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Applied Mathematics and Mechanics(English Edition) 2024年第6期45卷 983-1000页

作者： Xiaoyang SU Tong HU Wei ZHANG houjun kang Yunyue CONG Quan YUAN School of Civil Engineering and Architecture Guangxi UniversityNanning 530004China Scientific Research Center of Engineering Mechanics Guangxi UniversityNanning 530004China State Key Laboratory of Featured Metal Materials and Life-Cycle Safety for Composite Structures Guangxi UniversityNanning 530004China

Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical *** study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving *** the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable ***,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are *** demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also *** this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried *** results show the accuracy and efficiency of the TMM.

关键词： transfer matrix method(TMM) free vibration forced vibration functionally graded material(FGM) stepped beam

Analysis of in-plane 1:1:1 internal resonance of a double cable-stayed shallow arch model with cables’ external excitations

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Applied Mathematics and Mechanics(English Edition) 2019年第7期40卷 977-1000页

作者： Yunyue CONG houjun kang Tieding GUO College of Civil Engineering Hunan University Changsha 410082 China Key Laboratory for Damage Diagnosis of Engineering Structures of Hunan Province Hunan University Changsha 410082 China

The nonlinear dynamic behaviors of a double cable-stayed shallow arch model are investigated under the one-to-one-to-one internal resonance among the lowest modes of cables and the shallow arch and external primary resonance of cables. The in-plane governing equations of the system are obtained when the harmonic excitation is applied to cables. The excitation mechanism due to the angle-variation of cable tension during motion is newly introduced. Galerkin’s method and the multi-scale method are used to obtain ordinary differential equations (ODEs) of the system and their modulation equations, respectively. Frequency- and force-response curves are used to explore dynamic behaviors of the system when harmonic excitations are symmetrically and asymmetrically applied to cables. More importantly, comparisons of frequency-response curves of the system obtained by two types of trial functions, namely, a common sine function and an exact piecewise function, of the shallow arch in Galerkin’s integration are conducted. The analysis shows that the two results have a slight difference;however, they both have sufficient accuracy to solve the proposed dynamic system.

关键词： nonlinear dynamics cable-stayed system internal resonance primary resonance multi-scale method

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基于索-梁结构的斜拉桥非线性振动仿真研究

动力学与控制学报 2024年第5期22卷 16-23页

作者：康厚军尹昆苏潇阳郭铁丁丛云跃广西大学土木建筑工程学院南宁530004 广西大学工程力学研究中心南宁530004

本文建立了索-梁结构的有限元模型,对斜拉桥线性和非线性振动问题进行研究.首先对结构进行模态分析,发现结构振动表现出全局模态,局部模态以及混合模态,且索梁两者之间固有频率相互影响,对低阶频率影响较大,对高阶频率影响较小.其次,应... 详细信息

本文建立了索-梁结构的有限元模型,对斜拉桥线性和非线性振动问题进行研究.首先对结构进行模态分析,发现结构振动表现出全局模态,局部模态以及混合模态,且索梁两者之间固有频率相互影响,对低阶频率影响较大,对高阶频率影响较小.其次,应用有限元软件对索-梁结构的自由振动和强迫振动进行仿真研究.结果表明:整个自由振动过程中频率有先增大后减小的趋势,且最终小于真实频率;在强迫振动中,观察到了丰富的非线性振动现象,包括索的亚谐波共振和内共振,与以往的实验和理论研究结果定性上得到验证;为斜拉桥全桥非线性动力学分析提供参考.

关键词：斜拉桥索-梁结构有限元仿真非线性振动共振

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Dynamical modeling and non-planar coupled behavior of inclined CFRP cables under simultaneous internal and external resonances

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Applied Mathematics and Mechanics(English Edition) 2019年第5期40卷 649-678页

作者： houjun kang Tieding GUO Weidong ZHU Junyi SU Bingyu ZHAO Hunan Provincial Key Lab on Damage Diagnosis for Engineering Structures Hunan University Department of Mechanical Engineering University of Maryland College of Civil Engineering Hunan University

A dynamic model for an inclined carbon ?ber reinforced polymer(CFRP)cable is established, and the linear and nonlinear dynamic behaviors are investigated in detail. The partial differential equations for both the in-plane and out-of-plane dynamics of the inclined CFRP cable are obtained by Hamilton's principle. The linear eigenvalues are explored theoretically. Then, the ordinary differential equations for analyzing the dynamic behaviors are obtained by the Galerkin integral and dimensionless *** steady-state solutions of the nonlinear equations are obtained by the multiple scale method(MSM) and the Newton-Raphson method. The frequency-and force-response curves are used to investigate the dynamic behaviors of the inclined CFRP cable under simultaneous internal(between the lowest in-plane and out-of-plane modes) and external resonances, i.e., the primary resonances induced by the excitations of the in-plane mode,the out-of-plane mode, and both the in-plane mode and the out-of-plane mode, respectively. The effects of the key parameters, e.g., Young's modulus, the excitation amplitude,and the frequency on the dynamic behaviors, are discussed in detail. Some interesting phenomena and results are observed and concluded.

关键词： inclined carbon fiber reinforced polymer(CFRP)cable bifurcation nonlinear dynamics internal resonance external resonance

Interaction between uranium and humic acid(Ⅰ):Adsorption behaviors of U(Ⅵ) in soil humic acids

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Nuclear Science and Techniques 2007年第5期18卷 287-293页

作者： WEI Min LIAO Jiali LIU Ning ZHANG Dong kang houjun YANG Yuanyou YANG Yong JIN Jiannan Key Laboratory of Radiation Physics and Technology （Sichuan University） Ministry of Education Institute of Nuclear Science and Technology Sichuan University Chengdu 610064 China Institute of Nuclear Physics and Chemistry CAEP Mianyang 621900 China 不详

The adsorption behaviors of uranium on three soil humic acids (HAs), which were extracted from soils of different depths at the same site, were investigated under various experimental conditions. The adsorption results showed that U(Ⅵ) in solutions can be adsorbed by the three soil HAs, with the order of FHA (HA from 5 m depth of soil) >SHA (HA from the surface) >THA (HA from 10 m depth of soil) for adsorption efficiency in each desirable condition, and the adsorption reached equilibrium in about 240 min. Although the maximum adsorption efficiency was achieved at a suitable uranium concentration (10 mg·L-1 U(Ⅵ) for SHA and THA, 20 mg·L-1 U(Ⅵ) for FHA), the adsorption could be described with Langmiur isotherm or Freundlich isotherm equation. The L/S (liquid/solid, mL/g) ratio and pH were important factors influencing the adsorption in our adsorption system besides uranium concentration. The adsorption efficiency decreased with the increase of the L/S ratio and pH at the pH range of 2.0-3.0 for SHA and THA or 2.5-6.0 for FHA. However, no significant difference in adsorption of U(Ⅵ) was observed at the experimental temperature. All the results implied that humic substances have different characteristics in samples even collected at the same site.

关键词：腐殖狻土壤天然放射物环境放射学

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索-梁结构的模态正交性和非线性振动研究

中南大学学报（自然科学版） 2021年第10期52卷 3605-3612页

作者：姚彻康厚军湖南大学土木工程学院湖南长沙410082 广西大学工程力学研究中心广西南宁530004

通过理论推导、数值计算和模型验证对索梁模型的模态正交性问题进行分析,得到索-梁组合结构关于等效刚度正交性的表达式和量纲一情况下正交性的检验式。分别针对索-梁分离法、拖拽法、索-梁整体法这3种模态选取方式对应的索-梁系统的模... 详细信息

通过理论推导、数值计算和模型验证对索梁模型的模态正交性问题进行分析,得到索-梁组合结构关于等效刚度正交性的表达式和量纲一情况下正交性的检验式。分别针对索-梁分离法、拖拽法、索-梁整体法这3种模态选取方式对应的索-梁系统的模态正交性进行研究。研究结果表明:索-梁分离法选用简单三角函数模态时,各个模态之间均满足关于质量和刚度的正交关系;拖拽法中的模态是否满足正交性情况,需对实际情况进行具体分析;索-梁整体法中的模态在考虑拉索垂度时不满足正交性,在不考虑拉索垂度时满足正交性;比较不同模态设置方式的优劣性和适用性,发现不正交带来的耦合项对非线性动力学行为产生较大影响。

关键词：模态正交性非线性振动解耦相图

Energy transfer between components of a cable stayed beam model under the concentrated excitation:1:2 modal resonance

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Acta Mechanica Sinica 2022年第7期38卷 177-191,I0004页

作者： Yunyue Cong houjun kang Tieding Guo Xiaoyang Su College of Civil Engineering and Architecture Guangxi UniversityNanning530004China Scientific Research Center of Engineering Mechanics Guangxi UniversityNanning530004China College of Civil Engineering Hunan UniversityChangsha410082China

The present study aims to investigate the dynamic behaviors and energy transfer between components of a cable stayed beam structure subjected to a concentrated load,in which the primary resonance of the beam and one-to-two internal resonance between modes of the beam and the cable *** discretization and multiple time scales method are applied to derive the modulation equations of the system governing the amplitude and *** sags of span ratios are defined to modulate the internal *** response,amplitude response,phase diagram,Poincare map,and time history curves are calculated and used to investigate the modal resonance *** results demonstrate that the beam and the cable have two resonant peaks in frequency responses,where the beam always shows hardening spring property and the cable may present hardening and softening spring properties affected by sag to span *** system is prone to complex dynamic behavior with the small amplitude excitation in the primary resonance region.

关键词： Cable-stayed beam Concentrated excitation Nonlinear dynamics Frequency response Amplitude response

On internal resonance analysis of a double-cable-stayed shallowarch model with elastic supports at both ends

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Acta Mechanica Sinica 2022年第6期38卷 182-199,I0004页

作者： Xiaoyang Su houjun kang Tieding Guo Guirong Yan College of Civil Engineering Hunan UniversityChangsha 410082China College of Civil Engineering and Architecture Guangxi UniversityNanning 530004China Scientific Research Center of Engineering Mechanics Guangxi UniversityNanning 530004China Department of Civil Architectural and Environmental EngineeringMissouri University of Science and TechnologyRolla 65401USA

In previous research on the nonlinear dynamics of cable-stayed bridges,boundary conditions were not properly modeled in the *** order to obtain the nonlinear dynamics of cable-stayed bridges more accurately,a double-cable-stayed shallow-arch model with elastic supports at both ends and the initial configuration of bridge deck included in the modeling is developed in this *** in-plane eigenvalue problems of the model are solved by dividing the shallow arch(SA)into three partitions according to the number of cables and the piecewise functions are taken as trial functions of the ***,the in-plane one-toone-to-one internal resonance among the global mode and the local modes(two cables’modes)is investigated when external primary resonance *** ordinary differential equations(ODEs)are obtained by Galerkin’s method and solved by the method of multiple time *** stable equilibrium solutions of modulation equations are obtained by using the NewtonRaphson *** addition,the frequency-/force-response curves under different vertical stiffness are provided to study the nonlinear dynamic behaviors of the elastically supported *** validate the theoretical analyses,the Runge-Kutta method is applied to obtain the numerical ***,some interesting conclusions are drawn.

关键词： Cable-stayed bridge Internal resonance Vertical elastic support Eigenvalue,Nonlinear vibration

Interaction between uranium and humic acid (Ⅱ): complexation, precipitation and migration behavior of U(Ⅵ) in the presence of humic substances

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Nuclear Science and Techniques 2013年第3期24卷 18-26页

作者： LIAO Jiali WEN Wei LI Bing YANG Yuanyou ZHANG Dong kang houjun YANG Yong JIN Jiannan LIU Ning Key Laboratory of Radiation Physics and Technology Ministry of EducationInstitute of Nuclear Science and TechnologySichuan University Institute of Nuclear Physics and Chemistry CAEP

The complexation, precipitation, and migration behavior of uranium in the presence of humic acid (HA) or fulvic acid (FA) were investigated by cation exchange, ultrafiltration and dynamic experiment, respectively. The results showed that (i) complex equilibrium between the uranium and humic substances was achieved at approximately 72 h, (ii) the coordination number varied from 1:1 to 1:2 ( U(Ⅵ) : humic acid) as pH increased from 3 to 6; and (iii) , while the complex stability constant decreased when temperature increased, but increased with pH value. We found that the precipitation of uranyl could only be observed in presence of HA, and the precipitation was influenced by conditions, such as pH, uranium concentration, temperature, and the HA concentration. The maximum precipitation proportion up to 60% could be achieved in the condition of 40 mg/L HA solution at pH 6. We further observed that the migration behavior of uranium in soil in the presence of humic acid (HA) or fulvic acid (FA) was different from that in the presence of inorganic colloid, and the effect of humic substances (HS) was limited.

关键词：腐植酸类物质迁移行为双氧铀沉淀相互作用络合腐殖酸阳离子交换

理论力学研究性教学新探索:刚体运动基点法公式与连续介质速度场分解

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力学与实践 2023年第2期45卷 169-174页

作者：郭铁丁康厚军广西大学土木与建筑工程学院南宁530004 广西大学工程力学研究中心南宁530004

基础力学课程体系是现代工程教育的重要基础。理论力学作为力学课程体系的起点,提供了力学基本概念和原理。一方面,以离散体系(质点/刚体)为研究对象的理论力学与以连续体系(介质/变形微元体)为对象的连续介质力学,它们之间既存在密切... 详细信息

基础力学课程体系是现代工程教育的重要基础。理论力学作为力学课程体系的起点,提供了力学基本概念和原理。一方面,以离散体系(质点/刚体)为研究对象的理论力学与以连续体系(介质/变形微元体)为对象的连续介质力学,它们之间既存在密切联系又差异明显;另一方面,源于理论/经典力学的动力系统理论和非线性科学研究对应用力学学科产生了广泛影响。围绕这两个侧面,作者将在《理论力学研究性教学新探索》系列教研论文中阐释它们之间的联系。本篇探讨刚体运动基点法公式和连续介质速度场分解之间的关系,它们分别给出刚体模型和连续介质模型的速度分布规律,前者依赖刚体转动角速度矢量,而后者由速度梯度张量所刻画。本文将说明,两者存在对应理论关系,且刚体基点法公式是连续介质速度场分解的退化形式,即忽略变形效应。

关键词：理论力学刚体运动基点法公式连续介质速度场分解