Force Density Research Articles

Comparative analysis of methods for predicting train-induced vibrations

Railway systems cause more severe vibration pollution than road systems, and the vibration pollution caused by railway systems has been increasing annually over the past two decades. Despite this, there is limited investigation into the accuracy of train-induced vibration prediction methods. Therefore, the present study investigated the accuracy of the detailed and general procedures proposed by the US Federal Transit Administration (FTA) for predicting train-induced vibrations. The accuracy of these methods was determined by evaluating their predictions against in-situ measurements of ground vibration levels induced by passing trains. The field experiments conducted in this study involved the measurement of train-induced vibration levels, the estimation of line-source transfer mobility (LSTM) by dropping a weight on rail sleepers, the evaluation of force density levels, and the determination of ground LSTM by dropping a weight on the ground. In addition, graphs were plotted to determine the relationships of train-induced vertical vibration levels with train speed, distance from the track centreline, and train length. The study compared measured and predicted vibration levels to assess the accuracy of the FTA’s detailed and general prediction methods. Results indicate that detailed assessments tend to overestimate vibration levels, while an optimized general vibration assessment curve offers a more precise estimate. Additionally, on the basis of the measurement data, the study explored the impact of train length on ground vibration and demonstrated that track ballast can absorb vibration energy along the wave propagation path. A frequency propagation contour plot was also created to analyse vibration energy across different frequencies. These findings enhance the reliability of train-induced vibration prediction methods and provide insights for improving vibration mitigation strategies in urban railway systems.

Exploring Interatomic Electron Transfer and Metal-Ligand Binding Mechanism in Trimethylenemethane Iron Tricarbonyl: Insights from Potentials per Electron and Corresponding Force Density Fields.

This study employs an analysis of the per-electron potentials and the superposition of the electrostatic and kinetic force fields, Fes(r) and Fk(r), and the gradients of the potential energy and one-electron densities to investigate the binding mechanism in trimethylenemethane iron tricarbonyl complex (TMM)Fe(CO)3. Our approach permits the delineation of the "ligand-binding" force field generated by the metal nucleus but partially operating within the ligand atoms. A mechanical rationale for metal-ligand interactions is thus presented: In the corresponding area, the attractive force Fes(r) provides the backdrop against which the homotropic static force (r) and the heterotropic kinetic force Fk(r) exert attractive and repulsive influences, respectively, toward the metal nucleus on a portion of the electrons belonging to the ligand atoms. This area thus represents electron sharing, which emerges as a quantum chemical response against the metal-to-ligand electron transfer. It has been demonstrated that the response is facilitated by the decreased potential energy density in the vicinity of the interatomic surface. Our findings indicate that the polar coordination bonds in (TMM)Fe(CO)3 exhibit notable quantum chemical responses. However, the previously described nonbonded contact also features an unexpectedly pronounced response, despite the absence of a bond path. It can be proposed that the unforeseen response is a consequence of the formation of the 18-electron, closed valence shell, rather than an indication of the establishment of an organometallic chemical bond.

Vortex Phase Diagram and Pinning Mechanisms of Air‐Annealed FeTe0.8S0.2 Single Crystals

The vortex phase diagram and superconducting properties of air‐annealed FeTe0.8S0.2 single crystals are investigated. The annealed samples exhibit a superconducting transition, as confirmed by temperature‐dependent resistivity measurements. The thermally activated energy is calculated from the magnetotransport measurements, and the analysis shows that as the magnetic field increases, there is a crossover from single to collective vortex pinning. The vortex phase diagrams have been determined by analyzing magnetic field‐dependent resistivity, revealing the transitions from an unpinned vortex liquid region to a pinned vortex liquid state and further transition from this pinned state to a vortex glass state. Temperature‐dependent magnetization measurement determines the superconducting volume fraction. The critical current densities, as a function of the magnetic field (JC(H)), have been estimated from the magnetization versus magnetic field loops measured at various temperatures. Bean's critical state model estimates the JC values, and for an optimized annealed crystal, the self‐field JC at 2 K is . The normalized pinning force density in the samples is determined using the Dew Hughes model to identify the pinning mechanisms. The temperature‐dependent JC data analysis indicates the presence of ‐pinning in the samples. Theoretical models analyze experimental observations to understand the vortex pinning mechanisms.

Amplifying Colossal Thermal Expansion of a Martensitic Molecular Crystal through Interlayer Shear‐Induced Side‐Chain Liberation

AbstractMolecular crystals capable of colossal thermal expansion (TE) are fascinating owing to their substantial and continuous volume changes and reasonably linear responses to temperature. This makes them promising candidates for micromachine applications. Macroscopic motion is driven by subtle yet cooperative movements of molecules that respond to the thermal motions of dynamic functional units. The study of p‐TIPS‐DSB presented here offers a compelling case highlighting the relationship between the degree of dynamicity of functional units and TE behavior. In its α‐phase, the p‐TIPS‐DSB crystal undergoes an irreversible martensitic transition to the β‐phase, accompanied by significant cooperative interlayer shear. This process substantially enhances the mobility of the side‐chains driven by the increased free volume surrounding them. This nearly doubles the volumetric TE coefficient from 255.3 (10) to 444.9 (32) MK−1, particularly in the actuation direction from 175.0 (7) to 291.7 (20) MK−1, enabling about 4.5 % elongation/contraction. As demonstrated here, p‐TIPS‐DSB exhibits a decent force density (>1.4×107 N m−3) and precise motion control capabilities due to its hysteresis‐free and non‐abrupt TE nature. Furthermore, we demonstrated the limited operating distance of colossal TE materials can be amplified by utilizing levers, highlighting the high potential of these materials for use in micromachines.

Effects of Air Gaps on the Output Force Density in COMSOL Simulations of Biomimetic Artificial Muscles

Effects of Air Gaps on the Output Force Density in COMSOL Simulations of Biomimetic Artificial Muscles

Pump-Free Pneumatic Actuator Driven by the Vapor Pressure at the Gas-Liquid Equilibrium of Aqua Ammonia.

Currently, pneumatic soft actuators are widely used due to their impressive adaptability, but they still face challenges for more extensive practical applications. One of the primary issues is the bulky and noisy air compressors required to generate air pressure. To circumvent this critical problem, this work proposes a new type of air pressure source, based on the vapor pressure at the gas-liquid equilibrium to replace conventional air pumps. Compared with the previous phase transition method, this approach gains advantages such as generating gas even at low temperatures (instead of boiling point), more controllable gas output, and higher force density (since both ammonia and water contribute to the gas pressure). This work built mathematical models to explain the mechanism of converting energy to output action force from electrical energy and found the aqua ammonia system is one of the optimal choices. Multiple prototypes were created to demonstrate the capability of this method, including a pouch actuator that pushed a load 20,555 times heavier than its dead weight. Finally, based on the soft actuator, an untethered crawling robot was implemented with onboard batteries, showing the potentially extensive applications of this methodology.

Computational Multiscale Study of the Interaction Between the PDMS Polymer and Sunscreen-Related Pollutant Molecules

Sunscreen molecules play a critical role in protecting skin from ultraviolet radiation, yet their efficient detection and separation pose challenges in environmental and analytical contexts. In this work, we employ a multilevel modeling approach to investigate the molecular interactions between representative sunscreen molecules and the polydimethylsiloxane (PDMS) polymer, a material widely recognized for its sorbent properties. Our goal is to explore how these interactions can be fine-tuned to facilitate the effective separation of sunscreen molecules in portable membrane inlet mass spectrometry (MIMS) systems, potentially leading to the development of new membrane materials. Using a combination of advanced computational techniques—force field molecular dynamics simulations, semiempirical GFN2-xTB, and density functional theory calculations—we assess the interaction strength and noncovalent interactions of sunscreen molecules, namely oxybenzone, naphthalene, benzo[a]anthracene, avobenzone, and 1,3,5-trichlorobenzene, with PDMS. Additionally, the effect of temperature on the interaction dynamics is evaluated, with the aim of extending the sorbent capacities of PDMS beyond light polar molecules to larger, polar sunscreen compounds. This study provides critical insights into the molecular-level interactions that may guide the design of novel membrane materials for efficient molecular separation.

Critical current characteristics and ampere force distribution of a novel HTS cable with different transposition lengths

Abstract Distribution characteristics of the current, ampere force and magnetic flux density (B [T]) of a novel high temperature superconducting (HTS) cable woven by transposed REBCO tapes under different transposition lengths are proposed, and these characteristics of the cable stacked with 3 REBCO tapes are also carried out in this paper for comparison. The objective is to enhance the current density and the compactness of the HTS tapes combination, and uniform the current, ampere force and magnetic flux density (B [T]) distributions. A 3D finite element model (FEM), based on Maxwell's equations without consideration of the displacement current, is established to describe the state of the system in the liquid nitrogen condition. The distributions characteristics, maximum and minimum values of current, ampere force and magnetic flux density (B [T]) show significant differences in the simulation results between the novel HTS cable woven by 3 transposed REBCO tapes and the cable stacked with 3 REBCO tapes. The simulated results show that the distribution characteristics are improved, with a more uniform distribution characteristic than that of the cable stacked with REBCO tapes. This is due to fully transposed REBCO tapes. In addition, the experimental E-I curve was also reached. The experimental results show that using a shorter transposition length in the cable can improve the critical current. However, A too small transposition length can cause significant damage to the HTS tape, resulting in deformation of the HTS tape and a reduction in the electromagnetic properties of the HTS tape. This affects the critical current of the HTS tape and, ultimately, the critical current of the cable. From the point of view of whether the production process is convenient, meets the requirements of economy and reduces costs, we need to find a suitable transposition length. The measured optimal transposition length is 95 mm for the cable woven by 3 REBCO tapes.
Ethical Compliance: All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards.

Electromagnetic force calculation within finite volume framework

ABSTRACT In this research, the comparison of force calculation methods in magnetostatic simulations within a cell-centered finite volume framework is presented. Various procedures for postprocessing of the magnetic vector potential field are laid out to obtain the surface and volume integrals of Maxwell’s stress tensor and the Lorentz force density. Two different magnetostatic problems with multiple operating points were modeled with the AVL FIRETM M. The force results have been verified by comparing them to the Ansys Maxwell and were validated on a benchmark case from a Testing Electromagnetic Analysis Methods (TEAM) workshop. The interpolation of the magnetic flux density on a multi-material interface is presented, and it is used in conjunction with the surface integral of Maxwell’s stress tensor for an efficient global force computation. For all observed cases, the calculated results correspond well to the results found in the literature. It was found that the accuracy of the volume integral of Maxwell’s stress tensor is dependent on the mesh quality and gradient calculation scheme. Employing the semi-structured mesh with Gauss’s gradient scheme results in force discrepancies of less than 3% between the surface and volume integral of Maxwell’s stress tensor. The convergence of the iterative solver is observed to be slower in the case of the materials with permeability jump, where discontinuities between the tangential component of the magnetic flux density and the normal component of the magnetic field intensity occur.

Unravelling the Enigmatic Nexus: Black Holes, Dark Matter, and the Interplay of Light, Gravity, and Electromagnetic Forces in Astrophysics and Astronomy

This research introduces a mathematical model positioning our physical reality within a ten-dimensional hyperspace, in which time acts as the unifying coordinate linking three-dimensional electric, magnetic, and gravitational spaces. Each domain is characterized by its respective field—electric, magnetic, or gravitational—and governed by intrinsic divergences and rotations, leading to a universal property known as Force Density, expressed in [N/m³]. This Force Density facilitates interactions among the distinct spaces while adhering to the principle of equilibrium, which posits that cumulative force densities from disturbances must consistently sum to zero. Building upon Einstein's General Relativity—which describes the curvature of spacetime by gravitational fields and assumes a constant light speed—this study proposes a perspective wherein light speed may vary during coherent laser beam interactions, prompting a re-examination of gravitational and luminous interactions across scales. The proposed model integrates the Stress-Energy Tensor and Gravitational Tensor, introducing a new tensor representation for black holes, termed Gravitational Electromagnetic Confinements, incorporating electromagnetic energy gradients and Lorentz transformations. This framework transcends traditional General Relativity, particularly evident in gravitational lensing. By reinterpreting Einstein's incorporation of the Gravitational Constant within the Energy-Stress Tensor, this work harmonizes gravity and light, offering insights into black hole solutions resonating with John Archibald Wheeler's 1955 research. Empirical data from Galileo satellites and MASER frequency measurements underscore discrepancies between established theories and this new model, enhancing the precision of gravitational observations. Through the confluence of Quantum Physics and General Relativity, as seen in approaches like String Theory, this interdisciplinary endeavor revisits the gravitational constant "G," redefining it while bridging theoretical frameworks, thus paving the way for breakthroughs in astronomical and astrophysical sciences.

A force-density framework for flexible multi-body dynamic analysis of clustered tensegrity structures

This paper develops a versatile and effective force-density framework for the flexible multi-body dynamic analysis of clustered tensegrity structures. In this framework, the force density is selected as the basic variable instead of force, and the clustered tensegrity structure is mathematically described in a vector and matrix form, encompassing topology, geometry, material, and force properties. A non-negative variable is defined as an indicator of the member stress state, and a complementary function is constructed to address the discontinuity issues that arise from the unidirectional axial stiffness of cables. Dynamic formulas are established within this force-density framework, with nodal coordinates selected as generalized parameters and formulations constructed in a matrix form. A complementary framework is established as an alternative for solving the dynamic equations, transforming the isolated steps of Newton’s iteration and cable state judgment (slack or tension) into a unified one, bringing more potential for improving solving efficiency. Numerical simulations are carried out to validate the approach, demonstrating that it effectively reveals the dynamic oscillation, tension changes, and cable slack behavior of clustered tensegrity structures during shape control. Comparative studies highlight the advantage of computational efficiency. The method proposed in this paper provides a robust mathematical model for studying clustered tensegrity structures, particularly regarding the shape control of deployable, active, and intelligent structures, aiding in understanding dynamic oscillation, tension changes, and cable slack behavior during their deformation. The methods can also be applied to cable net structures and other prestressed pin-jointed systems.

Effect of uncorrelated sources assumption on railway vibration modelling

In classical railway vibrations studies, wheel-rail contact points are considered as point sources uncorrelated from each other. This approach gives a more reliable source for vibration impact assessment studies along railways which can be based on in situ experimental measurements or on numerical models. This is also related to the fact that the combined wheel-rail roughness that cannot be perfectly known. This postulation allows using a line spectral force density combined with a line transfer mobility. However, all sources are generated by the same system (train, railway and ground) and are in reality correlated in some way. This paper investigates the effect of sources decorrelation on ground vibration estimation. Numerical models in time and frequency domain are used allowing comparisons for several identical configurations. Results are discussed in detail to understand the effect of sources uncorrelation approach.

Critical current density and AC magnetic susceptibility of high-quality FeTe0.5Se0.5 superconducting tapes

Iron telluride-selenium superconducting materials, known for their non-toxicity, ease of preparation, simple structure, and high upper critical fields, have attracted much research interest in practical application. In this work, we conducted electrical transport measurements, magneto-optical imaging, and AC magnetic susceptibility measurements on FeTe0.5Se0.5 superconducting long tapes fabricated via reel-to-reel pulsed laser deposition. Our transport measurements revealed a high critical current density that remains relatively stable even with increasing external magnetic fields, reaching over 1 × 105 A/cm2 at 8 K and 9 T. The calculated pinning force density indicates that normal point pinning is the primary mechanism in these tapes. The magneto-optical images demonstrated that the tapes show homogeneous superconductivity and uniform distribution of critical current density. The AC magnetic susceptibility measurements also confirmed their strong flux pinning nature of withstanding high magnetic field. Based on these characteristics, FeTe0.5Se0.5 superconducting tapes show promising prospects for applications under high magnetic field.

Simulating 2D Fluid Motion with the Smooth Particle Hydrodynamic Approach

Abstract Virtual two-dimensional (2D) fluid simulation is useful for directly simulating fluids in various situations, including geological simulations for landslides and fluid simulations for teaching. This research aims to simulate the behaviour of three different types of fluids (water, coconut oil, and glycerine) in a 2D container and analyse how these three types of fluids behave under various conditions, including interactions with boundaries. The research used Python programming to simulate fluids and the Wondershare Filmora X application to combine images. The Smooth Particle Hydrodynamics method simulated fluid in a 2D container with 10,000 particles by deriving the force density field directly from the Navier-Stokes equations. The Navier-Stokes equations were utilized to find the acceleration and velocity of fluid particles by considering external forces, internal forces, and gravity through this method. Acceleration and velocity were validated due to wall collisions, collisions with boundaries, and collisions between particles, which caused changes in particle position and velocity. During visualization, the fluid velocity decreased over time due to attenuation caused by interactions between neighbour particles, particles with boundaries, and particles with walls. From the simulation, it was observed that the fluid flowed from a higher place to a lower place, with fluid particles taking the shape of the container and the surface of the fluid forming waves. On the other hand, simulations with boundaries indicated that smaller gap sizes and higher viscosities led to increased difficulty in fluid penetration into the gap within the container.

Form-finding of optimal cable nets under self-weight based on the Force Density Method

Form-finding of optimal cable nets under self-weight based on the Force Density Method

An Experiment to Test a New Theory in Physics, Fundamentally Different From General Relativity, by Changing the Speed of Light in Electromagnetic Interaction

The fundamental foundation for Einstein’s Theory of General Relativity is the “Curvature of Space and Time” due to a Gravitational Field. In the “Theory o f General Relativity” Gravitational RedShift has been explained by a change in time and space resulting is a change in the observed frequency shift in the spectrum o f the light being emitted by far away Galaxies. The foundation for Einstein’s theory o f General Relativity is a constant value for the speed o f light in the absence of a gravitational field. In the “New Theory” the fundamental foundation is “Equilibrium”. Equilibrium for the “5 fundamental force densities in light” in any direction at any time and at any location. The New Theory describes a changing in the speed of light when corresponding monochromatic beams of light (highly coherent LASER beams) cross each other in different directions which effect would be in contradiction with the fundamental assumption in General Relativity of a constant speed of light. This experiment will be a deter mining test for the New Theory in Physics.

Form-Finding of Tensegrity Basic Unit with Equal Cable Length

Tensegrity is a lightweight, self-stressing, and self-stabilizing structure made up of cables and bars, with each member bearing either tension or compression but not affected by shear stress. This design allows for optimal utilization of the material properties of the members. In a tensegrity basic unit, the bar members are of equal length, while the cable members come in three lengths: lower-end surface horizontal cable, upper-end surface horizontal cable, and stayed cable. The tensegrity basic unit with equal cable length simplifies this further by ensuring that all cables are the same length, resulting in a structure with only two member lengths, i.e., bar length and cable length, enhancing interchangeability. In order to find the form without the action of external forces, the force density coefficient ratio is introduced. By performing a force balance analysis on any node of the unit, the equilibrium equation of the structure is determined, incorporating the additional constraint of equal cable length. Two methods are employed to ascertain the force density coefficient ratio of each member in the unit: the theoretical derivation method based on the stable configuration condition of the tensegrity basic unit with equal cable length, and the method of solving the characteristic equations of the force density matrix. A program is developed to validate the form-finding method using basic units with three, four, five, and six bars as examples. The results show that the model accurately represents the physical structure, confirming the reliability of the form-finding methods.

A Study of Differential Topology on the Magnetically Induced Isotropically Averaged Lorentz Force Density of a Few Simple Molecules.

Quantum chemical topology addresses the study of the chemical structure by applying the tools of differential topology to scalar and vector fields obtained by quantum mechanics. Here, the magnetically induced isotropically averaged Lorentz force density was computed and topologically analyzed for 11 small molecules. Critical points (attractors, repellers, and saddles) were determined and trajectories connecting the attractors computed. It is shown that kinds and numbers of the critical points are to some extent transferable in similar molecules. CC bonds of different orders are endowed with critical points of different kinds close to their center. The sum of topological indices of the isolated critical points is influenced by the presence of repellers on the outer part of the molecules.

Study on the influence mechanism of electromagnetic field on multifield coupling during the laser cladding Fe60 process

During laser cladding, microdefects such as pores, cracks, and segregation inevitably occur. Practical experience has shown that applying an electromagnetic field is an effective method for eliminating these microdefects during the cladding process. In the study, a multifield coupling three-dimensional numerical model was established for the electromagnetic field-assisted laser cladding Fe60 process. The instantaneous evolution law in the temperature field, flow field, and stress field under the influence of a magnetic field and without magnetic influence was calculated and revealed. At the same time, the two were compared and analyzed, focusing on the influence of an external electromagnetic field on the flow of molten pool Marangoni and its action mechanism. The results show that under the electromagnetic conditions applied in the study, the maximum magnetic induction intensity and the maximum Lorentz force density in the molten pool reach 0.13 T and 6.84 × 103 N/m3. Under the influence of magnetic force, the “double vortex” flow of Marangoni convection is asymmetrically distributed in the center of the molten pool. The fluid flow line has irregular flow and the circulation area generated at the front of the molten pool is larger in the corresponding scanning direction. Under the magnetic field influence, the overall flow velocity of the molten pool obviously increases, and the maximum flow velocity of the molten pool reaches 0.28 m/s. The study lays a significant theoretical foundation for revealing the mechanism of laser cladding assisted by a magnetic field.

Stiffness properties of regular p-bars tensegrity prisms under the compressive loading

The regular tensegrity prisms are a kind of fundamental unit, which can be formed into different configurations by different splicing approaches to achieve specific structural functions. Taking regular prisms as the research object, this article presents an analytical method for structural deformations under compressive loading. The structural parameters after loading can be obtained directly by solving the nonlinear force density equation, which simplifies the form-finding process. This article also studies the structural stiffness under different connection modes. By defining the twist angle change rate and internal force utilization rate, we can compare the relative deformation of different tensegrity prisms. The results show that the relative deformation of the three-bar prism is minimal, and it has the best stiffness.