Point Force Research Articles

Investigation of turbulence and skin friction modification in particle-laden channel flow using lattice Boltzmann method

Interaction between turbulence and particles is investigated in a channel flow. The fluid motion is calculated using direct numerical simulation (DNS) with a lattice Boltzmann (LB) method, and particles are tracked in a Lagrangian framework through the action of force imposed by the fluid. The particle diameter is smaller than the Kolmogorov length scale, and the point force is used to represent the feedback force of particles on the turbulence. The effects of particles on the turbulence and skin friction coefficient are examined with different particle inertias and mass loadings. Inertial particles suppress intensities of the spanwise and wall-normal components of velocity, and the Reynolds shear stress. It is also found that, relative to the reference particle-free flow, the overall mean skin-friction coefficient is reduced by particles. Changes of near wall turbulent structures such as longer and more regular streamwise low-speed streaks and less ejections and sweeps are the manifestation of drag reduction.

Theoretical Acoustic Prediction of the Aerodynamic Interaction for Contra-Rotating Fans

The theoretical prediction formula of far-field interaction tonal noise radiation by contra-rotating fans in free space with point force approximation is derived as the extension of the method of William K. Blake for the conventional stator–rotor interaction. Two primary mechanisms for interaction noise reduction are easily found based on a simple analysis of the formula, which are either to increase the order of the Bessel function of the first kind or to reduce the unsteady lift force. The latter can be realized by reducing the magnitude of the wake centerline velocity deficit or broadening the wake width, which are both related to the interstage separation distance. The aerodynamic and acoustic effects of inter-rotor axial spacing are studied experimentally. It is found that the axial spacing has little effect on aerodynamic performance of the contra-rotating fan, when the nondimensional inter-rotor axial gap based on the axial rotor chord varies in the measured range of 0.18–1.36. Sound pressure level follows an exponential decay law with interstage spacing, from which it is predicted that the three-dimensional rotor wake follows an exponential decay law as well and it decays much faster than the two-dimensional cascade wake. When the nondimensional inter-rotor axial gap is larger than 0.41, it has little effect on the noise level. On the contrary, the interaction noise is very sensitive to the axial spacing in the range below 0.41.

Vibration Analysis of Thin Plate Structures Subjected to a Moving Force Using Frequency‐Domain Spectral Element Method

A frequency‐domain spectral element method (SEM) is proposed for the vibration analysis of thin plate structures subjected to a moving point force. The thin plate structures may consist of multiple rectangular thin plates with arbitrary boundary conditions that form multispan thin plate structures, such as bridges. The time‐domain point force moving on a thin rectangular plate with arbitrary trajectory is transformed into a series of stationary point forces in the frequency domain. The vibration responses induced by the moving point force are then obtained by superposing all vibration responses excited by each stationary point force. For the vibration response of a specific stationary point force, the plate subjected to the specific stationary point force is represented by four spectral finite plate elements, which were developed in the authors’ previous work. The SEM‐based vibration analysis technique is first presented for single‐span thin plate structures and then extended to the multispan thin plate structures. The high accuracy and computational efficiency of the proposed SEM‐based vibration analysis technique are verified by comparison with other well‐known solution methods, such as the exact theory, integral transform method, finite element method, and the commercial finite element analysis package ANSYS.

Vibration analysis of a multi-span beam subjected to a moving point force using spectral element method

In this study, we propose a frequency domain spectral element method (SEM) for the vibration analysis of a multi-span beam subjected to a moving point force. This study is an extension of the authors\' previous study for a single-span beam subjected to a moving point force, where the two-element model-based SEM was applied. In this study, each span of a multi-span beam is represented by the Timoshenko beam model and the moving point force is transformed into the frequency domain as a series of each stationary point force distributed on the multi-span beam. The span at which a stationary point force is located is represented by two-element model, but all other spans are represented by one-element models. The vibration responses to a moving point force are obtained by superposing all individual vibration responses generated by each stationary point force. The high accuracy and computational efficiency of the proposed SEM are verified by comparing the solutions by SEM with exact analytical solutions by the integral transform method (ITM) as well as the solutions by the finite element method (FEM).

Wrinkling patterns in soft shells.

Curvature plays an important role in the morphological evolution of soft shells under stretch. Here, through a combination of experiment, theory and simulation, we investigate the behavior of a hemispherical soft shell subject to an increasing outward point force at its pole. In contrast to an inward point force inducing a polygonal pattern of buckling in the shell, we observe a four-stage morphological transition and symmetry breaking under an increasing outward point force. The shell undergoes axisymmetric deformation around its pole and then buckles into a non-axisymmetric shape with a number of shallow wrinkles emanating from the pole, followed by the emergence of crater-like deep crumples and ultimately a transformation into a wrinkled pseudocone. Our theoretical analysis and numerical simulations yield the critical conditions for the morphological transitions at each stage of deformation and reveal the underlying interplays between elastic bending and stretching energies and the curvature of the shell.

Численное моделирование ближнего акустического поля бесконечной пластины, возбуждаемой сосредоточенной силой

Численное моделирование ближнего акустического поля бесконечной пластины, возбуждаемой сосредоточенной силой

Experimental Study of the Debris Flow Slurry Impact and Distribution

In this study, we present a new method to calculate debris flow slurry impact and its distribution, which are critical issues for designing countermeasures against debris flows. There is no unified formula at present, and we usually design preventive engineering according to the uniform distribution of the maximum impact force. For conducting a laboratory flume experiment, we arrange sensors at different positions on a dam and analyze the differences on debris flow slurry impact against various densities, channel slopes, and dam front angles. Results show that the force of debris flow on the dam distributes unevenly, and that the impact force is large in the middle and decreases gradually to the both sides. We systematically analyze the influence factors for the calculation of the maximum impact force in the middle point and give the quantitative law of decay from the middle to the sides. We propose a method to calculate the distribution of the debris flow impact force on the whole section and provide a case to illustrate this method.

Effect of proton irradiation on microstructure evolution of permanent magnet

Nd2Fe14B rare earth and Sm2Co17 type permanent magnets have been widely used in the third generation of synchronous radiation light source and free electron laser facility in undulators and other components of particle accelerators. In addition, the permanent magnets are used in the radiation treatment system for cancer as a beam line component. Compared with Sm2Co17 type permanent magnet, Nd2Fe14B rare earth permanent magnet has the characteristics of large magnet energy product, rich starting materials and low price. Although its Curie point and coercive force are lower than those of Sm2Co17 type of permanent magnet, Nd2Fe14B rare earth permanent magnet is still widely used. As an important part of the accelerator, the magnetic loss phenomenon appears when permanent magnet is used in long-term irradiation environments, which affects the stability and quality of the beam. Therefore, it is important to investigate the magnet demagnetization induced by photon irradiation. Recently, there have appeared many researches of the phenomena of demagnetization for the permanent magnets under the irradiation of various kinds of particles. By using different research methods and experimental conditions, single particle irradiation is performed and then the effect of irradiation on magnetic loss is investigated by comparing the macro magnetic properties (such as magnetic flux loss rate, saturation magnetization, etc.). However, there are not any available reports on the microstructure investigations of permanent magnets after irradiation. Microstructure affects macroscopic magnetic properties. In order to discuss the microscopic demagnetization mechanism, the transmission electron microscope is used to characterize and analyze the microstructure evolutions of Sm2Co17 type permanent magnet and Nd2Fe14B rare earth permanent magnet before and after proton irradiation. The evolution of the number density of nanocrystal and its size distribution induced by proton irradiation are calculated. Moreover, the effect of microstructure evolution on macroscopic magnetic loss is discussed. The results indicate that the microstructure of permanent magnet transforms from single crystal structure to polycrystalline structure with the increase of the proton irradiation damage level. Nanocrystal and the matrix of permanent magnet have the same crystal structure. With the irradiation damage level increasing, the nanocrystal density of Nd2Fe14B first increases and then decreases, while the particle size distribution first increases and then keeps constant; the number density of nanocrystal of Sm2Co17 type permanent magnet gradually decreases, while particle size gradually increases, and comparing with Sm2Co17 type permanent magnet, the crystal structure of Nd2Fe14B permanent magnet shows an obvious tendency to be amorphous in 2 dpa irradiation damage level.

Numerical Analysis of Nonlocal Fracture Models in Hölder Space

In this work, we calculate the convergence rate of the finite difference approximation for a class of nonlocal fracture models. We consider two point force interactions characterized by a double well potential. We show the existence of a evolving displacement field in H\"{o}lder space with H\"{o}lder exponent $\gamma \in (0,1]$. The rate of convergence of the finite difference approximation depends on the factor $C_s h^\gamma/\epsilon^2$ where $\epsilon$ gives the length scale of nonlocal interaction, $h$ is the discretization length and $C_s$ is the maximum of H\"older norm of the solution and its second derivatives during the evolution. It is shown that the rate of convergence holds for both the forward Euler scheme as well as general single step implicit schemes. A stability result is established for the semi-discrete approximation. The H\"older continuous evolutions are seen to converge to a brittle fracture evolution in the limit of vanishing nonlocality.

Enhanced fatigue structural stress analysis of a heavy vehicle seam welded steel chassis frame: FEA model preparation, weld model description, fatigue stress calculation and correlation with 10 year operating experience

A FE seam weld model has been built for advanced fatigue structural stress analysis. The shell element model allows both weld toe and weld root fatigue assessment. In order to validate the model, this project deals with the complete analysis of a last decade manufactured vehicle for which experience feedback is possible. The vehicle structure is mainly built with steel sheets and the assembly is performed by seam welding. Shell element model is appropriate for FEA. The entire FEM preparation is presented hereafter and each step is detailed: 3D CAD weld building, mid-surface idealization, weld leg imprint creation, weld mesh connection and load application. Fatigue analysis is performed based on a fatigue limit approach and IIW FAT data. For every structure location a Haigh diagram is built. Different diagrams are presented for plain metal, cut edge, weld toe and weld root. The FEA results are post processed and each appropriate tensor component is taken into account. For plain metal, stress variation along the worst principal stress orientation is calculated. In welds, for both toe and root locations, the structural stress computation based on grid point forces extraction is described. Longitudinal shear stress in weld and at weld toe as well as weld longitudinal normal stress calculations are detailed. Fatigue results are displayed for each location over the whole chassis model. Finally, vehicles built during the last decade are inspected back from the customers experience field. Observed crack types and locations are compared to fatigue analysis predictions.

Dynamic Interaction Between Microtubules and the Nucleus Regulates Nuclear Movement During Neuronal Migration.

Fine structures of the mammalian brain are formed by neuronal migration during development. Newborn neurons migrate long distances from the germinal zone to individual sites of function by squeezing their largest cargo, the nucleus, through the crowded neural tissue. Nuclear translocation is thought to be orchestrated by microtubules, actin, and their associated motor proteins, dynein and myosin. However, where and how the cytoskeletal forces are converted to actual nuclear movement remains unclear. Using high-resolution confocal imaging of live migrating neurons, we demonstrated that microtubule-dependent forces are directly applied to the nucleus via the linker of nucleoskeleton and cytoskeleton complex, and that they induce dynamic nuclear movement, including translocation, rotation, and local peaking. Microtubules bind to small points on the nuclear envelope via the minus- and plus-oriented motor proteins, dynein and kinesin-1, and generate a point force independent of the actin-dependent force. Dynamic binding of microtubule motors might cause a continuously changing net force vector acting on the nucleus and results in a stochastic and inconsistent movement of the nucleus, which are seen in crowded neural tissues.

Electricity Generation System with Piezoelectric Element Using Acoustic Radiation Energy

In this study, a circular plate that is installing a piezoelectric element at its center is adopted as energy-harvesting system and is subjected to a harmonic point force. Because this system cannot avoid the influence of its acoustic radiation, the influence is considered theoretically using the equation of plate motion taking into account its radiation impedance and is estimated by the electricity generation efficiency, which is derived from the ratio of the electric power in the electricity generation and the mechanical power supplied to the plate. As a result, the efficiency is suppressed by the acoustic radiation from the plate, so that the efficiencies are so different in whether to take into consideration the radiation impedance or not. Because those results are verified by the electricity generation experiment and radiation acoustic energy has a hopeful prospect for improving the performance of this system, mechanical-acoustic coupling is used to make the most of the acoustic energy. Therefore, a cylinder that has the above plates at both ends is also adopted as the electricity generation system and mechanical-acoustic coupling is caused between the plate vibrations and an internal sound field into the cylindrical enclosure by subjecting one side of each plate to a harmonic point force. Then, the effect of coupling is evaluated by comparing with the efficiencies in the electricity generation system of only plate. Specifically, because the radiation impedance increases with the plate thickness, i.e., with the natural frequency of the plate, it is demonstrated that the effect of coupling becomes remarkable with increasing the thickness on the electricity generation efficiency.

Low-frequency sound radiation of infinite orthogonally rib-stiffened sandwich structure with periodic subwavelength arrays of shunted piezoelectric patches

In order to minimize the low-frequency sound radiation of an infinite orthogonally rib-stiffened sandwich structure, the periodic subwavelength arrays of shunted piezoelectric patches are introduced. Based on the piezoelectric shunt technique and effective medium method, the panels and piezoelectric patches are equivalent to two homogeneous facesheets. Then, considering all the inertia terms of the rib-stiffeners, a complete theoretical model is built for harmonic point force excitation by using Kirchhoff’s thin plate theory. The vibration displacements of the facesheets in wavenumber space are solved by Fourier transform technique to complete the prediction of vibroacoustic responses. Furthermore, the correctness and effectiveness of the present model are verified by sequentially using published analytical models, simulation results and theoretical predictions in strict accordance with two prerequisites. At last, the influence laws of key influencing parameters on the research structure are investigated. All the results demonstrate that the proposed structure can effectively attenuate the structural radiation.

Complex variable formulation for a rigid line inclusion interacting with a generalized singularity

Analytical solution for a rigid line inclusion embedded in an infinite-extended plane under non-uniform loading is still a challenging problem in inclusion mechanics, which has both theoretical and applied significance in material engineering. In this paper, by directly employing Kolosov–Muskhelishvili stress potentials, a rigid line inclusion interacting with a generalized singularity is addressed in the framework of plane deformation, with the help of the superposition principle. It should be pointed out that the generalized singularity in this study can represent a point force, an edge dislocation, a point moment, a point nucleus of strain, and even remote uniform load, etc. The solutions can be used as kernel functions for integral equation formulations of rigid line inclusion–substrate system models using the Green’s function method. With this framework, stress field and stress intensity factors at the line inclusion ends are analyzed. The application of the solutions is demonstrated with two simple examples: (i) the rigid line inclusion under remote loading is studied, and it is strictly confirmed with rigorous proof that the remote shear load will not arouse stress concentration; (ii) a rigid line inclusion interacting with a dislocation is investigated, and the full solution is given. These examples also partially validate the general solution derived this study.

Point force singularities outside a drop covered with an incompressible surfactant: Image systems and their applications

Image systems for Stokes flow singularities outside a drop covered with an incompressible surfactant are derived. They are used in finding the mobility matrix for two surfactant-laden drops of arbitrary sizes and the velocity of a microorganism outside a surfactant-covered drop.

Simultaneous shape and topology optimization of prestressed concrete beams

This paper presents a new optimization approach for the design of prestressed concrete beams. The prestressing tendon is modeled as a chain of linear segments that transfer point forces to the concrete domain according to the tendon’s angles. The concrete beam is modeled as a discretized continuum following density-based approaches to topology optimization. The shape of the tendon and the topology of the surrounding concrete are optimized simultaneously within a single problem formulation. A special filtering technique is developed in order to ensure that the tendon is covered by concrete, thus shape and topological variables are tightly coupled. Several test cases demonstrate the applicability of the proposed optimization procedure. The deformation of the optimized designs due to external loads is counteracted by the deformation due to prestressing, hence by tuning the force in the tendon the total deformation can approach zero. Consequently, the beams exhibit a compression-only response meaning that the common goal of prestressed concrete design is achieved.

Deflection modeling for a needle actuated by lateral force and axial rotation during insertion in soft phantom tissue

In prostate brachytherapy, radioactive seeds are implanted into the prostate for treatment of early-stage localized cancer. A major issue is seed displacement due to needle deflection, which is difficult to control as the needle is inserted manually. To address the problem and automate needle insertion, robotic systems, mathematical models for estimation and prediction and control algorithms have been developed. The method of choice for robotic steering of beveled-tip needles is predominantly intermittent axial needle rotation since this re-aligns the beveled tip and thus re-directs the needle. In this work, we present a method for needle steering to supplement axial needle rotation. A point force applied laterally to the needle near its point of insertion into tissue is used to displace the needle perpendicularly relative to its insertion axis. An advantage of this method is that the lateral force provides a continuous control input and thus continuous deflection control as opposed to axial needle rotation by 180 degrees in the 2D case of planar needle steering. Further, more control over deflection is possible as the lateral force provides direct shape change for the needle and improves the under-actuated nature of the needle. In order to predict and estimate needle deflection during insertion while applying both lateral force and axial rotation, a mechanics- and energy-based model for needle deflection is developed. Both single-layer and multi-layer tissue can be modeled if the tissue layer thickness is known. The accuracy of the model is validated experimentally. A comparison between the measured tip deflection and the model-based estimate shows only a small error. Moreover, control and sensitivity studies are carried out through insertion simulations using the model. The studies show the potentials and limitations for needle deflection reduction with various combinations of lateral force application and intermittent 180 degrees axial needle rotation.

A periodic set of edge dislocations in an elastic semi-infinite solid with a planar boundary incorporating surface effects

The 2-D problem of interacting periodic set of edge dislocations and point forces with planar traction-free surface of semi-infinite elastic solid at the nanoscale is considered. Complex variable based technique and Gurtin-Murdoch model of surface elasticity, which leads to the hypersingular integral equation in surface stress, are used. The solution of this equation and explicit formulas for stress field (Green functions) are obtained in terms of Fourier series. The detailed numerical investigation of stress field induced by the dislocations at the nanometer distance from the surface and the force acting on each dislocation in classical and non-classical (with surface stress) solutions is presented. It is shown that formulas derived for the periodic set of dislocations can be applied to the analysis of the interaction of a single dislocation with the surface as well. The fundamental solutions obtained in the work can be used for applying the boundary integral equation method to an analysis of defects such as cracks and inhomogeneities, periodically distributed at the nanometer distance from the boundary.

Spontaneous oscillations of elastic filaments induced by molecular motors.

It is known from the wave-like motion of microtubules in motility assays that the piconewton forces that motors produce can be sufficient to bend the filaments. In cellular phenomena such as cytosplasmic streaming, molecular motors translocate along cytoskeletal filaments, carrying cargo which entrains fluid. When large numbers of such forced filaments interact through the surrounding fluid, as in particular stages of oocyte development in Drosophila melanogaster, complex dynamics are observed, but the detailed mechanics underlying them has remained unclear. Motivated by these observations, we study here perhaps the simplest model for these phenomena: an elastic filament, pinned at one end, acted on by a molecular motor treated as a point force. Because the force acts tangential to the filament, no matter what its shape, this 'follower-force' problem is intrinsically non-variational, and thereby differs fundamentally from Euler buckling, where the force has a fixed direction, and which, in the low-Reynolds-number regime, ultimately leads to a stationary, energy-minimizing shape. Through a combination of linear stability theory, analytical study of a solvable simplified 'two-link' model and numerical studies of the full elastohydrodynamic equations of motion, we elucidate the Hopf bifurcation that occurs with increasing forcing of a filament, leading to flapping motion analogous to the high-Reynolds-number oscillations of a garden hose with a free end.

Finite difference time domain modelling of a point-excited elastic plate radiating into an acoustic cavity.

Finite difference time domain (FDTD) models are developed to solve the vibroacoustic problem of a thin elastic plate undergoing point force excitation and radiating into an acoustic cavity. Vibroacoustic modelling using FDTD can be computationally expensive because structure-borne sound wavespeeds are relatively high and a fine spatial resolution is often required. In this paper a scaling approach is proposed and validated to overcome this problem through modifications to the geometry and physical properties. This allows much larger time steps to be used in the model which significantly reduces the computation time. Additional reductions in computation time are achieved by introducing an alternative approach to model the boundaries between the air and the solid media. Experimental validation is carried out using a thin metal plate inside a small reverberant room. The agreement between FDTD and measurements confirms the validity of both approaches as well as the FDTD implementation of a thin plate as a three-dimensional solid that can support multiple wave types. Below the lowest room mode, there are large spatial variations in the sound field within the cavity due to the radiating plate; this indicates the importance of having a validated FDTD model for low-frequency vibroacoustic problems.