Element-free Galerkin method for free vibration of rectangular plates with interior elastic point supports and elastically restrained edges

The element-free Galerkin method is proposed to solve free vibration of rectangular plates with finite interior elastic point supports and elastically restrained edges.Based on the extended Hamilton＇s principle for the elastic dynamics system,the dimensionless equations of motion of rectangular plates with finite interior elastic point supports and the edge elastically restrained are established using the element-free Galerkin method.Through numerical calculation,curves of the natural frequency of thin plates with three edges simply supported and one edge elastically restrained,and three edges clamped and the other edge elastically restrained versus the spring constant,locations of elastic point support and the elastic stiffness of edge elastically restrained are obtained.Effects of elastic point supports and edge elastically restrained on the free vibration characteristics of the thin plates are analyzed.

AN EXACT SOLUTION FOR THE BENDING OF POINT-SUPPORTED ORTHOTROPIC RECTANGULAR THIN PLATES

A closed series solution is proposed for the bending of point-supported orthotropic rectangular thin plates. The positions of support points and the distribution of transverse loadare arbitrary. If the number of simply supported points gradually increases the solution can infinitely approach to Navier's solution. For the square plate simply supported on the middle of each edge and free at each corner, the results are very close to the numerical solutions in the past.

THE SYMMETRICAL BENDING OF AN ELASTIC CIRCULAR PLATE SUPPORTED AT KINTERNAL POINTS

This paper treats the symmetrical bending of a uniformly loaded circular plate supported at k internal points. The boundary displacement and slope are expanded in Fourier seriesr. The method proposed by [6] is applied. As both the governing differential equation and boundary conditions are satisfied exactly, we therefore obtain the analytic expression of the transverse deflectionul equation of the circular plate. This is an easy and effective methed.

EXTREME POINTS AND SUPPORT POINTS OF A CLASS OF ANALYTIC FUNCTIONS

Suppose that {b(n)} and {c(n)} are two positive sequences. Let F({b(n)}, {c(n)}) = {f(z) : f(z) is analytic in \z\ < 1, f(z) = z - Sigma(n=2)(+infinity) a(n)z(n), a(n) greater than or equal to 0, Sigma(n=2)(+infinity) b(n)a(n) less than or equal to 1 and Sigma(n=2)(+infinity) c(n)a(n) less than or equal to 1}. This article obtains the extreme points and support points of F({b(n)}, {c(n)}).

Three-dimensional elasticity solution of simple-supported rectangular plate on point supports, line supports and elastic foundation

This paper studies the bending of simple-supported rectangular plate on point supports, line supports and elastic foundation. On the basis of three-dimensional elasticity theory, the exact expressions of the displacement functions, which satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate, are analytically derived. The reaction forces of the in- termediate supports are regarded as the unknown external forces acting on the lower surface of the plate. The unknown coefficients are then determined by the boundary conditions on the upper and lower surfaces of the plate. Comparing the numerical results obtained from the proposed method to those obtained from Kirchhoff plate theory, Mindlin plate theory and those obtained from the commer- cial finite element software ANSYS, the high accuracy of the present method has been demonstrated.

THE SUPPORT POINTS AND EXTREME POINTS OF THE UNIT BALL OF H'_P~ 1

By the author denotes the areal measure on the unit disk . Let H'p = {f(z): f(z) is analytic in D and . Let B H 'p and. This article researches the support points and extreme points of B(H'p).

TRANSVERSE VIBRATION OF RECTANGULAR PLATES ELASTICALLY SUPPORTED AT POINTS ON EDGES

This paper studies transverse vibration of rectangular plates with two opposite edges simply supperted other two edges arbitrarily supported and free edges elaslically supported at points,A highly accurate solution is presented for calculating inherent frequencies and mode shape of rectangular platen elaslically supported at points. The number and location of these points on free edges may be completely arbitrary. This paper uses impulse function to represent reaction and moment at points. Fourter series is used to expand the impulse function along the edges. Characteristic equations satisfying all boundary conditions are given.Inherent frequencies and mode shape with any accutacy can be gained.

VIBRATIONS OF RECTANGULAR PLATES SUPPORTED AT CORNER POINTS

This paper discusses by energy theorem the methodof approximate computation for the lowest eigenfrequencies of rechmguhir plates,on which there are symmetrical concentrated masses,supported at corner points,In the case of seseral concentrated masses,by using the prineiple of superposition we mayfiml the reduneed coefficients of masses comveniently.llence we can louain the lowest eigenfrequencies of thin plates.In the paper a good mamy mmerical caleuhting eximples are inustrated

VIBRATION OF ARBITRARILY SHAPED MEMBRANES WITH ELASTICAL SUPPORTS AT POINTS

This paper presents a new method for solving the vibration of arbitrarily shaped membranes with ela.stical supports at points. The reaction forces of elastical supports at points are regarded as unknown external forces acting on the membranes. The exact solution of the equation of motion is given which includes terms representing the unknown reaction forces. The frequency equation is derived by the use of the linear relationship of the displacements with the reaction forces of elastical supports at points. Finally the calculating formulae of the frequency equation of circular membranes are analytically performed as examples and the inherent frequencies of circular membranes with symmetric elastical supports at two points are numerically calculated.

SUPPORTING AND SEPARATING SUBSETS FOR INVEX BODIES

Invex bodies represent an important class of bodies which are considered as a generalization of convex bodies.In this article,the author studies the supporting for this class of bodies as well as the separating subsets of two bodies.

THE UNIT BALL OF C-ALGEBRA AND DIFFERENTIABILITY OF SUPPORT FUNCTION

In this paper we show that the unit ball of an infinite dimensional commutative C-algebra lacks strongly exposed points, so they have no predual. Also in the second part, we use the concept of strongly exposed points in the Frechet differentiability of support convex functions.

水产养殖作业船转塘装置的设计

水产养殖作业船可以用于水草清理、饵料投放、施药、水质监测等,其工作范围不只限于单块水塘,但相邻水塘共用时往往需要通过人力来实现养殖作业船的转塘,这一过程费时费力。对此,设计一种养殖作业船转塘装置,通过两侧齿轮与架空齿条的啮合及底部滚轮与转移轨道的导向来形成对作业船的三点支撑。为保证养殖作业船能无阻碍地通过堤坝,特地设计计算了架空齿条上坡段、水平段和下坡段的高度和角度。将养殖作业船的螺旋桨改造成明轮,其为转塘爬坡提供动力的同时也能有效防止水草缠绕。现有应用表明,该装置大大提升了水产养殖过程中的转塘效率,既提高了作业船的利用率,也降低了总体投入成本,因此具有一定的推广价值。

海南炼化100万t/a乙烯项目配套码头设计要点

为总结和推广乙烯项目配套码头设计经验,以海南炼化100万t/a乙烯项目配套码头设计为例,提出该工程设计需解决的关键技术问题包括:装卸货种多、船型种类多且跨度较大、建设期重大件运输保障、复杂地质条件下的水工结构设计、深厚抛石堤上工艺管架基础设计等问题。通过分析船型和地质条件,优化装卸工艺和总平面布置以及创新结构设计,有效解决了设计难点。

三层正放四角锥预应力网架稳定性分析

网架以其优良的工程性能成为大跨度结构的首选结构类型之一。为改善传统网架结构在大跨度条件下变形大、用钢量大的缺陷,文中通过对网架施加预应力的方式,达到增强结构整体刚度和承载能力的目的。预应力的施加必然会对网架的稳定性能造成影响,其中支承形式对网架结构的稳定性影响较大。并通过对网架施加不同预应力后进行稳定性分析,得到不同预应力布索方式对网架稳定性影响,为网架的实际工程建设提供参考。

保障生态产品价值实现的生态积分体系研究

现有生态积分实践缺乏对应理论指导,存在分散性与自发性特征,未能充分实现其应有价值。基于生态积分现实基础与理论渊源的分析,从基础理论支撑体系、实践操作模型体系、基本制度规范体系视角对构建生态积分体系进行了研究,结果表明:生态积分体系是一个由基础理论支撑体系、实践操作模型体系和基本制度规范体系三者构成的有机体。其中,生态积分基础理论支撑体系是由本源理论、前置理论、运行理论与预测理论有机形成的内循环平面理论体系;生态积分实践操作模型体系是由生态积分规则、生态积分平台、生态积分兑换结合形成的三向联动体系;生态积分基本制度规范体系是由原则要求与基本维度两个方面构筑而成的制度规范体系。

基于激光诱导击穿光谱(LIBS)的煤灰熔点快速检测

由于劣质煤的存在,燃煤时锅炉内极易出现结渣问题,不仅降低了煤的利用率、电厂的经济效益,且使火电厂存在安全隐患,如管壁超温爆管等,不符合国家节能减排的发展战略要求。因此炉内结渣是影响火电机组和气化工艺可靠运行的关键因素之一,准确预测灰熔点可以提前调整炉膛出口温度以避免结渣。采用激光诱导击穿光谱仪(LIBS)对33个火电厂常用煤燃烧后得到的煤灰样品采集其中所有元素的光谱,分别建立煤灰中的所有元素的谱线强度与煤灰熔点的随机森林模型、支持向量机回归模型和线性回归模型,直接预测煤灰熔点温度。采用基于马氏距离(MD)的异常数据剔除算法和基于稀疏矩阵的基线估计与降噪算法(BEADS),对粉煤灰样的全光谱数据进行了预处理。将全部数据划分为70%训练集和30%测试集,并以平均相对误差(MRE)作为判断模型拟合程度的标准,其中随机森林模型对粉煤灰熔点的预测平均相对误差(MRE)为54.74%,支持向量机回归模型的预测平均相对误差为60.08%,而线性回归模型的预测平均相对误差达到了9.78%。研究结果表明,线性回归模型对煤灰熔点的预测结果更准确。将便携式LIBS光谱仪与机器学习算法相结合,用于煤灰熔点的快速检测,可有效避免锅炉结渣问题,实现火电厂安全性和经济效益的同步提高,有广阔的发展前景。

一种精密测量仪器的快速对接机构

为了保证两精密测量仪器快速对接与分离的高精密性和稳定性,设计了一种高精密重复定位的快速对接机构。采用三点支撑[1]的方式,保证需要对接的两仪器拥有较高的重复定位误差,并且误差恒定。通过紧扣机构和旋钮构成对接紧扣装置,实现两仪器六自由度锁紧的高可靠性和稳定性,并且实现对接与分离的快速性。设计安装限位功能,以保证安装位置的重复性。分析了对接机构原理,并对重复定位误差的不确定度因素进行了简要分析。最后,通过设计试验来检测两精密测量仪器重复定位的误差,试验结果表明,快速对接机构具有较高的重复定位误差,证明设计合理。

基于多目标优化的精密机床T形床身双三点支承设计

支承方式是精密机床床身的刚度的重要影响因素之一,而良好的机床刚度对机床整体的加工精度提升有着重要意义。为提高机床的动静态特性,基于多目标优化法和有限元计算,提出一种双三点支承加辅助支承的支撑方法,并利用某精密卧式加工中心床身进行详细的验证。研究结果表明,通过多目标优化算法设计的支承方式,相比于工程上常用的支承方法,一阶固有频率提高15.29%,X向前后导轨平均变形分别减少59%、6%,验证了所提出方法的有效性和正确性。

采煤机搬运车悬挂系统智能控制与调平策略研究

为降低采煤机搬运车在装载和运输中倾覆风险,分析常用的位置误差调平法和角度误差调平法的优缺点,在此基础上提出改良的位置误差调平法。通过分析计算求得平台上各点在竖直方向上的坐标;通过计算平台平面方程结合各支撑点几何关系,得出各点竖直方向运动速度,形成了悬挂系统调平控制策略。通过AMESim和Simulink联合仿真建立了悬挂系统的仿真模型,并采用了边界稳定法和试凑法确定比例、积分、微分三项系数及其模糊放大系数,从而利用模糊PID控制器优化了多路阀动态响应特性,减小了响应过程中的超调量。仿真结果表明:在悬挂系统升降过程中,各支撑点间的竖直位移差均不超过2.0 mm,且各悬挂缸压力差小于0.1 MPa,不会出现虚腿现象。最后通过试验分析了悬挂系统的控制性能,结果表明:实际升降过程中的最大位移误差小于5.0 mm;结合采煤机搬运车尺寸计算得到,车身平台在长度方向上的倾角为9.16×10^(-4)rad,在宽度方向上的倾角为1.27×10^(-3)rad,在工作允许范围内,验证了方案的有效性。研究内容为悬挂系统调平策略和克服调平过程中的“虚腿”现象提供了新的思路。