Motions Of Nodes Research Articles

A Finite Element Model for Static Performance Analysis of Gas Foil Bearings Based on Frictional Contacts

In gas foil bearings, frictional contacts are one of the main factors that affect bearing performance, which is highly nonlinear. Using a finite element method, this article presents a nonlinear model for static performance analysis of foil bearings based on frictional contacts. The model incorporates the top foil and the interactions between bumps by modeling the foil structure with beam elements. The penalty method and the node-to-segment contact scheme are utilized to model the contacts of the structure. The stick–slip motions of the contact nodes are considered. Because the contact behavior is path dependent when the friction is taken into account, a step-by-step incremental iterative method is used for solution, in which the calculation at the present step is based on the results from the previous step. An algorithm is designed to determine the contact states, and the calculation at the next incremental step will not be performed until all contact states meet the check conditions in the present step. To couple the structure domain with the fluid film, each iterative step of the pressure calculation using the finite difference method is regard as an incremental step. This model is validated by comparisons with published results. Using this model, hysteretic behavior caused by friction and dissipative properties of the foil structure are analyzed under static condition.

The Theory and New Unified Formulas of Displacement-Type Local Absorbing Boundary Conditions

ABSTRACTA series of classical absorbing boundary conditions (ABCs), including paraxial-approximation ABCs, Liao’s multi-transmitting formula (MTF), Higdon ABCs, and some other related techniques, have the common feature that the motion of an arbitrary artificial boundary node at each timestep is directly predicted from the motions of some adjacent nodes at several previous timesteps. They are expressed in somewhat equivalent forms, contain similar control parameters, and have comparable accuracy and stability in numerical simulations. This study develops a theoretical framework called displacement-type (a more exact name would be “prediction-type” or “extrapolation-type”) local ABCs to merge these boundary conditions. The idea of this theory mainly originates from the versatility of MTF, which uses a unified formula to approximate the propagation of outgoing waves through each boundary node. This idea can be generalized to other displacement-type local ABCs to unify their expressions and to optimize their applications. These ABCs have two basic control parameters; one is the boundary order, and the other is adjustable computational wave velocities. Considering the poor performance of paraxial ABCs and the slight imperfections in MTF and Higdon ABCs, we propose two new unified formulas to be the starting points of expressing, evaluating, and applying displacement-type local ABCs. One formula is an optimized MTF by introducing various computational wave velocities. The other formula is a generalized Higdon boundary formula, which is established in a unified local coordinate and uses the adjustable computational wave velocities. The rule of choosing boundary parameters for the absorption of acoustic and elastic waves is discussed in detail. Numerical tests validate the proposed theory and formulas. Issues on numerical stability are briefly reviewed and tested in simulation examples. This is still an active research topic related to displacement-type local ABCs.

TCDS: A Time-Relevant Graph Based Topology Control in Triple-Layer Satellite Networks

In a triple-layer satellite (TLS) network with GEO, MEO and LEO, maintaining connectivity of topology confronts the challenge of intermittent visibility due to periodically orbital motions of nodes. To address this issue, in this letter, we develop a time-relevant graph called as space-time graph (STG) model for depicting the topological structure with fine granularity, by taking into account time-domain and spatial-domain properties. With STG, a Time-evolving Connected Dominating Set (TCDS) algorithm is proposed to construct a backbone network for efficient topology control with high spatial and temporal accessibility of the triple-layer network. The simulation results demonstrate better efficiency of the proposed algorithm with respects to the average hop and connectivity probability, compared with time-evolving multi-layered clustering (TEMC) algorithm and single time-slot clustering (STC) algorithm.

Vibrational Characteristics of Two-Dimensional Composite Structures of Hexagonal Boron Nitride and Graphene

We use an eigenmode analysis to investigate normal mode vibrations of hexagonal boron nitride (h-BN) and of various types of graphene and h-BN composites. The vibrational spectrum of pristine h-BN structure was a rescaled one of pristine graphene. The vibrational spectra of graphene and h-BN composites with zigzag and with armchair boundaries were just mixtures of the vibrational spectra of the pristine structures of graphene and h-BN, respectively. The vibrational spectrum of h-BN doped with a graphene quantum dot was similar to that of h-BN, and the vibrational spectrum of graphene doped with a small piece of boron nitride was similar to that of graphene. We found that the resemblance of the vibrational spectra was closely related to the similarities of the lattice structures. Using the amplitude analysis, we were able to identify the eigenmodes of the various composites as motions of nodes in the graphene region or in the h-BN region or at the interfacial boundaries between them.

Formation of collective conformational degrees of freedom during macromolecular chain folding dynamics in a viscous medium

Computational methods were used to study the dynamics of the formation of the collective conformational degrees of freedom in the relaxation folding of a model biopolymer chain of 50 nodes in a viscous medium; the model has been described previously. Collective conformational motions of the nodes were shown to arise due to friction forces in a viscous medium. The collective motions have several typical forms, including a wave of differently directed motions of chain nodes that propagates from one end of the chain to another (like a soliton) in response to a pertubation in terminal group position. Individual nodes located at the middle of the chain make approximately equal contributions to the total energy dissipation rate. The end nodes contribute approximately 2–4 times more than internal nodes to the total energy dissipation. The results of numerical experiments are consistent with the theoretical concept developed earlier to describe the dynamics of linear macromolecular chains in a viscous medium in the limit of a very large number of nodes.

A supplementary note on constructing the general Earth's rotation theory

AbstractRepresenting a post-scriptum supplementary to a previous paper of the authors Brumberg & Ivanova (2011) this note aims to simplify the practical development of the Earth's rotation theory, in the framework of the general planetary theory, avoiding the non–physical secular terms and involving the separation of the fast and slow angular variables, both for planetary–lunar motion and Earth's rotation. In this combined treatment of motion and rotation, the fast angular terms are related to the mean orbital longitudes of the bodies, the diurnal and Euler rotations of the Earth. The slow angular terms are due to the motions of pericenters and nodes, as well as the precession of the Earth. The combined system of the equations of motion for the principal planets and the Moon and the equations of the Earth's rotation is reduced to the autonomous secular system with theoretically possible solution in a trigonometric form. In the above–mentioned paper, the Earth's rotation has been treated in Euler parameters. The trivial change of the Euler parameters to their small declinations from some nominal values may improve the practical efficiency of the normalization of the Earth's rotation equations. This technique may be applied to any three-axial rigid planet. The initial terms of the corresponding expansions are given in the Appendix.

SU-GG-T-22: An Adaptive Strategy for Simultaneous Treatment of the Prostate and Pelvic Lymph Nodes

Purpose: Certain prostate cancer patients are treated with simultaneous irradiation of pelvic lymph nodes and the prostate gland. One common method to compensate for prostate motion is to shift the patient based on implanted prostate markers. However, the pelvic lymph nodes move little relative to the bony anatomy. In this study, we evaluate an adaptive strategy designed to ensure that radiation is delivered accurately to both the prostate and the pelvic lymph nodes. Materials and Methods:Treatment plans devised using clinical planning CT data and structures were optimized to deliver 50 Gy to the expanded prostate and seminal vesicles and 45 Gy to the lymph nodes. We used megavoltage conebeam CT data acquired during treatment to create a model of daily anatomical variations. The treatment plan and structures were transferred to this new model. The prostate, seminal vesicles, bladder, and rectum structures were shifted according to the position of prostate markers. The lymph node volumes were transferred according to the bony anatomy. In total, four plans were prepared: 1) the original plan 2) original plan shifted to match prostate motion 3) aperture morphing to compensate for prostate motion, and 4) aperture morphing followed by segment weight optimization. Results: When the isocenter is shifted to track the prostate, the prostate received the correct dose while lymph nodes were underdosed. In one example, we found that D‐95% reduced to 3500 cGy. Aperture morphing alone was not sufficient to deliver the correct dose to both the lymph nodes and prostate. However, aperture morphing followed by segment weight optimization improved coverage of the nodes and prostate. Conclusions: Our results demonstrate that aperture morphing combined with segment weight optimization is an adaptive strategy that can be used to compensate for the independent motions of the lymph nodes and prostate. Research sponsored by Prowess Inc.

Actuating Mechanism and Design of a Cylindrical Traveling Wave Ultrasonic Motor Using Cantilever Type Composite Transducer

BackgroundUltrasonic motors (USM) are based on the concept of driving the rotor by a mechanical vibration excited on the stator via piezoelectric effect. USM exhibit merits such as simple structure, quick response, quiet operation, self-locking when power off, nonelectromagnetic radiation and higher position accuracy.Principal FindingsA cylindrical type traveling wave ultrasonic motor using cantilever type composite transducer was proposed in this paper. There are two cantilevers on the outside surface of cylinder, four longitudinal PZT ceramics are set between the cantilevers, and four bending PZT ceramics are set on each outside surface of cantilevers. Two degenerate flexural vibration modes spatially and temporally orthogonal to each other in the cylinder are excited by the composite transducer. In this new design, a single transducer can excite a flexural traveling wave in the cylinder. Thus, elliptical motions are achieved on the teeth. The actuating mechanism of proposed motor was analyzed. The stator was designed with FEM. The two vibration modes of stator were degenerated. Transient analysis was developed to gain the vibration characteristic of stator, and results indicate the motion trajectories of nodes on the teeth are nearly ellipses.ConclusionsThe study results verify the feasibility of the proposed design. The wave excited in the cylinder isn't an ideal traveling wave, and the vibration amplitudes are inconsistent. The distortion of traveling wave is generated by the deformation of bending vibration mode of cylinder, which is caused by the coupling effect between the cylinder and transducer. Analysis results also prove that the objective motions of nodes on the teeth are three-dimensional vibrations. But, the vibration in axial direction is minute compared with the vibrations in circumferential and radial direction. The results of this paper can guide the development of this new type of motor.

The Chaotic Motion of the Solar System

AbstractIn a previous paper (Laskar, Nature, 338, 237-238), the chaotic nature of the solar system excluding Pluto was established by the numerical computation of the maximum Lyapunov exponent of its secular system over 200 Myr. In the present an explanation is given for the exponential divergence of the orbits: it is due to the transition from libration to circulation of the critical argument of the secular resonance 2(g4−g3)−(s4−s3) related to the motions of perihelions and nodes of the Birth and Mars. An other important secular resonance is identified: (g1−g5)−(s1−s2). Its critical argument stays in libration over 200 Myr with a period of about 10 Myr and amplitude from 85° to 135°. The main features of the solutions of the inner planets are now identified when taking these resonances into account. Estimates of the size of the chaotic regions are determined by a new numerical method using the evolution with time of the fundamental frequencies. The size of the chaotic regions in the inner solar system are large and correspond to variations of about 0.2 arcsec/year in the fundamental frequencies. The chaotic nature of the inner solar system can thus be considered as robust against small variations of the initial conditions or of the model. The chaotic regions related to the outer planets frequencies are very thin except for g6 which present variations sufficiently large to be significant over the age of the solar system.

The chaotic motion of the solar system: A numerical estimate of the size of the chaotic zones

In a previous paper (J. Laskar, Nature 338, (237–238)), the chaotic nature of the Solar System excluding Pluto was established by the numerical computation of the maximum Lyapunov exponent of its secular system over 200 myr. In the present paper an explanation is given for the exponential divergence of the orbits: it is due to the transition from libration to circulation of the critical argument of the secular resonance 2 ( g 4 − g 3) − ( s 4 − s 3) related to the motions of perihelions and nodes of Earth and Mars. Another important secular resonance is identified: ( g 1 − g 5) − ( s 1 − s 2). Its critical argument stays in libration over 200 myr with a period of about 10 myr and amplitudes from 85 to 135°. The main features of the solutions of the inner planets are now identified when taking these resonances into account. Estimates of the size of the chaotic regions are determined by a new numerical method using the evolution with time of the fundamental frequencies. The chaotic regions in the inner Solar System are large and correspond to variations of about 0.2 arcsec/year in the fundamental frequencies. The chaotic nature of the inner Solar System can thus be considered as robust against small variations in the initial conditions or in the model. The chaotic regions related to the outer planet frequencies are very thin except for those of g 6 which present variations sufficiently large to be significant over the age of the Solar System.