Timoshenko梁在热冲击下的瞬态动力响应

研究了矩形截面简支Timoshenko梁在热冲击载荷作用下的动力响应.首先由分离变量法求得了梁的温度响应,然后采用微分求积法(DQM)分别对位移形式的动力学方程及初边值条件在空间域和时间域进行离散.数值求解离散后的代数方程组,得到了梁在热冲击下的动态位移和应力响应.分析了相关物理和几何参数对动态位移响应和动态应力响应的影响,考察了数值结果的收敛性.数值结果表明,对该类问题采用DQ法求解具有简洁可靠、计算效率高的特点.     

基于小波分析的Timoshenko梁裂缝识别研究

采用等效转动弹簧代替梁内的不扩展横向裂缝,研究Timoshenko裂缝梁的横向振动特性,建立了一种与有限元分析相结合的、基于模态参数的小波分析识别Timoshenko梁内裂缝的方法。以一简支梁为例,通过建立含横向不扩展裂缝的Timoshenko梁的有限元模型,用Lanczos法对结构的模态进行了计算分析,求出了基本振型和转角模态。分别应用mexh小波和db小波为母小波对二者做小波变换,进行多尺度分析,通过小波系数模极大值位置识别出梁内的裂缝。并对识别结果进行对比,发现识别Timoshenko梁裂缝时,基于转角模态小波变换的方法对小波基、尺度的要求较低,变换后的小波系数线更为平滑,奇异性特征更为明显,故运用转角模态小波变换来识别Timoshenko梁裂缝,较之运用基本振型小波变换的方法更为方便、有效。该方法对Timoshenko梁裂缝识别的工程应用具有参考价值。     

屈曲粘弹性Timoshenko斜梁的混沌运动区域分析

由于各向同性粘弹性体剪应力-角应变的本构关系与应力-应变的本构关系相似，据此可以得到屈曲粘弹性Timoshenko斜梁在铅垂外扰力作用下的动力方程，采用Melnikov法及Galerkin原理研究了屈曲粘弹性Timoshenko斜梁的混沌运动，并讨论分析了倾斜角、剪切变形、长厚比、外阻尼与内阻尼比对屈曲粘弹性梁混沌运动区域的影响。     

磁场作用下轴向运动功能梯度Timoshenko梁的振动特性

轴向运动结构的工程振动问题一直是动力学领域中的重要课题之一。为了更全面地分析工程中的振动,针对磁场作用下轴向运动功能梯度Timoshenko 梁的振动特性展开论述。基于梁的动力学方程组和相应的简支边界条件,应用复模态方法,得到不同参数时固有频率和衰减系数与轴向运动速度的对应关系。采用微分求积法分析磁场作用下前四阶固有频率和衰减系数随轴向运动速度的变化,并与复模态方法的结果进行对比验证。数据结果表明复模态方法得到的结果是精确解析解。衰减系数呈现不对称性,耦合固有频率呈现分离性。随着轴速、磁场强度和功能梯度指数的增大,梁的固有频率减小;随着支撑刚度参数的增大,梁的固有频率增大。     

Timoshenko梁的行波与模态的混合控制方法

基于Timoshenko梁理论，采用行波控制和独立模态空间混合方法。对悬臂梁的振动主动控制问题进行了研究。采用行波方法实现了对Timoshenko梁结构的振动控制。首先。采用模态控制方法，控制低频振动。而后，采用行波控制方法吸收高频振动能量，实现结构的振动控制。可见，行波／模态混合控制提高了振动控制精度和系统的鲁棒性。本文给出了悬臂梁振动的混合控制策略，最后给出了数值仿真结果。     

城市轨道交通槽型梁结构噪声计算与分析

该文用模态叠加法对城市轨道交通槽型梁进行车-轨-桥耦合动力计算,借助SYSNOISE求出模态声传递向量MATVs,进而用MATVs和梁的模态坐标响应计算桥梁的结构噪声。噪声计算值与实测值在频率分布和幅值上有较高的一致性,证明振动与噪声数值模型的可靠性。槽型梁结构噪声的线性声压级峰值频率为40Hz~80Hz,数值计算表明：动力分析只需考虑轮轨竖向接触即可满足结构噪声计算要求;考虑200Hz以下的声源激励和100Hz以下的结构模态作为边界条件可达到较好的噪声计算精度;调节轨下胶垫的刚度能有效减小结构振动,降低结构噪声2dB~3dB;声压级和车速有强线性关系。     

基于Timoshenko梁理论的微细立铣刀动力学建模

应用Timoshenko梁理论综合考虑了微细立铣刀特殊结构及其高转速工况引起的剪切效应和惯性效应,建立了微细立铣刀悬伸部分的动力学模型;分析了所建立的模型的收敛性问题,通过试验验证了模型的准确性,并与欧拉梁理论计算结果和有限元软件仿真结果比较,证明了模型的适用性;利用建立的微细立铣刀动力学模型,研究了微细立铣刀刀头直径、刀头部分长径比和刀颈半锥角等刀具结构参数对刀具固有频率的影响。模型可用于微细立铣刀的参数化设计和优化,改善其动力学特性。     

复合材料叠层梁的冲击响应特性

用平面应力模型来模拟复合材料叠层梁，得到了正交各向异性叠层梁的频率和模态函数，并用间接模态叠加法（IMSM）求得了叠层梁的瞬态响应。针对正交各向异性单层梁，把研究结果与Timoshenko梁结果进行了的比较，说明了厚度效应对冲击响应的重要影响。对叠层梁受冲击过程中其内部的应力特征及波传播现象进行了分析。     

基于Timoshenko梁理论的薄壁梁弯扭耦合分析

该文主要以截面形心与剪切中心不重合的等截面空间薄壁梁为研究对象。以Timoshenko梁理论和薄壁杆件理论为基础,考虑横向剪切变形以及横向剪力和二次剪应力所产生的翘曲,将转角位移和翘曲位移采取独立插值,利用虚功原理推导出薄壁截面空间梁元的弯扭耦合刚度矩阵。算例表明:所建立的模型具有很好的精度,满足工程应用;当截面有非对称轴时,计算须考虑弯扭耦合的影响。     

质量偏心Timoshenko梁的振动波特性研究

在研究船舶、潜艇等工程结构的低频振动时,通常可以将其简化为质量在截面内分布非均匀的梁结构,此质量偏心会引起弯-纵耦合。针对弯-纵耦合的质量偏心Timoshenko梁,推导了其截止频率的解析表达式;探讨了质量偏心对其纵振波、传播弯曲波及衰减弯曲波波数的影响规律;研究了三组波数下纵向/弯曲位移比随频率及质量偏心的变化。分析结果表明,质量偏心会降低梁的截止频率,偏心率越大,降低越明显;弯曲衰减波会在截止频率处转变为弯曲传播波;质量偏心使得非频散的纵向振动波转变为频散波;纵向振动与弯曲振动的耦合在质量偏心率或频率增大时,会进一步加强。     

Sensitizing according to Courant the Timoshenko beam finite element solution

Courant has presented in two articles from years 1923 and 1943 a formulation where a conventional variational principle is ‘sensitized’ by appending the variational expression with terms of higher order which vanish for the actual solution. The purpose of the article is to raise interest to this sensitizing idea. The idea is explained and applied in connection with the finite element solution of the Timoshenko beam problem. A certain kind of patch test is employed for the determination of the sensitizing parameter values. Equal‐order approximation for the beam axis deflection and the cross‐section rotation with linear two‐noded elements is used. Sensitizing is found to remove the locking behaviour. Sensitizing without a variational principle and connections with the stabilized formulations in finite element fluid mechanics problems are discussed. The concept of the sensitized principle of virtual work is introduced. References to applications of the patch test in more than one dimension are finally given. Copyright © 2000 John Wiley & Sons, Ltd.     

开尔文模型粘弹性Timoshenko梁的动力分析与应用

基于Kelvin模型张量形式本构关系导出粘弹性Timoshenko梁自由振动微分方程组,给出两端简支粘弹性梁的固有频率解析解。对粘弹性梁的振动特性进行了分析和比较。以此计算材料开尔文模型粘弹性阻尼系数,结果表明,该方法准确可靠。     

Free vibrations of a multi-span Timoshenko beam carrying multiple spring-mass systems

Structural elements supporting motors or engines are frequently seen in technological applications. The operation of a machine may introduce additional dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli-Euler single-span beams carrying a number of spring-mass system and Bernoulli-Euler multi-span beams carrying multiple spring-mass systems are plenty, but on Timoshenko multi-span beams carrying multiple spring-mass systems is fewer. This paper aims at determining the natural frequencies and mode shapes of a Timoshenko multi-span beam. The model allows to analyse the influence of the shear effect and spring-mass systems on the dynamic behaviour of the beams by using Timoshenko Beam Theory (TBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1–4 span beams are studied. The natural frequencies of Timoshenko multi-span beam calculated by using secant method for non-trivial solution are compared with the natural frequencies of multi-span beam calculated by using Bernoulli-Euler Beam Theory (EBT) in literature; the mode shapes are presented in graphs.     

变截面压电层合梁自由振动分析

考虑压电材料的质量效应和刚度效应,将表面粘贴或埋入式压电悬臂梁看作变截面梁,研究压电材料对智能结构固有特性的影响。基于一阶剪切变形理论导出压电层合梁的抗弯刚度和横向剪切刚度,计及梁的剪切变形和转动惯量,采用Timoshenko理论推导变截面压电层合梁的频率方程。给出了T300/970压电层合梁和硬铝压电层合梁的前3阶固有频率,并和有限元结果、等截面梁的计算结果进行比较。计算表明,压电材料对压电结构固有频率和固有振型的影响显著,在以振动控制为目标的压电结构动力学建模过程中,有必要考虑压电材料的质量和刚度。     

弹性支持的无限铁木辛柯梁对移动振动质量的响应

针对具有弹性基础的无限梁在移动的振动质量激励下的响应问题,采用考虑剪切变形和转动惯量的铁木辛柯梁理论建立梁的微分方程,并利用双重傅立叶变换求解,得到梁的运动方程。最后,通过一个数值计算的实例,分析了振动质量以及其移动的速度对梁的响应的影响。结果表明,振动质量本身对梁的响应的影响不可忽视。     

Delaminating buckling model based on nonlocal Timoshenko beam theory for microwedge indentation of a film/substrate system

A novel model built on the basis of nonlocal Timoshenko beam theory is presented for delaminating buckling in the microwedge indentation test of a thin film on an elastic substrate. Two size effects are accounted for in the proposed model. One is the delamination size effect, and the other is the film thickness effect. The influence of the elastic deformation in the substrate and the indentation-induced impression or notch on the buckling behaviors are taken into consideration by employing coupled line springs as the boundary conditions of the buckled film. The critical stress for buckling, the energy release rate and the phase angle of the interface delamination crack are calculated and compared with those by classical beam theories. Sensitivity of the two size effects is observed.     

An analytical method for free vibration analysis of Timoshenko beam theory applied to cracked nanobeams using a nonlocal elasticity model

This paper is concerned with the free transverse vibration of cracked nanobeams modeled after Eringen's nonlocal elasticity theory and Timoshenko beam theory. The cracked beam is modeled as two segments connected by a rotational spring located at the cracked section. This model promotes discontinuities in rotational displacement due to bending which is proportional to bending moment transmitted by the cracked section. The governing equations of cracked nanobeams with two symmetric and asymmetric boundary conditions are derived; then these equations are solved analytically based on concerning basic standard trigonometric and hyperbolic functions. Besides, the frequency parameters and the vibration modes of cracked nanobeams for variant crack positions, crack ratio, and small scale effect parameters are calculated. The vibration solutions obtained provide a better representation of the vibration behavior of short, stubby, micro/nanobeams where the effects of small scale, transverse shear deformation and rotary inertia are significant.     

移动荷载作用下弹性半空间Timoshenko梁的临界速度

根据梁的波速和半空间波速的相对关系,将Timoshenko梁-半空问系统分成四种不同情况。在梁与半空间相互作用的等效刚度和Timoshenko梁-半空间的弥散方程的基础上。利用弥散曲线，研究了移动荷载的临界速度。这四种情况分别为：软梁-硬半空间系统。次软梁-硬半空间系统，次硬梁-软半空间系统，硬梁-软半空间系统。研究表明，Timoshenko梁在移动荷载作用下的临界速度取决于梁的波速和半空间波速的相对关系；半空间的Rayleigh波波速始终是一个临界速度，当荷载速度达到Rayleigh波波速时．系统响应会趋于无穷大；对软梁-硬半空间系统，梁的剪切波速和压缩波速也是临界速度；对次软梁-硬半空间系统，梁的剪切波速是临界速度，并且还存在一个最小临界速度；对（次）硬梁-软半空间系统．粱的波速不再是临界速度。但也存在一个最小临界速度。