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Bending of euler-bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach

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Acta Mechanica Sinica 2018年第5期34卷 871-882页

作者： M.Faraji Oskouie R.Ansari H.Rouhi Department of Mechanical Engineering University of GuilanP.O.Box 3756RashtIran Department of Engineering Science Faculty of Technology and EngineeringEast of GuilanUniversity of GuilanRudsar-Vajargah 44891-63157Iran

Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale *** studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases,such as bending analysis of cantilevers,and recourse must be made to the integral *** this article,a novel numerical approach is developed for the bending analysis of euler-bernoulli nanobeams in the context of strain-and stress-driven integral nonlocal *** numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential ***,the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential ***,in each case,the governing equation is obtained in both strong and weak *** solve numerically the derived equations,matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration *** is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned ***,it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.

关键词： Eringen's nonlocal theory Stress-driven model Strain-driven model euler-bernoulli beam Numerical approach Paradox

HOLOMORPHIC AND DIFFERENTIABLE PROPERTIES OF THE C_0-SEMIGROUP ASSOCIATED WITH THE euler-bernoulli BEAM EQUATIONS WITH STRUCTURAL DAMPING

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Science China Mathematics 1992年第5期35卷 547-560页

作者：黄发伦黄永忠郭发明 Department of Mathematics Sichuan University Chengdu 610064 PRC

In recent years more attention has been paid to the mathematical model for aflying ve-hicle which can be considered as an euler--bernoulli beam equation with damping. Its character is that the boundary conditions satisfied by the elastic and damping operators are non-local and coupling to each other. It is a difficult problem how to study the mathematicalproperties of this system. This paper provides an approach to study this problem, unifies andcovers all of the previous work. The results obtained are very convenient for applications tothe initial boundary-value problems of linear hyperbolic equations with variable coefficientsand damping.

关键词： euler-bernoulli beam equation damping holomorphism differentiability.

含多维随机变量的广义概率密度演化方程解析解:以euler-bernoulli梁为例

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力学学报 2024年第9期56卷 2659-2668页

作者：周永峰李杰同济大学土木工程学院上海200092 同济大学土木工程防灾国家重点实验室上海200092

广义概率密度演化方程的解析解,不仅具有重要理论价值,而且具有校验数值解、进而标定数值算法误差的作用.以euler-bernoulli简支梁为例,推导给出了梁受迫振动时跨中位移响应所对应的广义概率密度演化方程解析解.包括非平稳非高斯随机载... 详细信息

广义概率密度演化方程的解析解,不仅具有重要理论价值,而且具有校验数值解、进而标定数值算法误差的作用.以euler-bernoulli简支梁为例,推导给出了梁受迫振动时跨中位移响应所对应的广义概率密度演化方程解析解.包括非平稳非高斯随机载荷作用下的解(包含2维随机变量)以及同时考虑载荷随机性和结构参数随机性时的解(分别包含2维、4维和5维随机变量).分析结果表明,真实的概率密度演化是一个十分复杂的过程,远不能用简单的概率分布函数加以描述.这一进展,可为概率密度演化理论的进一步深入研究提供一个方面的基础.

关键词：广义概率密度演化方程解析解 euler-bernoulli 梁受迫振动多维随机变量

The Response of Viscously Damped euler-bernoulli Beam to Uniform Partially Distributed Moving Loads

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Applied Mathematics 2012年第3期3卷 199-204页

作者： Folake Oyedigba Akinpelu Department of Pure and Applied Mathematics Ladoke Akintola University of Technology Ogbomoso Nigeria

The paper investigates the response of non-initially stressed euler-bernoulli beam to uniform partially distributed moving loads. The governing partial differential equations were analyzed for both moving force and moving mass problem in order to determine the behaviour of the system under consideration. The analytical method in terms of series solution and numerical method were used for the governing equation. The effect of various beam observed that the response amplitude due to the moving force is greater than that due to moving mass. It was also found that the response amplitude of the moving force problem with non-initial stress increase as mass of the mass of the load M increases.

关键词： Viscously Damped euler-bernoulli Beam Uniform Partially Distributed and Moving Loads

Analysis of Vibration of the euler-bernoulli Pipe Conveying Fluid by Dynamic Stiffness Method and Transfer Matrix

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Journal of Applied Mathematics and Physics 2020年第1期8卷 172-183页

作者： Yunfeng Li Yundong Li Naveed Akbar School of Automation & Information Engineering Sichuan University of Science & Engineering Zigong China School of Mathematics and Statistics Sichuan University of Science & Engineering Zigong China

The dynamic stiffness method and Transfer method is applied to study the vibration characteristics of the euler-bernoulli pipe conveying fluid in this paper. According to the dynamics equation of the pipe conveying fluid, the element dynamic stiffness is established. The vibration characteristic of the single-span pipe is analyzed under two kinds of boundary conditions. The results compared with the literature, which has a good consistency. Based on this method, natural frequency and the critical speed of the two types of multi-span pipe are deserved. This paper shows that the dynamic stiffness method and transfer matrix is an effective method to deal with the vibration problem of pipe conveying fluid.

关键词： Dynamic Stiffness Transfer Matrix euler-bernoulli Pipe

边界带有干扰的euler-bernoulli梁方程的输出反馈稳定

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中北大学学报（自然科学版） 2015年第2期36卷 103-107页

作者：卢小瑞山西金融职业学院基础部山西太原030008

通过恰当地选择输出信号,将不确定干扰入常微分方程系统,从而可以利用高增益观测器来估计不确定干扰,这样未知干扰可以由其估计值抵消掉.理论证明,该方案是行之有效的.

关键词：边界控制干扰 euler-bernoulli 梁方程状态观测

Large deformation analysis of a cantilever beam made of axially functionally graded material by homotopy analysis method

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Applied Mathematics and Mechanics(English Edition) 2019年第10期40卷 1375-1386页

作者： Xin LIN Yixin HUANG Yang ZHAO Tianshu WANG School of Astronautics Harbin Institute of TechnologyHarbin 150001China School of Aerospace Engineering Tsinghua UniversityBeijing 100084China

Large deformation of a cantilever axially functionally graded (AFG) beam subject to a tip load is analytically studied using the homotopy analysis method (HAM). It is assumed that its Young’s modulus varies along the longitudinal direction according to a power law. Taking the solution of the corresponding homogeneous beam as the initial guess and obtaining a convergence region by adjusting an auxiliary parameter, the analytical expressions for large deformation of the AFG beam are provided. Results obtained by the HAM are compared with those obtained by the finite element method and those in the previous works to verify its validity. Good agreement is observed. A detailed parametric study is carried out. The results show that the axial material variation can greatly change the deformed configuration, which provides an approach to control and manage the deformation of beams. By tailoring the axial material distribution, a desired deformed configuration can be obtained for a specific load. The analytical solution presented herein can be a helpful tool for this procedure.

关键词： large deformation beam axially functionally graded (AFG) material euler-bernoulli beam homotopy analysis method (HAM)

VIBRATION ANALYSIS OF A BEAM WITH EMBEDDED SHAPE MEMORY ALLOY WIRES

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Acta Mechanica Solida Sinica 2013年第5期26卷 536-550页

作者： Mohammad Mehdi Barzegari Morteza Dardel Alireza Fathi Department of Mechanical Engineering Babol University of Technology

In this study, analytical relations for evaluating the exact solution of natural fre- quency and mode shape of beams with embedded shape memory alloy （SMA） wires are presented. Beams are modeled according to euler-bernoulli, Timoshenko and third order beam （Reddy） the- ories. A relation is obtained for determining the effect of axial load generated by the recovery action of pre-strained SMA wires. By defining some dimensionless quantities~ the effect of different me- chanical properties on the frequencies and mode shapes of the system are carefully examined. The effect of axial load generated by SMA wires with buckling load and frequency jump is accurately studied.

关键词： shape memory alloy natural frequency mode analysis frequency jump euler-bernoulli Timoshenko third order beam buckling

Stability of the time variable elastic system

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Science China(Technological Sciences) 1996年第1期39卷 92-102页

作者：于景元李胜家朱广田 Institute of Information and Control Beijing 100037China Institute of Systems Science Chinese Academy of SciencesBeijing 100080China

It is proved that the existence,uniqueness,and stability of the solution of the elastic system were caused by the slender flying vehicle.

关键词： euler-bernoulli beam equation time variable system damping exponential stability.