Analysis of Low-Frequency Vibrational Modes and Particle Rearrangements in Marginally Jammed Amorphous Solid under Quasi-Static Shear

We present the numerical simulation results of a model granular assembly formed by spherical particles with tIertzian interaction subjected to a simple shear in the athermal quasi-static limit. The stress-strain curve is shown to separate into smooth, elastic branches followed by a subsequent plastic event. Mode analysis shows that the lowest-frequency vibrational mode is more localized, and eigenvalues and participation ratios of low- frequency modes exhibit similar power-law behavior as the system approaches plastic instability, indicating that the nature of plastic events in the granular system is also a saddle node bifurcation. The analysis of projection and spatial structure shows that over 75% contributions to the non-affine displacement field at a plastic instability come from the lowest-frequency mode, and the lowest-frequency mode is strongly spatially correlated with local plastic rearrangements, inferring that the lowest-frequency mode could be used as a predictor for future plastic rearrangements in the disordered system jammed marginally.

Influence of vibration mode on the screening process

The screening of particles with different vibration modes was simulated by means of a 3D discrete element method (3D-DEM). The motion and penetration of the particles on the screen deck were analyzed for linear, circular and elliptical vibration of the screen. The results show that the travel velocity of the particles is the fastest, but the screening efficiency is the lowest, for the linear vibration mode. The circular motion resulted in the highest screening efficiency, but the lowest particle travel velocity. In the steady state the screening efficiency for each mode is seen to increase gradually along the longitudinal direction of the deck. The screening efficiency increment of the circular mode is the largest while the linear mode shows the smallest increment. The volume fraction of near-mesh size particles at the underside is larger than that of small size particles all along the screen deck. Linear screening mode has more near-mesh and small size particles on the first three deck sections, and fewer on the last two sections, compared to the circular or elliptical modes.

Vibrating Particles System Algorithm for Solving Classification Problems

Big data is a term that refers to a set of data that,due to its largeness or complexity,cannot be stored or processed with one of the usual tools or applications for data management,and it has become a prominent word in recent years for the massive development of technology.Almost immediately thereafter,the term“big data mining”emerged,i.e.,mining from big data even as an emerging and interconnected field of research.Classification is an important stage in data mining since it helps people make better decisions in a variety of situations,including scientific endeavors,biomedical research,and industrial applications.The probabilistic neural network(PNN)is a commonly used and successful method for handling classification and pattern recognition issues.In this study,the authors proposed to combine the probabilistic neural network(PPN),which is one of the data mining techniques,with the vibrating particles system(VPS),which is one of the metaheuristic algorithms named“VPS-PNN”,to solve classi-fication problems more effectively.The data set is eleven common benchmark medical datasets from the machine-learning library,the suggested method was tested.The suggested VPS-PNN mechanism outperforms the PNN,biogeography-based optimization,enhanced-water cycle algorithm(E-WCA)and the firefly algorithm(FA)in terms of convergence speed and classification accuracy.

Magnetic Charge Theory Part 4: Fermion Angular Momentum

The magnetic charge concept is further developed to define the vibrational motion of a charged particle moving in the ether/dark matter. The angular momentum of the resulting motion is derived to be ħ/2 at all velocities. The vibrational motion also provides additional justification for the Coulomb and gravitational forces not having a singularity. Additional insights into antimatter composition and annihilation are also developed.

Kinematics and dynamics of a particle on a non-simple harmonic vibrating screen

The motion of a particle on a screen is directly affected by the motion of the screen if airflow and inter- granular friction are ignored. To study this effect, a mathematical model was established to analyze the motion of a planar reciprocating vibrating screen, and a matrix method was employed to derive its equa- tion of motion. The motion of the screen was simulated numerically and analyzed using MATLAB. The results show that the screen undergoes non-simple harmonic motion and the law of motion of each point in the screen is different. The tilt angle of the screen during screening is not constant but varies according to a specific periodic function. The results of numerical simulations were verified through experiments. A high-speed camera was used to track the motion of three points in the longitudinal direction of the screen. The balance equation for forces acting on a single particle on the screen was derived based on the non-simple harmonic motion of the screen, These forces were simulated using MATLAB. Different types of particle motion like slipping forward, moving backward, and being tossed to different parts of the screen were analyzed. A vibro-impact motion model for a particle on the non-simple harmonic vibrating screen was established based on the nonlinear law of motion of the particle. The stability of fixed points of the map is discussed. Regimes of different particle behaviors such as stable periodic motion, period-doubling bifurcation motion, Hopf bifurcation motion, and chaotic motion were obtained. With the actual law of motion of the screen and the behavior of a particle on the screen, a theoretical basis for design optimization of the screen is provided.

Experiments on densifying packing of equal spheres by two-dimensional vibration

Densification of mono-sized sphere packings using two-dimensional （2D） vibration was experimentally studied. The effects of vibration mode, amplitude and frequency, feeding method, and container size on packing density were systematically analyzed. Useful results were obtained.

Physical study on the vibrated packing densification of mono-sized cylindrical particles

Systematic physical experiments examining the packing densification of mono-sized cylindrical parti- cles subject to 3D mechanical vibration were carried out. The influence of vibration conditions such as vibration time, frequency, amplitude, vibration strength, container size, and the aspect ratio and spheric- ity of the particle on the packing density were analyzed and discussed. For each initial packing density with a certain aspect ratio, operating parameters were optimized to achieve much denser packing. The results indicate that the packing density initially increases with vibration time and then remains con- stant. The effects of vibration frequency and amplitude on the packing densification have similar trends, i.e. the packing density first increases with the vibration frequency or amplitude to a high value and then decreases; too large or small frequency or amplitude does not enhance densification. Increasing the container size can reduce container wall effects and help achieve a high packing density. Varying the particle aspect ratio and sphericity can lead to different dense random packing structures. Overall, based on results of the examined systems, the highest random packing density obtained in an infinite sized container can reach 0.73, which agrees well with corresponding numerical and analytical results in the literature.

Energy dissipation mechanism and experiment of particle dampers for gear transmission under centrifugal loads

As a passive means of vibration reduction, particle damping is mainly applied to the horizontal or vertical steady field. However, it is seldom applied to centrifugal fields. Under high speed and heavy loading, the vibration of tooth surfaces of gear transmissions becomes more severe shortening gear service life and augmenting noise. Under centrifugal loading, the particle system exhibits different characteristics, for example, particles are extruded at the end farthest from the center. We investigated gears with drilled via holes filled with damping particles. Using the discrete-element method, we developed an energy dissipation model for the particle system accounting for friction and inelastic collisions. Energy dissipation and damping characteristics of this system were analyzed. Experiments were also conducted with the gear system having different particle filling rates. The results show that this filling rate is an important parameter associated with particle damping in a centrifugal field. An unsuitable filling rate would significantly reduce damping effectiveness. With changes in rotation speed and load, the gear transmission system has different optimal filling rates. The results provide guidelines for the application of particle damping in centrifugal fields of gear transmissions.

Experimental study on the 3D vibrated packing densification of binary sphere mixtures

The packing densification of binary spherical mixtures under 3D mechanical vibration was studied experimentally. The influences of vibration frequency （ω）, volume fraction of large spheres （XL）, sphere size ratio （r, diameter ratio of small to large spheres）, and container size （D） on the random binary packing density （p） were systematically analyzed. For any given set of conditions, there exist optimal ω and XL to realize the densest random binary packing; too large or small ω and XL is not helpful for densification. The influences of both r and D on p are monotonic; either reducing r or increasing D leads to a high value of p. With all other parameters held constant, the densest random packing occurs when XL is dominant, which is in good agreement with the Furnas relation. Moreover, the highest random binary packing density obtained in our work agrees well with corresponding numerical and analytical results in the literature.