THE APPLICATION OF WEINSTEIN-CHIEN′S METHOD——THE UPPER AND LOWER LIMITS OF FUNDAMENTAL FREQUENCY OF RECTANGULAR PLATES WITH EDGES ARE THE MIXTURE OF SIMPLY SUPPORTED PORTIONS AND CLAMPED PORTIONS

In this paper, the method of relaxed boundary conditions is applied to rectangular plates with edges which are a sort of the mixture of simply supported portions and clamped portions, so that the lower limit of fundamental frequency of such plates is evaluated. A kind of polynomial satisfying the displacement boundary conditions is designed, os that it is enabled to evaluate the upper limit of fundamental frequency by Ritz' method. The practical calculation examples solved by these methods have given satisfactory results. At the end of this paper, it is pointed out that the socalled exact solution of such plates usually evaluated by the force superposition method is essentially a kind of lower limit of solution, if the truncated error of series which occurs in actual calculation is considered.

Charge density at the nucleus and radial behavior of ground state for lithium-like ions with Z=21 to 30

By using the full-core plus correlation （FCPC） type wave functions, the accurate charge densities p（0） at the nucleus and the radial expectation values of the ground states for the lithium-like systems with Z =- 21 to 30 are obtained. The determinantal conditions and the electron-nucleus cusp condition are used to calculate the inequalities of the upper and the lower bounds to p（0） with two or more expectation values. These inequalities, derived by Angulo and Dehesa [Phys. Rev. A 44 1516 （1991）], are verified to be also valid for these ions with higher nuclear charge. The present results show that the wave functions used in this paper are satisfactory in the whole configuration space for these ions with higher nuclear charge.

ON MONOTONE ITERATIVE METHOD FOR INITIAL VALUE PROBLEMS OF NONLINEAR SECOND-ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

Using the monotone iterative method and Monch Fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differential equations in Banach spaces are studied. Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained.

EXISTENCE AND UNIQUENESS FOR SECOND-ORDER VECTOR BOUNDARY VALUE PROBLEM OF NONLINEAR SYSTEMS

This paper is concerned with the following second-order vector boundary value problem ：x^R=f（t,Sx,x,x＇）,0〈t〈1,x（0）=A,g（x（1）,x＇（1））=B,where x,f,g,A and B are n-vectors. Under appropriate assumptions,existence and uniqueness of solutions are obtained by using upper and lower solutions method.

ON THE EXISTENCE OF SOLUTION OF A NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEM ARISING FROM A LIQUID METAL FLOW

In this paper, we discuss the existence of solution of a nonlinear two-point boundary value problem with a positive parameter Q arising in the study of surfacetension-induced flows of a liquid metal or semiconductor. By applying the Schauder's fixed-point theorem, we prove that the problem admits a solution for 0 ≤ Q ≤ 14.306.It improves the result of 0 ≤ Q ＜ 1 in [2] and 0 ≤ Q ≤ 13.213 in [3].

Existence Results for Systems of Nonlinear Caputo Fractional Differential Equations

We aim, in this work, to demonstrate the existence of minimal and maximal coupled quasi-solutions for nonlinear Caputo fractional differential systems with order q ∈ (1,2). Our approach is based on mixed monotone iterative techniques developed under the concept of lower and upper quasi-solutions. Our results extend those obtained for ordinary differential equations and fractional ones.

基于时程分析法的中美隔震设计对比研究

介绍了中国《建筑隔震设计标准》(GB/T 51408—2021)(以下简称《隔标》)和美国Minimum design loads and associated criteria for buildings and other structures(ASCE 7-16)隔震设计的相关要求,并针对基于《建筑抗震设计规范》(GB 50011—2010)(2016年版)(以下简称《抗规》)设计的某9度区近场隔震结构,进行了两国规范的设计对比。按《抗规》设计的隔震结构,仍然能满足《隔标》的设计要求。ASCE 7-16对于隔震支座考虑了老化和环境、测试、制造等因素引起的性能参数变化,并按隔震支座的上限及下限属性进行了结构设计。基于相同地震概率水准(50年超越概率2%)的设计对比研究表明,ASCE 7-16的等效侧力法计算值高于《隔标》,按ASCE 7-16要求选择的地震波反应谱明显高于《隔标》,其时程分析结果也大于中国规范,对隔震支座的性能要求更高。

矿井传感器风量最小平衡修正量研究

在智能化开采时代,高性能的实时通风网络解算对于矿山通风系统的安全管理至关重要,而初始迭代风量对解算性能具有显著影响。由于传感器难以避免地存在测量误差且布置稀疏,利用传感器监测数据难以分配全风网初始风量。首先,将矿井通风网络视为网络流模型,并对传统的有上下界网络流模型进行改进,以使之能够基于存在测量误差的传感器风量进行全风网风量分配。其次,用风量平差模型对传感器误差导致的节点风量不平衡进行最小平衡量修正。试验模拟和现场试验均表明了研究方法的可行性和有效性。在现场试验中,传感器分支的风量平均修正率为0.66%,平均风量修正值为0.09 m^(3)/s。该方法能够对任意位置布置且存在测量误差的传感器的风量进行全风网的风量初始化分配。

“下病上治”整脊法治疗腰骶后关节病的效果

目的 评价“下病上治”整脊法治疗腰骶后关节病的临床效果。方法 选取2020年10月至2022年5月中国中医科学院望京医院、首都医科大学电力教学医院、黑龙江中医药大学附属第二医院门诊治疗160例腰骶部后关节疾病患者,按照随机数字表法将其分为治疗组和对照组,每组80例。对照组采用推拿手法治疗,治疗组采用“下病上治”整脊法治疗,两组均治疗2个疗程。比较两组治疗前后视觉模拟评分法(VAS)评分与腰椎活动度。结果 治疗后,两组VAS评分较治疗前降低,且治疗组低于对照组(P<0.05)。治疗后,两组腰椎前屈、后伸、左侧屈、右侧屈、左旋转、右旋转均大于治疗前,且治疗组大于对照组(P<0.05)。治疗组临床疗效优于对照组(P<0.05)。结论“下病上治”整脊法治疗腰骶后关节病效果优于推拿手法治疗。

压载荷下Ⅰ-Ⅱ复合型中心裂纹板弹塑性屈曲载荷研究

为了研究含裂纹结构承载能力,采用有限元方法建立压载荷下Ⅰ-Ⅱ复合型中心裂纹板模型,计算裂纹板弹塑性屈曲载荷,讨论相对裂纹长度(a/w)、裂纹倾角(θ)、板宽(w)、板厚(t)、边界条件对弹塑性屈曲载荷及其变化规律的影响。对于上下夹持中心裂纹板,随着裂纹长度和裂纹倾角的增大,板宽越大,中心裂纹板屈曲载荷对裂纹越敏感,中心裂纹板承载能力受到裂纹长度和裂纹倾角的影响越明显。弹塑性屈曲载荷随着板厚的增大而增大,并且随着裂纹倾角的增大,板厚越大,屈曲载荷的下降程度越显著。上下简支中心裂纹板与上下夹持中心裂纹板的屈曲载荷变化规律基本一致,且上下夹持中心裂纹板的屈曲载荷显著大于上下简支中心裂纹板的屈曲载荷。给出不同边界条件下弹塑性屈曲载荷与相对裂纹长度、裂纹倾角的回归关系式。通过中心裂纹板弹塑性屈曲试验发现,采用压缩力学性能计算弹塑性屈曲载荷更接近试验结果,试验屈曲载荷的变化规律与有限元模拟计算结果一致。研究结果对含裂纹结构的承载能力评价具有参考价值。

一种高精度四辊板带材轧机支撑辊偏心辨识的研究

板带轧机中上下支撑辊偏心信号是较为典型的一种频率相近的周期波,如果仍采用传统的快速傅立叶变换(FFT)辨识该偏心信号就很难保证结果的精准性与可靠性。对此,在本课题中,笔者经过广泛且深入地探索与研究推出了可有效解决此问题的新辨识方法,即最小二乘法(LS),该算法的实现过程依托经典且成熟的观测矩阵理论,利用2范数最小的终止准则完成求解操作,并从中确定出最相近的特征参数。算例计算结果显示:当上下支撑辊的频率差为和,FFT所辨识的幅值和相角均严重失真,而LS方法所辨识的幅值精度分别可达0.064%和0.127%,相角的辨识精度分别为0.076%和0.0286%。同时利用某四机架板带连轧生产的实际采集的轧制力数据作为辨识目标,通过分析各个机架的轧辊偏心的影响,可以看出在246Hz处的轧辊偏心信号被很好地辨识。因此笔者提出的这种新方法可提供准确、可靠的辨识结果,而且不容易受外部干扰,进而从源头上提高了识别效率,保证了识别的精准度。

上软下硬地层CSM整体式止水帷幕施工关键技术

上软下硬地层且富水环境中,基坑止水帷幕的施工质量直接影响基坑开挖安全和变形控制。依托青岛市地铁7号线周村站深大基坑工程,从施工机械、施工方法和信息化角度探讨CSM工法,形成整体式止水帷幕施工关键技术。系统研究了CSM刀盘选型与配置,浆液材料配合比,双轮铣头多点喷浆技术及注浆参数,浆液制备、存储方法,跳打搭接循环施工方法,以及CSM钻进全过程数据信息化监测方法。基于现场监测结果,CSM工法水泥土墙深基本超出设计墙深0.5%,基坑开挖过程外围水位最大降深为1.5m,右邻省道最大沉降值为13.1mm,基坑开挖安全,表明CSM整体式止水帷幕适应性强、成墙质量好。

上软下硬地层地铁盾构施工地表沉降模拟分析

为了研究上软下硬地层地铁盾构掘进引起的地表沉降规律,以某地铁工程大岭山东站—松山湖站区间盾构掘进项目为依托,通过实测和数值模拟,对比分析上软下硬地层盾构掘进及硬层比对地表沉降规律的影响。结果表明:单双线盾构掘进地表横向沉降规律分别呈V形和W形变化;盾构掘进时对前后地表变形影响的范围约为40 m,其中前方5 m至后方15 m范围内的地表沉降变化率最大;地表沉降随地质硬层比的增加逐渐减小,硬层比为16.7%~83.3%时,地表沉降变化较大,可将硬层比83.3%、16.7%作为上软下硬复合地层研究的上下限。

一类带(p,q)-Laplace算子离散问题正解的存在性

运用上下解方法获得了一类半正离散(p,q)-Laplace问题■正解的存在性,其中,p> q> 1,参数λ> 0,T> 2为固定的整数,■在无穷远处满足p-次线性条件,在0处可能奇异。

一类半线性椭圆型方程解的存在性与渐近性

本文研究了一类带有Hardy项的半线性椭圆型方程,利用上下解方法和比较原则,获得了该问题最大解和最小解的存在性以及正解在原点附近的渐近估计式。

黄土区大跨度隧道开挖技术探讨

临洮(安家咀)至临夏一级公路百和隧道均为Ⅴ级围岩,主要有黄土浅埋段、岩质地段、黄土深埋段、小净距段以及黄土深埋段等情况,针对不同的围岩情况和地质条件,有针对性的采用CD法、上下台阶留核心土法及三台阶分步法进行开挖。

某地下矿山上下矿体同时开采的安全性协调

针对国内某地下金属矿山,通过确定开采范围及对象、开采技术条件分析、采矿方法选择、矿块布置、矿块生产能力分析及矿块生产搭配协调,来保障上下主矿体采用空场法同时开采的安全性。该文的研究对于地下矿山上下矿体采用空场法同时开采时,上下采区安全关系的协调具有一定的指导作用。

一类带参数的超线性椭圆型方程边值问题的可解性

本文研究了一类椭圆型方程Dirichlet边值问题的可解性,其中,非线性项包含了线性部分、参数及在无穷远处为超线性的部分。利用不动点定理及上下解方法来证明了该问题在参数λ充分小时正解的存在性;在非线性项满足Lipschitz连续及参数λ充分小时解的唯一性定理;同时论证了在一定条件下解的不存在性定理。最后分别给出了定理的应用实例。

Periodic boundary value problem for the first order functional differential equations with impulses

This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.

Parameter vertex method and its parallel solution for evaluating the dynamic response bounds of structures with interval parameters

In this article, we propose a parameter vertex method to determine the upper and lower bounds of the dynamic response of structures with interval parameters, which can be regarded as an extension of the matrix vertex method proposed by Qiu and Wang. The matrix vertex method requires considerable computation time and encounters the dependency problem in practice,thereby limiting its application in engineering. The proposed parameter vertex method can avoid the dependency problem, and the number of possible vertex combinations in the proposed method is significantly less than that in the matrix vertex method.The parameter vertex method requires that each matrix element in the dynamic differential equation is monotonic with respect to the uncertain parameter, and that the dynamic response reaches its extreme value when the uncertain parameter is at its endpoint.To further reduce the runtime, both vertical and transversal parallel algorithms are introduced and integrated into the parameter vertex method to improve its computational efficiency. Two numerical examples are presented to demonstrate the proposed method combined with both parallel algorithms. The performances of the two parallel algorithms are thoroughly studied. The parameter vertex method combined with parallel algorithm can be used for large-scale computing.