考虑附加质量的中心刚体-柔性梁系统的动力学特性研究

对有附加质量的中心刚体-柔性梁系统的动力学特性进行了研究。柔性梁为等截面的Euler Bernoulli梁,针对柔性梁变形场使用假设模态法进行了离散,并运用第二类拉格朗日方程推导出系统的动力学方程后,采用Matlab编制了动力学仿真软件。首先讨论了附加质量对系统的固有频率与振型的影响,其次讨论了在大范围运动已知和未知的条件下,不同位置附加质量的中心刚体-柔性梁系统的刚柔耦合动力学特性,对带有附加质量的中心刚体-柔性梁系统的中心刚体转角、梁末端位移响应以及中心刚体角速度的仿真结果进行了分析。结果表明:附加质量从柔性梁固定端向自由端移动时,柔性梁前五阶固有频率近似地呈现周期性变化;附加质量所处位置的不同,对于系统的刚柔耦合动力学响应以及系统振型的影响十分明显。     

柔性体的刚-柔耦合动力学分析

对柔性梁的刚-柔耦合动力学特性进行分析.从连续介质力学理论出发,在纵向变形位移中计及了耦合变形量,用Jourdain速度变分原理导出了柔性梁的刚-柔耦合动力学方程.定量地研究了非惯性系下柔性梁的动力学性质,比较了在不同转速下零次近似模型和耦合模型的振动频率的差异.为了确定零次近似模型的适用范围,引入与转速和基点加速度有关的相关系数,提出了零次近似模型的适用判据为相关系数小于0.1.在此基础上,进一步研究在大范围运动是自由的情况下柔性梁的大范围运动和变形运动的耦合机理,计算了带平动刚体的柔性梁的大范围运动规律,揭示零次近似模型和耦合模型的刚-柔耦合动力学性质的根本差异.     

旋转功能梯度智能结构的刚-柔耦合动力学分析

基于一次耦合模型理论建立了中心刚体-压电层-功能梯度材料智能梁系统的刚柔耦合动力学模型．研究了开环状态下将压电材料作为传感器的压电效应和质量刚度效应对系统动力学特性的影响．通过仿真算例与另两种不同建模理论（传统零次近似耦合模型、一次近似耦合模型）作了对比．随着中心刚体外驱动力矩的增大,零次近似耦合模型和一次近似耦合模型计算结果逐渐发散,而本文的一次耦合模型的计算结果始终保持收敛,较其他近似耦合模型具有一定优势．对三种不同的结构的计算结果表明,压电材料的压电效应对系统的动力学特性影响显著,压电材料的质量刚度效应也会影响智能梁的动力学行为,前者比后者的影响大得多．此外,功能梯度材料功能梯度指数对系统动力学特性的影响也较大．     

考虑尺度效应的微梁刚柔耦合动力学分析

不少微观实验已经证实,微尺度领域材料的力学性能存在尺度效应.文章以转动刚体、柔性微梁组成的刚柔耦合系统为研究对象,采用偶应力理论(又称 Cosserat理论)研究微梁动力学特性的尺度效应,运用拉格朗日方程推导出系统考虑尺度效应的一次近似刚柔耦合动力学方程.仿真结果表明,较该文提出的一次近似耦合模型,传统的零次近似耦合模型在刚体作高速旋转时不能正确地描述微梁的动力学行为;尺度效应使微梁振动的振幅减小,频率增大.     

风力发电塔的自振特性分析

将风力发电塔视为带有附加质量的变截面悬臂梁,进行横向振动的自振特性分析.采用直接模态摄动法建立风力发电塔自振特性的近似求解方法,与采用梁单元模型和壳单元模型的有限元法的计算结果相比较.数值计算结果表明直接模态摄动法具有较好的精度,形成了半解析解形式.     

旋转悬臂梁的刚柔耦合动力学建模与频率分析

对固结于转动刚体上外接柔性梁的刚柔耦合动力学建模和频率特性进行了研究,在精确描述柔性梁非线性变形的基础上,利用Hamilton变分原理和假设模态法,在计入柔性梁由于横向变形而引起的轴向变形二阶耦合量的条件下,推导出考虑"动力刚化"项的一次近似耦合模型。首先忽略柔性梁纵向变形的影响,给出一次近似简化模型,引入无量纲变量,对简化模型做无量纲化处理,分析梁固有频率对模态截断数的依赖性;其次研究在一次近似简化模型和零次近似简化模型下,调谐角速度与共振现象的关系;最后分析一次近似耦合模型的动力特性。研究发现,为保证计算的精度,模态截断数应随无量纲角速度的增大而增加,合理的模态截断数具有收敛值;一次近似简化模型下悬臂梁横向弯曲振动不存在共振调谐角速度,一次耦合模型下柔性梁并没有出现屈曲失稳现象。现有典型文献的相关结论是值得商榷的。     

中心刚体-柔性梁系统的最优跟踪控制

对考虑阻尼影响的中心刚体-柔性梁系统的动力特性和主动控制进行研究. 研究 中考虑了3种动力学模型：一次近似耦合模型、一次近似简化模型和线性化模型. 一次近 似模型中同时考虑了柔性梁的轴向变形和横向变形. 若在一次近似耦合模型中忽略轴向变 形的影响,则可得出一次近似简化模型. 线性化模型是对一次近似简化模型的线性化处理. 另外研究中考虑了3种阻尼因素：结构阻尼、风阻、中心刚体轴承处的阻尼. 控制设计采 用最优跟踪控制方法. 给出了从物理测量中提取模态坐标的滤波器方法. 研究结果显 示,一次近似简化模型能够有效地对系统的动力学行为进行描述;阻尼对系统的动力学特 性有着重要影响;当系统大范围运动为低速时,模态滤波器能够较好地提取出控制律所需 的模态坐标,最优跟踪控制方法能够使得系统跟踪所期望的运动轨迹,并且柔性梁的弹性 振动可得到抑制.     

基于初应力法的作大范围运动柔性梁动力学建模理论研究

研究了初应力法的作大范围运动柔性梁的建模理论.根据连续介质理论,考虑应变-位移中的非线性项,用一致质量有限元法对柔性梁进行离散,基于Jourdain速度变分原理导出定轴转动下大范围运动为自由的柔性梁刚-柔耦合动力学方程.从其刚柔耦合动力学方程出发,考虑在大范围运动已知情况下的结构动力学方程.通过引入准静态概念,把其结构动力学方程转化为准静态方程.对纵向和横向变形节点坐标进行坐标分离,解出与纵向变形相关的准静态方程,得到准静态时的纵向应力表达式,从而获得附加刚度项.并对此非惯性系下作大范围运动柔性梁的结构动力学方程进行数值仿真,对零次近似模型、一次近似模型、初应力法动力学模型的仿真结果进行分析,揭示三种模型的动力学性质的差异.     

旋转运动柔性梁的假设模态方法研究

采用假设模态法对旋转运动柔性梁的动力特性进行研究，给出简化的控制模型. 首先采用Hamilton原理和假设模态离散化方法，在计入柔性梁由于横向变形而引起的轴向变形的二阶耦合量的条件下，推导出基于柔性梁变形位移场一阶完备的一次近似耦合模型，然后对该模型进行简化，忽略柔性梁纵向变形的影响，给出一次近似简化模型，最后将采用假设模态离散化方法的结果与采用有限元离散化方法的结果进行了对比研究. 研究中考虑了两种情况：非惯性系下的动力特性研究和系统大范围运动为未知的动力特性研究. 研究结果显示，当系统大范围运动为高速时，在假设模态离散化方法中应增加模态数目，较少的模态数目将导致较大误差. 一次近似简化模型能够较好地反映出系统的动力学行为，可用于主动控制设计的研究.     

基于能量法的载流单层碳纳米管振动特性研究

以非局部弹性理论为基础,考虑了碳纳米管的小尺度效应;采用欧拉-伯努利梁模型,基于能量法给出了载流单层碳纳米管的振动频率近似解;并通过具体算例,应用振动频率近似解公式求解了悬臂单层纳米管的频率值,进而研究了管内流体流速、碳纳米管小尺度参数对悬臂梁一阶振动频率及振型的影响,并将得到的结论与已有文献的结果进行比较,证明了振动频率近似解的正确性。     

Dynamic analysis of a flexible hub-beam system with tip mass

For a dynamic system of a rigid hub and a flexible cantilever beam, the traditional hybrid coordinate model assumes the small deformation in structural dynamics where axial and transverse displacements at any point in the beam are uncoupled. This traditional hybrid coordinate model is referred as the zeroth-order approximation coupling model in this paper, which may result in divergence to the dynamic problem of some rigid–flexible coupling systems with high rotational speed. In this paper, characteristics of a flexible hub-beam system with a tip mass is studied. Based on the Hamilton theory and the finite element discretization method, and in consideration of the second-order coupling quantity of the axial displacement caused by the transverse displacement of the beam, the rigid–flexible coupling dynamic model (referred as the first-order approximation coupling (FOAC) model in this paper) and the corresponding model in non-inertial system for the flexible hub-beam system with a tip mass are presented firstly, then the dynamic characteristics of the system are studied through numerical simulations under twos cases: the large motion of the system is known and is unknown. Simulation and comparison studies using both the traditional zeroth-order model and the proposed first-order model show that even small tip mass may affect dynamic characteristics of the system significantly, which may result in the largening of vibrating amplitude and the descending of vibrating frequency of the beam, and may affect end position of the hub-beam system as well. The effect of the tip mass becomes large along with the increasing of rotating speed of large motion of the system. When the large motion of the system is at low speed, the traditional ZOAC model may lead to a large error, whereas the proposed FOAC model is valid. When the large motion is at high speed, the ZOAC model may result in divergence to the dynamic problem of the flexible hub-beam system, while the proposed second model can still accurately describe the dynamic hub-beam system.     

带集中质量的旋转柔性曲梁动力学特性分析

本文对带集中质量的平面内旋转柔性曲梁动力学特性进行了研究.基于绝对节点坐标法推导出曲梁单元,其中该曲梁单元采用Green-Lagrangian应变,并根据曲梁变形前后的曲率变化和曲率的精确表达式计算了曲梁单元弹性力所作的虚功.通过虚功原理,利用$\delta$函数和中心刚体与悬臂曲梁之间的固支边界条件,建立了带集中质量的旋转柔性曲梁非线性动力学模型.基于该模型,本文仿真计算了悬臂曲梁的纯弯曲问题和带有刚柔耦合效应的旋转柔性曲梁动力学响应问题,以此分别讨论了所提出曲梁单元的收敛性和动力学模型的正确性.进一步应用D'Alembert原理,将旋转曲梁等效为带离心力的无旋转曲梁,通过线性摄动处理得到系统的特征方程,以此分别研究了旋转角速度、初始曲率和集中质量对曲梁动力学特性的影响.最后重点分析了旋转曲梁的频率转向和振型切换问题,并阐述了两者之间的相互关系.研究结果表明:随着旋转角速度的增大,曲梁的频率特性与直梁的频率特性相近,以及曲梁拉伸变形占主导的模态振型会提前.      

An image encryption algorithm based on compound homogeneous hyper-chaotic system

A new dynamic model of a rotating flexible beam with a concentrated mass located in arbitrary position is derived based on the absolute nodal coordinate formulation, and its modal characteristics are investigated in this paper. To consider the concentrated mass at an arbitrary location of the beam, a Dirac’s delta function is used to express the mass per unit length of the beam. Based on the proposed dynamic model, the frequency analysis is performed. The nonlinear equation is transformed into the linear one via employing the linear perturbation analysis method. The stiffness matrix of static equilibrium of the system under the deformed condition is obtained, in which the effect of coupling between the longitudinal deformation and transversal deformation is included. This means even if only the chordwise bending equation is solved, the longitudinal vibration effect can be still considered. As we know, once the longitudinal deformation is large, it will significantly affect the chordwise bending vibration. So the proposed model in this paper is more accurate than the traditional dynamic models which are usually lack of the coupling terms between the longitudinal deformation and transversal deformation. In fact, the traditional dynamic models for the chordwise vibration analysis in the existing literature are usually linear due to neglecting the coupling terms, and consequently, they are only suitable for the modal characteristic analysis of a beam under small deformations. In order to get some general conclusions of the natural frequencies and mode shapes, the equation which governs the chordwise bending vibration of the rotating beam is transformed into a dimensionless form. The dynamic model presented in this paper is nonlinear and can be conveniently used to analyze the modal characteristics of a rotating flexible beam with large deformations. To demonstrate the power of the new dynamic model presented in this paper, the dynamic simulations involving the comparisons between the different frequencies obtained using the model proposed in this paper and the models in the existing literature and the investigating in frequency veering and mode shift phenomena are given. The simulation results show that the angular velocity of the flexible beam will give rise to the phenomena of the natural frequency loci veering and the associated mode shift which is verified in the previous studies. In addition, the phenomena of the natural frequency loci veering rather than crossing can be observed due to the changing of the magnitude of the concentrated mass or of the location of the concentrated mass which are found for the first time. Furthermore, there is an interesting phenomenon that the natural frequency loci will veer more than once due to different types of mode coupling between the bending and stretching vibrations of the rotating beam. At the same time, the mode shift phenomenon will occur correspondingly. Additionally, the characteristics of the vibration nodes are also investigated in this paper.     

Single-walled boron nitride nanotube as nano-sensor

Nowadays, the eye-catching characteristics of boron nitride nanotubes, in particular, the capability of sensing nano-objects, have opened up new prospects to develop the bio-/nano-sensing technologies. This research deals with physically affected single-walled boron nitride nanotubes (SWBNNT) as nano-sensors for sensing attached nanoscale objects. Three different boundary conditions including simply supported at both ends, clamped-free and clamped-clamped are considered to illustrate the vibrational behaviour of SWBNNTs as nano-sensor. The Rayleigh and Timoshenko beam theories are employed to model the SWBNNT. Also, the nonlocal strain gradient model is utilized to capture the size-dependent effects. One of the major factors in the scrutiny of mass nano-sensors is pertinent to the variation in frequency shift magnitudes against the number and mass weight values of attached nanoparticles. Herein, the effects of the nonlocal and material length scale parameters, the number and location of nano-objects, the rotary inertia and mass weight magnitudes of attached nanoparticles, the aspect ratio of SWBNNT, electrical potential and different boundary conditions on the variation in frequency shift and resonant frequency are analysed.     

Wave-based control of planar motion of beam-like mass–spring arrays

Wave-based control (WBC) is a simple and relatively new technique for motion control of under-actuated flexible systems. To date it has been mainly applied to rectilinear lumped flexible systems. The current work focuses on a development of WBC to control two-dimensional beam-like structures in which an actuator, attached to one end, acts to translate and rotate the structure through an arbitrary path in the plane. In this work, first a lumped model of a beam is developed using mass–spring arrays. The lumped beam model is of interest here as a benchmark control challenge. It can also be considered as a model of various lumped or distributed mass structures. To check the latter, the mode shapes and frequencies are first compared with those of classical beam theory. This involved a new technique to find mode shapes and frequencies for arrays. The control strategy is then presented and tested for a range of manoeuvres. As a system to be controlled, the mass–spring array presents many challenges. It has many degrees of freedom, many undamped vibration modes, is highly under-actuated, and sensing of system states is difficult. Despite these challenges, WBC performs well, combining a fairly rapid response with active vibration damping and zero steady-state error. The controller is simple to implement and of low order. It does not need or use any system model and is very robust to system changes.     

Modeling of system dynamics of a slewing flexible beam with moving payload pendulum

When a tower crane is handling payload via rotation and moving the carriage simultaneously the jib structure and the payload can be modeled as a system consisting of a slewing flexible clamed-free beam with the spherical payload pendulum that moves along the beam. The present work completes the dynamic modeling of the system mentioned above. The clamed-free beam attached to a rotating hub is modeled by Euler–Bernoulli beam theory. The payload is modeled as a sphere pendulum of point mass attached to via massless inextensible cable the carriage moving on the rotating beam. Non-linear coupled equations of motion of the in- and out-of-plane of the beam and the payload pendulum are derived by means of the Hamilton principle. Some remarks are made on the equations of motion.     

旋转内接功能梯度材料梁刚柔热耦合动力学特性研究

对具有旋转内接功能梯度材料(functionally graded material,FGM) 梁系统的刚柔热耦合动力学特性进行研究。假定梁为Euler–Bernoulli 型,由双组分材料制成,其力学性能参数沿厚度方向呈幂律变化。考虑柔性梁的横向弯曲变形和轴向拉伸变形,并计入横向弯曲引起的纵向缩短,即非线性耦合项。采用假设模态法离散柔性梁的变形场,运用第二类 Lagrange 方程推导出系统的一次近似刚柔热耦合动力学方程,并编制旋转内接FGM梁动力学仿真软件。然后通过仿真算例详细研究了各种无量纲参数及温度变化对系统固有频率、临界转速以及动力学特性的影响。研究表明：内接FGM梁的径长比、功能梯度系数以及温度变化对系统的动力学特性均有较大影响。

     

Dynamic characteristics of a beam and distributed spring-mass system

This paper studies dynamic characteristics of a beam with continuously distributed spring-mass which may represent a structure occupied by a crowd of people. Dividing the coupled system into several segments and considering the distributed spring-mass and the beam in each segment being uniform, the equations of motion of the segment are established. The transfer matrix method is applied to derive the eigenvalue equation of the coupled system. It is interesting to note from the governing equations that the vibration mode shape of the uniformly distributed spring-mass is proportional to that of the beam at the attached regions and can be discontinuous if the natural frequencies of the spring-masses in two adjacent segments are different. Parametric studies demonstrate that the natural frequencies of the coupled system appear in groups. In a group of frequencies, all related modes have similar shapes. The number of natural frequencies in each group depends on the number of segments having different natural frequencies. With the increase of group order, the largest natural frequency in a group monotonically approaches the natural frequency of corresponding order of the bare beam from the upper side, whereas the others monotonically move towards those of the independent spring-mass systems from the lower side. Numerical results show that the frequency coupling between the beam and the distributed spring-mass mainly occurs in the low order of frequency groups, especially in the first group. In addition, vibratory characteristics of the coupled system can be approximately represented by a series of discrete multi-degrees-of-freedom system. It also demonstrates that a beam on Winkler elastic foundation and a beam with distributed solid mass are special cases of the proposed solution.