GENERAL SOLUTION FOR INTERACTION OF SOLITARY WAVES INCLUDING HEAD-ON COLLISIONS

A general solution of the Boussinesq equation is presented which solves the problem of interaction of any number of right-going and left-going solitary waves.The solution relies on the exact solu- tion of Gardner,Greene,Kruskal,and Miura(1967),and has the same degree of accuracy as that solution, but has a wider scope of application.It is much simpler than,but as accurate as,Hirota's exact solu- tion(1973)of the Boussinesq equation,to which the present solution is compared for the simplest case of two solitary waves in head-on collision.

ON HEAD-ON COLLISION BETWEEN TWO GKDV SOLITARY WAVES IN A STRATIFIED FLUID

In this paper,using the reductive perturbation method combined with the PLK method and two-parameter expansions,we treat the problem of head-on collision between two solitary waves described by the generalized Korteweg-de Vries equation (the gKdV equation) and obtain its second-order approximate solution.The results show that after the collision,the gKdV solitary waves preserve their profiles and during the collision,the maximum amplitute is the linear superposition of two maximum amplitudes of the impinging solitary waves.

Use of Finite Element Analysis for the Prediction of Driver Fatality Ratio Based on Vehicle Intrusion Ratio in Head-On Collisions

To estimate the aggressivity of vehicles in frontal crashes, national highway traffic safety administration (NHTSA) has introduced the driver fatality ratio, DFR, for different vehicle-to-vehicle categories. The DFR proposed by NHTSA is based on the actual crash statistical data, which makes it difficult to evaluate for other vehicle categories newly introduced to the market, as they do not have sufficient crash statistics. A finite element (FE) methodology is proposed in this study based on computational reconstruction of crashes and some objective measures to predict the relative risk of DFR associated with any vehicle-to-vehicle crash. The suggested objective measures include the ratios of maximum intrusion in the passenger compartments of the vehicles in crash, and the transmitted peak deceleration of the vehicles’ center of gravity, which are identified as the main influencing parameters on occupant injury. The suitability of the proposed method is established for a range of bullet light truck and van (LTV) categories against a small target passenger car with published data by NHTSA. A mathematical relation between the objective measures and DFR is then developed. The methodology is then extended to predict the relative risk of DFR for a crossover category vehicle, a light pick-up truck, and a mid-size car in crash against a small size passenger car. It is observed that the ratio of intrusions produces a reasonable estimate for the DFR, and that it can be utilized in predicting the relative risk of fatality ratios in head-on collisions. The FE methodology proposed in this study can be utilized in design process of a vehicle to reduce the aggressivity of the vehicle and to increase the on-road fleet compatibility in order to reduce the occupant injury out- come.

Head-on collision of ring dark solitons in Bose-Einstein condensates

The ring dark solitons and their head-on collisions in a Bose-Einstein condensates with thin disc-shaped potential are studied. It is shown that the system admits a solution with two concentric ring solitons, one moving inwards and the other moving outwards, which in small-amplitude limit, are described by the two cylindrical KdV equations in the respective reference frames. By using the extended Poincaré-Lighthill-Kuo perturbation method, the analytical phase shifts following the head-on collisions between two ring dark solitary waves are derived. It is shown that the phase shifts decrease with the radial coordinate r according to the r-1/3 law and depend on the initial soliton amplitude and radius.

HEAD-ON COLLISION BETWEEN TWO mKdV SOLITARY WAVES IN A TWO-LAYER FLUID SYSTEM

In this paper, based on the equations presented in [2], the head-on collision between two solitary waves described by the modified KdV equation (the mKdVequation, for short) is investigated by using the reductive perturbation method combined with the PLK method. These waves propagate at the interface of a two-fluid system, in which the density ratio of the two fluids equals the square of the depth ratio of the fluids. The second order perturbation solution is obtained. It is found that in the case of disregarding the nonuniform phase shift, the solitary waves preserve their original profiles after collision, which agrees with Fornberg and Whitham's numerical result of overtaking collision[6] whereas after considering the nonuniform phase shift, the wave profiles may deform after collision.

Head-on collision between two hydroelastic solitary waves with Plotnikov-Toland's plate model

Head-on collision between two hydroelastic solitary waves propagating at the surface of an incompressible and ideal fluid covered by a thin ice sheet is analytically studied by means of a singular perturbation method. The ice sheet is represented by the Plotnikov-Toland model with the help of the special Cosserat theory of hyperelastic shells and the Kirchhoff-Love plate theory,which yields the nonlinear and conservative expression for the bending forces. The shallow water assumption is taken for the fluid motion with the Boussinesq approximation. The resulting governing equations are solved asymptotically with the aid of the Poincaré-Lighthill-Kuo method,and the solutions up to the third order are explicitly presented. It is observed that solitary waves after collision do not change their shapes and amplitudes. The wave profile is symmetric before collision, and it becomes, after collision, unsymmetric and titled backward in the direction of wave propagation. The wave profile significantly reduces due to greater impacts of elastic plate and surface tension. A graphical comparison is presented with published results, and the graphical comparison between linear and nonlinear elastic plate models is also shown as a special case of our study.

Modeling of nonlinear envelope solitons in strongly coupled dusty plasmas:Instability and collision

Modeling of instability and collision of nonlinear dust-acoustic（NDA） envelope solitons in strongly coupled dusty plasmas（SCDPs） is theoretically investigated. The SCDPs consists of strongly correlated negatively variable-charged dust grains and weakly correlated Boltzmann electrons and ions. Using the derivative expansion perturbation technique, a nonlinear Schr dinger-type（NLST） equation for describing the propagation of NDA envelope solitons is derived. Moreover,the extended Poincar′e–Lighthill–Kuo（EPLK） method is employed to deduce the analytical phase shifts and the trajectories after the collision of NDA envelope solitons. In detail, the results show that both modulation instability and phase shift after collision of NDA envelope solitons will modify with the increase in the effects of the viscosity, the relaxation time, and the dust charge fluctuation. Crucially, the modeling of dust-acoustic envelope solitons collision, as reported here, is helpful for understanding the propagation of NDA envelope solitons in strongly coupled dusty plasmas.

发动机转静子同轴度偏心工艺优化研究

中涵道比涡扇发动机高压涡轮单元体安装时,由于存在套齿配合间隙、轴承径向游隙和弹性支座变形的同轴度影响因素,使得高压涡轮转子封严篦齿发生偏心向下,造成与静子空气挡油圈的碰磨故障。利用有限元静力学方法,分析得到弹性支座具体形位变化,利用最小二乘法原理,计算得到转子封严篦齿的偏心量。提出一种新型高压涡轮转静子偏心装配工艺,设计高压涡轮模拟工艺轴,基于工艺轴安装时套齿配合间隙与轴承径向游隙的装配偏差,结合发动机真轴装配偏差影响因素,综合得到静子空气挡油圈的最终偏心调整量,可实现高压涡轮转静子的封严间隙优化同心,避免发动机转静子发生碰磨,解决了发动机振动过大、轴承腔漏油等问题。该工艺方法经过装配试验验证有效,研究结果可为其他型号发动机转静子同轴度装配工艺设计提供参考。

Nonreciprocal Head-on Collision Between Two Nonlinear Solitary Waves in Granular Metamaterials with an Interface

In this work,the head-on collision and transmission with nonreciprocal properties of opposite propagating solitary waves are studied,in which the interface between different granular chains is considered.Due to the discontinuity of two periodic granular systems,the transmitted and reflected solitary waves are produced.The head-on collision appears at the interface and the reductive perturbation method is applied to derive the generated solitary waves.According to the derivation and numerical simulation,we can find that the transmitted and reflected solitary waves can propagate with the same speed when they locate at the same chain.Moreover,the influences of both the arrangement and prestress are discussed.It is found that the amplitude and velocity of solitary waves become larger because of a bigger prestress,which result in the nonreciprocal collision and transmission in the granular mechanical metamaterials.This study is expected to be helpful for the design and application of elastic wave metamaterials and mechanical diodes with nonlinear solitary waves.

Head-on Collision

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multi-solitons interaction multicomponent plasma extended Poincare–Lighthill–Kuo method head-on collision

The propagation and interaction between ion acoustic multi-solitons in an unmagnetized multicomponent plasma consisting of fluid hot ions, positrons and both hot and cold electrons, are investigated by employing the extended Poincare–Lighthill–Kuo（PLK） method. Two different Kortewege-de Vries（K-dV） equations are derived. The Hirota＇s method is applied to get the K-dV multi-solitons solution. The phase shift due to the overtaking and head- on collision of the multi-solitons is obtained.

碰摩转子系统在轴向推力作用下的分岔研究

推导建立了碰摩转子在轴向推力作用下的非线性动力学方程,分别以质量偏心和转子转速比为控制参数,对碰摩转子横向振动和轴向振动的分岔等非线性特性进行了数值分析。仿真分析表明:转子横向振动分岔图中,存在周期1运动、周期2运动及复杂的拟周期运动等。同时,从转子轴向振动分岔图可以看到系统以一种拟周期路径方式运动,随着质量偏心的增大,系统会突变为混沌运动,且会一直持续下去。分析结果为实际转子系统的碰摩故障分析提供了必要的理论依据。

偏心圆轮沿斜面纯滚动至连续弹跳的动力学分析

研究了第十一届全国周培源大学生力学竞赛团体赛中轮子跳高试题的偏心圆轮方案,建立了无初速度释放的偏心圆轮沿斜面纯滚动到连续跳动的动力学理论模型,分析了弹跳现象的产生条件,研究了纯滚动到连续弹跳的动力学过程,给出了斜面倾角、初始释放角和摩擦系数等因素对跳跃行为的影响。

列车收缩管吸能防爬器耐撞性研究

为提升列车车辆在偏心碰撞和倾斜碰撞场景下列车车辆的耐撞性,提出一种收缩管吸能防爬器。该吸能结构在碰撞过程中,其收缩吸能管和吸能座圆锥面产生摩擦作用,收缩吸能管产生径向收缩变形吸收冲击动能,提升非正心碰撞场景下列车吸能结构的吸能特性。采用准静态拉伸试验得到吸能管材料的本构模型,并通过台车冲击试验验证所建立有限元模型的有效性。通过数值仿真,研究偏心碰撞、倾斜碰撞等工况下该结构的变形及吸能特性。研究结果表明:该吸能结构适用于较大偏心距对撞和倾斜碰撞工况,且其关键结构设计参数对吸能结构的吸能特性和耐撞性有较大影响,其中吸能管壁厚对耐撞性参数(比吸能SEA和峰值力PCF)影响更为明显,合理选择关键结构设计参数可以有效提高吸能特性。

汶川地震中斜交连续梁桥震害机理研究

汶川地震中,斜交桥区别于直桥的典型震害现象为主梁的面内刚体转动。为研究其震害机理,以2跨及3跨预应力混凝土斜交连续梁桥为研究对象,建立数值分析模型,分析碰撞效应和结构偏心效应对主梁转角的影响。分析结果表明,斜交连续梁桥在地震作用下导致梁体面内刚体转动的主要原因是梁体与桥台或桥联间的碰撞效应与结构偏心效应。

汽车二维偏心碰撞事故再现模型适用性分析

为了实现汽车二维偏心碰撞事故的再现仿真分析,在介绍传统偏心碰撞动力学模型与轨迹模型的基础上,分别对其适用性问题进行了理论分析。以实际交通事故为例,分别利用PC-Crash软件与传统模型进行仿真再现分析。通过将二者的再现分析结果与事故现场上车辆遗留痕迹进行对比,实际分析了传统轨迹再现模型的可靠性。

用偏心碰撞理论分析车祸

用偏心碰撞理论分析了两个车祸特例 ,求出了碰前两车各自的速度及碰后转动的角速度 .

防止管模与拖辊发生碰撞的自动跟随弹簧减振系统

通过适当选择机架质量和隔振弹簧刚度可以使机架自动跟随滚动支撑的偏心转子 (管模 )的运动 ,从而避免滚动支撑的偏心转子和固定在机架上的拖辊之间发生有害碰撞 ,同时减小整个系统的振动和噪声。

重型拖挂卡车撞击桥墩的数值仿真及碰撞力特征分析

车辆撞击桥梁事故中,车辆结构形式对碰撞事故后果的影响显著。基于有限元软件LS-DYNA建立了精细的集装箱卡车数值模型,并对重型卡车碰撞桥墩过程进行了数值模拟。通过与实车撞击实验中的车辆破坏形态进行对比,确认了本文数值模型的合理性。基于该集装箱卡车模型,本文研究了不同车辆参数对车辆碰撞力的影响,其中包括集装箱货物刚度、车辆与桥墩的偏心距以及车辆速度等因素。讨论了各个参数对碰撞力变化特征及碰撞力峰值的影响规律。

船舶货舱区侧撞桥墩有限元仿真分析

当船舶横穿水道、失控漂移或者船舶规避正面碰撞等情况下,船舶将有可能与桥墩发生侧撞。由于侧撞时船体附连水质量较大,舷侧与桥墩接触面积也很大,故其对桥梁的撞击危害是不容忽视的。本文以某大型跨江桥梁工程为背景,应用非线性有限元软件MSC.Dytran,选取3000DWT油船在3.0 m/s的失控速度下,船舶货舱区侧撞桥梁墩身的有限元仿真试验,并且分析了不同偏心距条件下撞击力和能量的演变过程。仿真试验表明,在同等条件下船舶侧撞的危害不亚于船首正撞。同时,建议将初始侧撞击力控制在足够安全的范围内,而通过增设桥墩的防撞保护装置能实现这一目标。