition, EGaIn NW arrays are found to be fabricated by pulling multiple EGaIn droplets on a substrate simultaneously. The average diameter of the obtained NW was approximately 0.6 μm and the length of the NW depended on the amount of droplet anchored on the substrate. The EGaIn NWs fabricated in this study may be used for three-dimensional wiring for integrated circuits, the tips of scanning probe microscopes, and field electron emission arrays. Full article

The onset of convection in the form of magneto-inertial waves in a rotating fluid sphere permeated by a constant axial electric current is studied in this paper. Thermo-inertial convection is a distinctive flow regime on the border between rotating thermal convection and wave propagation. It occurs in astrophysical and geophysical contexts where self-sustained or external magnetic fields are commonly present. To investigate the onset of motion, a perturbation method is used here with an inviscid balance in the leading order and a buoyancy force acting against weak viscous dissipation in the next order of approximation. Analytical evaluation of constituent integral quantities is enabled by applying a Green’s function method for the exact solution of the heat equation following our earlier non-magnetic analysis. Results for the case of thermally infinitely conducting boundaries and for the case of nearly thermally insulating boundaries are obtained. In both cases, explicit expressions for the dependence of the Rayleigh number on the azimuthal wavenumber are derived in the limit of high thermal diffusivity. It is found that an imposed azimuthal magnetic field exerts a stabilizing influence on the onset of inertial convection and as a consequence magneto-inertial convection with azimuthal wave number of unity is generally preferred. Full article