Search Results (77)

The dynamic behavior of a double-beam configuration subjected to a harmonic moving load was studied in this paper. The model was built to represent the wheel–track system that was composed of two infinite Timoshenko beams joined by uniformly spaced sleepers and supported by a continuous viscoelastic foundation. The response of the coupled beams to a moving harmonic excitation was first derived, after which the wheel–rail interaction was incorporated through a generalized Fourier series formulation. The associated Fourier coefficients were obtained from a finite system of algebraic equations imposed by the wheel–track contact conditions. The numerical simulation was carried out to compare the predictions of the Timoshenko and Euler–Bernoulli beam assumptions and to explore the influence of load speed and excitation frequency on the dynamic characteristics of the double-beam system. Comparative analysis reveals that Timoshenko beam theory predicts larger vertical displacements for rail, slab, and sleeper near the model’s cut-off frequencies (20 Hz and 30 Hz) than Euler–Bernoulli theory, with higher load velocities reducing the first cut-off frequency and amplifying peak amplitudes. The dynamic response exhibits two critical velocities at sub-cut-off frequencies, where rail displacements increase with load velocity, whereas this trend reverses when the load frequency meets or exceeds the cut-off frequencies, and no distinct peaks occur at 25 Hz and 40 Hz. The research findings are of great significance for the vibration propagation and vibration disaster prevention for shield tunnels during the train operation. Full article

This study presents a unified, design-oriented equation for the torsion constant J of linearly tapered, non-prismatic rectangular members, covering two canonical geometries: (i) singly tapered bars, in which only the depth varies linearly along the longitudinal axis, and (ii) doubly tapered bars, in which both width and depth vary linearly. The formulation provides the spatial variation J(x) and enables evaluation of the associated shear stress distribution and angle of twist. Accuracy is assessed against classical elasticity solutions—Prandtl’s membrane analogy, single- and double-Fourier series solutions—as well as independent finite element analyses, demonstrating close agreement over a broad parametric range. A dimensionless coefficient $\varnothing (x)=J(x)/(b_2^3{h}_2)$ is introduced to elucidate trends: $\varnothing$ approaches 1/3 in the prismatic, very-narrow limit $({\lambda }_h={\lambda }_b=1,\alpha \approx 0)$, consistent with the exact solution; $\varnothing$ increases with increasing taper ratios in depth and width (${\lambda }_h,{\lambda }_b$) and decreases with increasing cross-sectional aspect ratio α. The proposed equation consolidates the treatment of tapered rectangular members into a single, practical framework, offering a computationally efficient tool for preliminary sizing and detailed design verification. Full article

This paper investigates the problem of tracking targets with unknown but fixed 3D star-convex shapes using point cloud measurements. While existing methods typically model shape parameters as random variables evolving according to predefined prior models, this evolution process is often unknown in practice. We propose a particular approach within the Expectation Conditional Maximization (ECM) framework that circumvents this limitation by treating shape-defining quantities as parameters estimated directly via optimization. The objective is the joint estimation of target kinematics, extent, and orientation in 3D space. Specifically, the 3D shape is modeled using a radial function estimated via double Fourier series (DFS) expansion, and orientation is represented using the compact, singularity-free axis-angle method. The ECM algorithm facilitates this joint estimation: an Unscented Kalman Smoother infers kinematics in the E-step, while the M-step estimates DFS shape parameters and rotation angles by minimizing regularized cost functions, promoting robustness and smoothness. The effectiveness of the proposed algorithm is substantiated through two experimental evaluations. Full article

In this study, a novel adsorbent was developed by synthesizing Zn-Al layered double hydroxide (LDH) incorporated with silver nanoparticles (Ag-NPs), and its effectiveness in bromide removal from aqueous solutions was systematically evaluated. The X-ray Diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FTIR) analyses confirmed the integration of Ag-NPs within the LDH, ensuring uniform chemical composition and structural integrity. A series of controlled batch trials, each varying a single parameter (adsorbent dose, contact time, or temperature) confirmed that over 95% of bromide (initially 5320 μg/L) was removed under optimized conditions. LDH/Ag-NPs exhibited superior performance, with kinetics well described by a second-order reaction model. Thermodynamic analysis confirmed the spontaneous and exothermic nature of bromide adsorption, with ΔG° values ranging from −2.03 to −0.73 kJ/mol as the temperature increased from 22 °C to 52 °C. In continuous-flow experiments, packed-bed column tests illustrated that LDH/Ag-NPs maintained more effective bromide removal than LDH alone over extended periods. Conductivity measurements further supported this enhancement, with LDH/Ag-NPs reducing final conductivity to 139 µS/cm, compared to 212 µS/cm for LDH. Furthermore, this study revealed the notable antimicrobial activity of LDH/Ag-NPs, as evidenced by a significant reduction in bacterial growth compared to LDH alone, highlighting its dual functionality for both bromide adsorption and water disinfection. Overall, the incorporation of Ag-NPs into LDH offers a promising strategy for developing multifunctional and sustainable water treatment systems. Full article

The ultra-high-speed rocket sled plays an important role in the ground test by simulating altitude flight. Rocket sleds can only be lifted for a short time with thermally uninsulated superconductors moving among an eddy-current-induced copper array. For the purpose of durable lifting, an electrodynamic suspension (EDS) with a permanent magnet (PM) Halbach array moving over a conductor plate can be adopted to upgrade the rocket sled. The earlier study built a two-dimensional (2D) model for the PM EDS system. Yet, 2D modelling in our earlier research ignored the magnetic field variation along both widths of the Halbach array and conductor plate. This resulted in a more than 50% error between the analytical electromagnetic forces with both the three-dimensional (3D) simulated and experimental results. To reduce the error, this paper puts forward more accurate analytical electromagnetic force formulas by a 3D modelling method encompassing both widths of the Halbach array and conductor plate. The 3D model was built by periodically extending the PM EDS system along both directions of the width and length. Then, by double Fourier series expansion and omitting high-order components, the electromagnetic forces can be approximated by brief formulas. Moreover, lift-to-weight and lift-to-drag optimization are discussed. Finally, the correctness of the 3D electromagnetic force formulas was verified by both the numerical simulation and experiment. Full article

The present work aims to validate the computational simulation model that determines the static deflection experienced by rectangular flat plates along the longest edge when subjected to uniform and hydrostatic pressures, proposed as a state observer for active control. The plates are isotropic and simply supported on their four edges. The pressures do not exceed the plate material’s elastic limit. The solutions in the analytical form of the partial differential equation of flat plates established by Kirchoff theory are first determined by Fourier double series. On the other hand, simulations are performed using the Finite Element Computational Model (MEF) using ANSYS Workbench17 software. Full article

By examining Fourier–Legendre series pairs $\mathcal{F}\left(y\right)$ and $\mathcal{G}\left(y\right)$, fifteen classes of symmetric and asymmetric bivariate series will systematically be investigated. A compendium of 360 remarkable summation formulae will be established. They may serve as a complementary work to the paper by Chu and Campbell (The Ramanujan Journal (2023)). Full article

The article presents results of an analytical and numerical modeling of electron fluid motion and heat generation in a rectangular conductor at an alternating electric potential. The analytical solution is based on the series expansion solution (Fourier method) and double series solution (method of eigenfunction decomposition). The numerical solution is based on the lattice Boltzmann method (LBM). An analytical solution for the electric current was obtained. This enables estimating the heat generation in the conductor and determining the influence of the parameters characterizing the conductor dimensions, the parameter M (phenomenological transport time describing momentum-nonconserving collisions), the Knudsen number (mean free path for momentum-nonconserving) and the Sh number (frequency) on the heat generation rate as an electron flow passes through a conductor. Full article

This study presents a spectro-geometric vibration model for analyzing free as well as forced vibration properties for FGM cylindrical double-walled shells with internal structures. The boundary conditions and coupling effects are modeled using an artificial virtual spring approach, which allows for the simulation of arbitrary boundary and coupling conditions by varying the elastic spring stiffness coefficients. The spectral geometry method is employed to represent the displacement variables of the FGM substructure, overcoming the discontinuity phenomenon commonly observed when traditional Fourier series are used. The dynamic equations of the FGM cylindrical double-walled shell with an internal structure are derived using the first-order shear deformation assumption and the Rayleigh–Ritz method, and the corresponding vibration solutions are computed. The model’s reliability and prediction accuracy are confirmed through convergence checks and numerical comparisons. Additionally, parametric studies are conducted to examine the influence of material constants, position parameters, and geometric parameters on the shell’s inherent characteristics and steady-state response. Full article

A wide band range can cover more of the characteristic spectral lines of substances, and thus analyze the structure and composition of substances more accurately. In order to broaden the band range of spectral instruments, an ultra-wide-band Fourier transform infrared spectrometer is designed. The incident light of the spectrometer is constrained by a secondary imaging scheme, and switchable light sources and detectors are set to achieve an ultra-wide band coverage. A compact and highly stable double-moving mirror swing interferometer is adopted to generate optical path difference, and a controller is used to stabilize the swing of the moving mirrors. A distributed design of digital system integration and analog system integration is adopted to achieve a lightweight and low-power-consumption spectrometer. High-speed data acquisition and a transmission interface are applied to improve the real-time performance. Further, a series of experiments are performed to test the performance of the spectrometer. Finally, the experimental results show that the spectral range of the ultra-wide-band Fourier transform infrared spectrometer covers 0.770–200 μm, with an accurate wave number, a spectral resolution of 0.25 cm⁻¹, and a signal-to-noise ratio better than 50,000:1. Full article

This paper presents a carrier waves phase shifting method to reduce the dc-link capacitor current for a dual three-phase permanent magnet synchronous motor drive system. Dc-link capacitors absorb the ripple current generated at the input due to the harmonics of the pulse width modulation (PWM). The size, cost, reliability, and lifetime of the dc-link capacitor are negatively affected by this ripple current flowing through it. The proposed method is especially appropriate for common dc-link capacitors for a dual inverter system driving two PMSMs. In this paper, the input current of each inverter is analyzed using Double Fourier Analysis, and the harmonic components of the dc-link capacitor current are determined. The carrier wave phase shifting method is proposed to reduce the magnitude of the harmonics and thus reduce the dc-link capacitor current. Furthermore, the optimum angle between the carrier waves for the maximum reduction in the dc-link capacitor current is analyzed and simulated for different scenarios considering the speed and load torque of the PMSMs. The proposed method is verified through experiments and PMSMs are driven by three-phase voltage source inverters (VSIs) modulated with Space Vector Pulse Width Modulation (SVPWM), which is the most common PWM strategy. The proposed method reduces the dc-link capacitor current by 60%, thereby significantly decreasing the required dc-link capacitance, the volume of the drive system, and its cost. Full article

Based on domain decomposition, a semi-analytical method (SAM) is applied to analyze the free vibration of double-curved shells of revolution with a general curvature radius made from graphene nanoplatelet (GPL)-reinforced porous composites. The mechanical properties of the GPL-reinforced composition are assessed with the Halpin–Tsai model. The double-curvature shell of revolution is broken down into segments along its axis in accordance with first-order shear deformation theory (FSDT) and the multi-segment partitioning technique, to derive the shell’s functional energy. At the same time, interfacial potential is used to ensure the continuity of the contact surface between neighboring segments. By applying the least-squares weighted residual method (LWRM) and modified variational principle (MVP) to relax and achieve interface compatibility conditions, a theoretical framework for analyzing vibrations is developed. The displacements and rotations are described through Fourier series and Chebyshev polynomials, accordingly, converting a two-dimensional issue into a suite of decoupled one-dimensional problems. The obtained solutions are contrasted with those achieved using the finite element method (FEM) and other existing results, and the current formulation’s validity and precision are confirmed. Example cases are presented to demonstrate the free vibration of GPL-reinforced porous composite double-curved paraboloidal, elliptical, and hyperbolical shells of revolution. The findings demonstrate that the natural frequency of the shell is related to pore coefficients, porosity, the mass fraction of the GPLs, and the distribution patterns of the GPLs. Full article

Core–shell nanostructures are powerful platforms for the development of novel nanoscale drug delivery systems with sustained drug release profiles. Coaxial electrospinning is facile and convenient for creating medicated core–shell nanostructures with elaborate designs with which the sustained-release behaviors of drug molecules can be intentionally adjusted. With resveratrol (RES) as a model for a poorly water-soluble drug and cellulose acetate (CA) and PVP as polymeric carriers, a brand-new electrospun core–shell nanostructure was fabricated in this study. The guest RES and the host CA molecules were designed to have a reverse gradient distribution within the core–shell nanostructures. Scanning electron microscope and transmission electron microscope evaluations verified that these nanofibers had linear morphologies, without beads or spindles, and an obvious core–shell double-chamber structure. The X-ray diffraction patterns and Fourier transform infrared spectroscopic results indicated that the involved components were highly compatible and presented in an amorphous molecular distribution state. In vitro dissolution tests verified that the new core–shell structures were able to prevent the initial burst release, extend the continuous-release time period, and reduce the negative tailing-off release effect, thus ensuring a better sustained-release profile than the traditional blended drug-loaded nanofibers. The mechanism underlying the influence of the new core–shell structure with an RES/CA reverse gradient distribution on the behaviors of RES release is proposed. Based on this proof-of-concept demonstration, a series of advanced functional nanomaterials can be similarly developed based on the gradient distributions of functional molecules within electrospun multi-chamber nanostructures. Full article

As more and more numerical and analytical solutions to the linear neutron transport equation become available, verification of the numerical results becomes increasingly important. This presentation concerns the development of another benchmark for the linear neutron transport equation in a benchmark series, each employing a different method of solution. In 1D, there are numerous ways of analytically solving the monoenergetic transport equation, such as the Wiener–Hopf method, based on the analyticity of the solution, the method of singular eigenfunctions, inversion of the Laplace and Fourier transform solutions, and analytical discrete ordinates in the limit, which is arguably one of the most straightforward, to name a few. Another potential method is the PN (Legendre polynomial order N) method, where one expands the solution in terms of full-range orthogonal Legendre polynomials, and with orthogonality and series truncation, the moments form an open set of first-order ODEs. Because of the half-range boundary conditions for incoming particles, however, full-range Legendre expansions are inaccurate near material discontinuities. For this reason, a double PN (DPN) expansion in half-range Legendre polynomials is more appropriate, where one separately expands incoming and exiting flux distributions to preserve the discontinuity at material interfaces. Here, we propose and demonstrate a new method of solution for the DPN equations for an isotropically scattering medium. In comparison to a well-established fully analytical response matrix/discrete ordinate solution (RM/DOM) benchmark using an entirely different method of solution for a non-absorbing 1 mfp thick slab with both isotropic and beam sources, the DPN algorithm achieves nearly 8- and 7-place precision, respectively. Full article

This paper investigates the issue of leakage current at the transmitter in the Dynamic Wireless Power Transfer (DWPT) system for electric vehicles and puts forward a novel bilateral resonant compensation topology structure based on the conventional LCC-S architecture. Based on the LCC-S framework, a circuit model was developed for traditional (unilateral)/bilateral resonant compensation topologies. The Fourier series voltage-to-earth expansions for the power supply rail were deduced for both topologies. Subsequently, the voltage-to-earth waveforms for the power supply rail were obtained by utilizing the Fourier series expansions of the voltage-to-earth and the corresponding circuit simulation models. The results demonstrate the efficacy of the bilateral resonant compensation topology in mitigating higher-order harmonics of the voltage to earth on the power supply rail by effectively suppressing the distortion in the leakage current and minimizing its conduction. The effectiveness of the double-ended resonant compensation topology in suppressing leakage current conduction has been verified through experimental tests and waveform comparisons of the voltage to earth and leakage current on the power supply rail under two different topologies. Through experimental testing, during which the unilateral/bilateral resonant compensation topologies were compared, an analysis was conducted on the waveforms of the voltage to earth and leakage current of the power supply rail. The results verified the effectiveness of the bilateral resonant compensation topology in mitigating the conduction of leakage current. This study provides empirical evidence supporting the use of the bilateral resonant compensation topology for suppressing leakage current in power rail applications. Full article