Search Results (41)

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

In this paper, an equation describing nonlinear wave phenomena on the surface of magnetically active plasma in the approximation of the complete homogeneity of processes along the direction of the constant magnetic field is obtained. One of its solutions, in the form of a pulse having the shape of rapidly decaying oscillations with a changing period, is found to essentially depend on the magnitude of the magnetic field and shown to be approximately described by a specially selected analytical function. A detailed analytical analysis of the properties of another solitary wave formation existing under conditions of resonant coincidence of its carrier frequency with the corresponding value of its eigen surface oscillations in the considered cold semi-infinite plasma, in which a constant magnetic field is directed along its boundary, is also carried out. The conditions for the excitation of wave disturbances are determined, and analytical expressions that adequately describe the space–time structure of nonlinear waves are proposed. Full article

Distributed parameter systems (DPSs) frequently appear in industrial manufacturing processes, with complex characteristics such as time–space coupling, nonlinearity, infinite dimension, uncertainty and so on, which is full of challenges to the modeling of the system. At present, most DPS modeling methods are offline. When the internal parameters or external environment of DPS change, the offline model is incapable of accurately representing the dynamic attributes of the real system. Establishing an online model for DPS that accurately reflects the real-time dynamics of the system is very important. In this paper, the idea of reinforcement learning is creatively integrated into the three-dimensional (3D) fuzzy model and a reinforcement learning-based 3D fuzzy modeling method is proposed. The agent improves the strategy by continuously interacting with the environment, so that the 3D fuzzy model can adaptively establish the online model from scratch. Specifically, this paper combines the deterministic strategy gradient reinforcement learning algorithm based on an actor critic framework with a 3D fuzzy system. The actor function and critic function are represented by two 3D fuzzy systems and the critic function and actor function are updated alternately. The critic function uses a TD (0) target and is updated via the semi-gradient method; the actor function is updated by using the chain derivation rule on the behavior value function and the actor function is the established DPS online model. Since DPS modeling is a continuous problem, this paper proposes a TD (0) target based on average reward, which can effectively realize online modeling. The suggested methodology is implemented on a three-zone rapid thermal chemical vapor deposition reactor system and the simulation results demonstrate the efficacy of the methodology. Full article

Machines operate under increasingly harsher contact conditions, causing significant wear and contact fatigue. Sub-surface stresses are responsible for the premature contact fatigue of rolling element bearings, meshing gears, and cam–follower pairs. Surface protection measures include hard, wear-resistant coatings. Traditionally, contact integrity has been predicted using classical Hertzian contact mechanics. However, the theory is only applicable when the contact between a pair of ellipsoidal solids of revolution may be considered as a rigid indenter penetrating a semi-infinite elastic half-space. Many coatings act as thin bonded elastic layers that undergo considerably higher pressures than those predicted by the classical theory. Furthermore, inelastic deformation of bonded solids can cause plastic flow, work-hardening, and elastoplastic behaviour. This paper presents a comprehensive, integrated contact mechanics analysis that includes induced sub-surface stresses in concentrated counterformal finite line contacts for all the aforementioned cases. Generated pressures and deformation are predicted for hard coated surfaces, for which there is a dearth of relevant analysis. The contact characteristics, which are of particular practical significance, of many hard, wear-resistant advanced coatings are also studied. The paper clearly demonstrates the importance of using efficient semi-analytical, detailed holistic contact mechanics rather than the classical idealised methods or empirical numerical ones such as FEA. The novel approach presented for the finite line contact of thin-layered bonded solids has not hitherto been reported in the open literature. Full article

This work investigates the solvability of the generalized Hilfer fractional inclusion associated with the solution set of a controlled system of minty type–fuzzy mixed quasi-hemivariational inequality (FMQHI). We explore the assumed inclusion via the infinite delay and the semi-group arguments in the area of solid continuity that sculpts the compactness area. The conformable Hilfer fractional time derivative, the theory of fuzzy sets, and the infinite delay arguments support the solution set’s controllability. We explain the existence due to the convergence properties of Mittage–Leffler functions (${\mathbb{E}}_{\alpha ,\beta }$), that is, hatching the existing arguments according to FMQHI and the continuity of infinite delay, which has not been presented before. To prove the main results, we apply the Leray–Schauder nonlinear alternative thereom in the interpolation of Banach spaces. This problem seems to draw new extents on the controllability field of stochastic dynamic models. Full article

Numerical seismic wave field simulation is essential for studying the dynamic responses in semi-infinite space, and the absorbing boundary setting is critical for simulation accuracy. This study addresses spherical waves incident from the free boundary by applying dynamic equations and Rayleigh damping. A new multi-directional viscous damping absorbing boundary (MVDB) method is proposed based on regional attenuation. An approximate formula for the damping value is established, which can achieve absorbing the boundary setting by only solving the mass damping coefficients without increasing the absorbing region grid cells or depending on the spatial and temporal walking distance. The validity and stability of the proposed method are proven through numerical calculations with seismic sources incident from different angles. Meanwhile, the key parameters affecting the absorption of the MVDB are analyzed, and the best implementation scheme is provided. In order to meet the requirements of mediums with different elastic parameters for boundary absorption and ensure the high efficiency of numerical calculations, the damping amplitude control coefficients k can be set between 1.02 and 1.12, the thickness of the absorbing region L is set to 2–3 times of the wavelength of the incident transverse wave, and the thickness of the single absorbing layer is set to the size of the discrete mesh of the model Δl. Full article

In this paper, a radial gradient seismic metamaterial (RGSM) is proposed. The structural unit cell is composed of an external square soil embedded with a triangular-cross-sectioned steel ring, which is filled at different angles of multiple steel rings to form a supercell. The dispersion curve and attenuation spectrum of the unit cell are calculated by the finite element method, and the opening mechanism of the band gap is explained by analyzing the modes at the band gap boundary. The influence of geometric parameters and material parameters on the band gap is further studied, and the optimized supercell radial gradient seismic metamaterial (OS-RGSM) structure is designed through structure and parameter optimization. The ultra-low broadband excellent band gap in the range of 2.35–20 Hz for seismic Lamb waves is realized, and its three-dimensional frequency response and displacement field diagram are calculated. In addition, the attenuation characteristics of the optimized supercell seismic metamaterial on the seismic surface wave are calculated and analyzed. It is found that the attenuation can reach more than 50% in the ultra-low frequency range of 3.5–9 Hz. The seismic wave barrier is verified by the vibration transmission characteristics of RGSM under finite period and dynamic time history analysis. The results show that RGSM can effectively shield from seismic Lamb waves in the ultra-wideband with the starting frequency of 2.35 Hz and can also effectively attenuate the seismic surface wave in semi-infinite space. Full article

The current study demonstrates the existence of solutions to a multidimensional functional integral equation with multivalued feedback. We seek solutions for the multidimensional functional problem that is defined, continuous, and bounded on the semi-infinite interval. Our proof is based on the technique associated with measures of noncompactness by a given modulus of continuity in the space in $BC\left({\mathbb{R}}_{+}\right).$ Also, some sufficient conditions are investigated to demonstrate the asymptotic stability of the solutions to that multidimensional functional equation. Additionally, we give an example and some particular cases to illustrate our outcomes. Full article

In this paper, we discuss the existence of solutions for a hybrid cubic delayed integral inclusion with fractal feedback control. We are seeking solutions for these hybrid cubic delayed integral inclusions that are defined, continuous, and bounded on the semi-infinite interval. Our proof is based on the technique associated with measures of noncompactness by a given modulus of continuity in the space in $BC\left(R_{+}\right).$ In addition, some sufficient conditions are investigated to demonstrate the asymptotic stability of the solutions of that integral inclusion. Finally, some cases analyzed are in the presence and absence of the control variable, and two examples are provided in order to indicate the validity of the assumptions. Full article

Let H be an infinite-dimensional separable complex Hilbert space and $B\left(H\right)$ the algebra of all bounded linear operators on H. In this paper, we characterized the linear maps $\varphi :B\left(H\right)\to B\left(H\right)$, which are surjective up to compact operators preserving the set of left semi-Weyl operators in both directions. As an application, we proved that $\varphi$ preserves the essential approximate point spectrum if and only if the ideal of all compact operators is invariant under $\varphi$ and the induced map $\phi$ on the Calkin algebra is an automorphism. Moreover, we have $ind\left(\varphi \right(T\left)\right)=ind\left(T\right)$ if both $\varphi \left(T\right)$ and T are Fredholm. Full article

In this paper, the plane wave diffraction from a semi-infinite parallel-plate waveguide with five-layer material loading is rigorously analyzed for H-polarization using the Wiener–Hopf technique. The Fourier transform of the scattered field is introduced and boundary conditions are applied in the transform domain to formulate the problem as simultaneous Wiener–Hopf equations, which are solved by the factorization and decomposition procedure leading to exact and approximate solutions. The scattered field in real space is explicitly derived by taking the Fourier inverse of the solution in the transform domain. For the region inside the waveguide, the scattered field is represented by the waveguide TM modes, and the field outside the waveguide is evaluated asymptotically by applying the saddle-point method to obtain a far-field expression. Numerical examples of the radar cross section (RCS) for various physical parameters are presented, and far-field scattering characteristics of the waveguide are discussed in detail. Full article

Numerical methods have gained momentum among specific engineering problems that must be solved in such a manner that accuracy and speed are the two most important aspects to consider regarding the output. This paper presents a fast, semi-analytical method (SAM) and original mathematical algorithms to determine the pressure distribution and von Mises stress for spur gears’ meshing teeth. The SAM begins with the Hartnett approach, based on Boussinesq’s equation for the half-space theory of linear elasticity, which implicitly means an infinite width of the gear flank. To simulate more realistic quarter-space conditions, corrections based on virtual mirror pressure are introduced in the computational algorithm. Mathematical surfaces modeling is an important aspect for spur gears as an intermediate stage to determine the pressure distribution and von Mises stress. Shaft misalignment changes the contact problem from symmetric, in which the half- or quarter-space model can be used, to asymmetric. In the latter case, the model must determine the entire contact area. The obtained output is validated by comparisons between our original FEA results and results from the literature using SAMs and FEA. Full article

Slope failures, subsidence, earthworks, consolidation of waste dumps, and erosion are typical active deformation processes that pose a significant hazard in current and abandoned mining areas, given their considerable potential to produce damage and affect the population at large. This work proves the potential of exploiting space-borne InSAR and airborne LiDAR techniques, combined with data inferred through a simple slope stability geotechnical model, to obtain and update inventory maps of active deformations in mining areas. The proposed approach is illustrated by analyzing the region of Sierra de Cartagena-La Union (Murcia), a mountainous mining area in southeast Spain. Firstly, we processed Sentinel-1 InSAR imagery acquired both in ascending and descending orbits covering the period from October 2016 to November 2021. The obtained ascending and descending deformation velocities were then separately post-processed to semi-automatically generate two active deformation areas (ADA) maps by using ADATool. Subsequently, the PS-InSAR LOS displacements of the ascending and descending tracks were decomposed into vertical and east-west components. Complementarily, open-access, and non-customized LiDAR point clouds were used to analyze surface changes and movements. Furthermore, a slope stability safety factor (SF) map was obtained over the study area adopting a simple infinite slope stability model. Finally, the InSAR-derived maps, the LiDAR-derived map, and the SF map were integrated to update a previously published landslides’ inventory map and to perform a preliminary classification of the different active deformation areas with the support of optical images and a geological map. Complementarily, a level of activity index is defined to state the reliability of the detected ADA. A total of 28, 19, 5, and 12 ADAs were identified through ascending, descending, horizontal, and vertical InSAR datasets, respectively, and 58 ADAs from the LiDAR change detection map. The subsequent preliminary classification of the ADA enabled the identification of eight areas of consolidation of waste dumps, 11 zones in which earthworks were performed, three areas affected by erosion processes, 17 landslides, two mining subsidence zone, seven areas affected by compound processes, and 23 possible false positive ADAs. The results highlight the effectiveness of these two remote sensing techniques (i.e., InSAR and LiDAR) in conjunction with simple geotechnical models and with the support of orthophotos and geological information to update inventory maps of active deformation areas in mining zones. Full article

Very well-drained lands could have a positive impact in various soil health indicators such as soil erosion and soil texture. A drainage system is responsible for properly aerated soil. Until today, in order to design a drainage system, a big challenge remained to find the subsurface drain spacing because many of the soil and hydraulic parameters present significant uncertainties. This fact also creates uncertainties to the overall physical problem solution, which, if not included in the preliminary design studies and calculations, could have bad consequences for the cultivated lands and soils. Finding the drain spacing requires the knowledge of the unsteady groundwater movement, which is described by the linear Boussinesq equation (Glover-Dumm equation). In this paper, the Adomian solution to the second order unsteady linear fuzzy partial differential one-dimensional Boussinesq equation is presented. The physical problem concerns unsteady drain spacing in a semi-infinite unconfined aquifer. The boundary conditions, with an initially horizontal water table, are considered fuzzy and the overall problem is translated to a system of crisp boundary value problems. Consequently, the crisp problem is solved using an Adomian decomposition method (ADM) and useful practical results are presented. In addition, by application of the possibility theory, the fuzzy results are translated into a crisp space, enabling the decision maker to make correct decisions about both the drain spacing and the future soil health management practices, with a reliable degree of confidence. Full article

A solution is proposed for ground surface settlement induced in fractional-generalised Kelvin semi-infinite space by distributed loads, based on the fractional differential theory. The effects of four main parameters—the differential order, the two shear moduli and the coefficient of viscosity—on the settlements are analysed using a numerical example, and a parametric-sensitivity analysis is conducted. The results show that the fractional-order generalised Kelvin model is more flexible than the conventional integer-order generalised Kelvin model since it can account for the rate of the deceleration creep phase; therefore, a wider range of mechanical properties of viscoelastic materials can be described with fewer parameters, and the differential order has a higher sensitivity than the other three parameters. Finally, the model is used to identify and fit the parameters to the data of the field-bearing plate rheological tests. The fit results of the fractional-order generalised Kelvin model, unlike those of the integer-order generalised Kelvin model, are closer to the measured results and can more accurately describe the rock’s rheological behaviour at the test location. Full article