Dynamic behaviour of axially moving nanobeams based on nonlocal elasticity approach

In this article, transverse free vibrations of axially moving nanobeams subjected to axial tension are studied based on nonlocal stress elasticity theory. A new higher-order differential equation of motion is derived from the variational principle with corresponding higher-order, non-classical boundary conditions. Two supporting conditions are investigated, i.e. simple supports and clamped supports. Effects of nonlocal nanoscale, dimensionless axial velocity, density and axial tension on natural frequencies are presented and discussed through numerical examples. It is found that these factors have great influence on the dynamic behaviour of an axially moving nanobeam. In particular, the nonlocal effect tends to induce higher vibration frequencies as compared to the results obtained from classical vibration theory. Analytical solutions for critical velocity of these nanobeams when the frequency vanishes are also derived and the influences of nonlocal nanoscale and axial tension on the critical velocity are discussed.

Conformal analysis of fundamental frequency of vibration of simple-supported elastic ellipse-plates with concentrated substance

Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elastic plates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with interpolation points mutual iterative between odd and even sequences in boundary region is provided, as well as the conformal mapping function which can be described by real number region between complicated region and unit dish region is carried out. Furthermore, in the in-plane state of constant stress, vibrating function is completed by unit dish region method for simple-supported elastic plates with concentrated substance of complicated vibrating region, and the coefficient of fundamental frequency of the plate is analyzed. Meanwhile, taking simple-supported elastic ellipse-plates as an example, the effects on fundamental frequency caused by eccentric ratio, the coefficient of constant in-plane stress, as well as the concentrated substance mass and positions are analyzed respectively.

Nanoscale mass sensing based on vibration of single-layered graphene sheet in thermal environments

Based on vibration analysis, single-layered graphene sheet （SLGS） with multiple attached nanoparticles is developed as nanoscale mass sensor in thermal environments. Graphene sensors are assumed to be in simplysupported configuration. Based on the nonlocal plate the- ory which incorporates size effects into the classical theory, closed-form expressions lot the frequencies and relative fre- quency shills of SLGS-based mass sensor are derived using the Galerkin method. The suggested model is justified by a good agreement between the results given by the present model and available data in literature. The effects of tem- perature difference, nonlocal parameter, the location of the nanoparticle and the number of nanoparticles on the relative frequency shift of the mass sensor are also elucidated. The obtained results show that the sensitivity of the SLGS- based mass sensor increases with increasing temperature difference.

The Interface Stress Field in the Elastic System Consisting of the Hollow Cylinder and Surrounding Elastic Medium Under 3D Non-Axisymmetric Forced Vibration

The paper develops and employs analytical-numerical solution method for the study of the time-harmonic dynamic stress field in the system consisting of the hollow cylinder and surrounding elastic medium under the non-axisymmetric forced vibration of this system.It is assumed that in the interior of the hollow cylinder the point-located with respect to the cylinder axis,non-axisymmetric with respect to the circumferential direction and uniformly distributed time-harmonic forces act.Corresponding boundary value problem is solved by employing of the exponential Fourier transformation with respect to the axial coordinate and by employing of the Fourier series expansion of these transformations.Numerical results on the frequency response of the interface normal stresses are presented and discussed.

Transversal vibrations of double-plate systems

This paper presents an analytical and numerical analysis of free and forced transversal vibrations of an elastically connected double-plate system. Analytical solutions of a system of coupled partial differential equations, which describe corresponding dynamical free and forced processes, are obtained using Bernoulli＇s particular integral and Lagrange＇s method of variation constants. It is shown that one-mode vibrations correspond to two-frequency regime for free vibrations induced by initial conditions and to three-frequency regime for forced vibrations induced by one-frequency external excitation and corresponding initial conditions. The analytical solutions show that the elastic connec- tion between plates leads to the appearance of twofrequency regime of time function, which corresponds to one eigenamplitude function of one mode, and also that the time functions of different vibration modes are uncoupled, for each shape of vibrations. It has been proven that for both elastically connected plates, for every pair of m and n, two possibilities for appearance of the resonance dynamical states, as well as for appearance of the dynamical absorption, are present. Using the MathCad program, the corresponding visualizations of the characteristic forms of the plate middle surfaces through time are presented.

On Axially Symmetric Vibrations of Fluid Filled Poroelastic Spherical Shells

Employing Biot’s theory of wave propagation in liquid saturated porous media, waves propagating in a hollow poroelastic closed spherical shell filled with fluid are studied. The frequency equation of axially symmetric vibrations for a pervious and an impervious surface is obtained. Free vibrations of a closed spherical shell are studied as a particular case when the fluid is vanished. Frequency as a function of ratio of thickness to inner radius is computed in absence of dissipation for two types of poroelastic materials each for a pervious and an impervious surface. Results of previous works are obtained as a particular case of the present study.

Mapping analysis of vibrating fundamental frequency for simple-supported elastic rectangle-plates with concentrated mass

By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between complicated region and unite dish region was carried out. Aiming at calculating the vibrating fundamental frequency of special-shaped, elastic simple-supported rectangle-plates, in the in-plane state of constant stress, the vibration function of this complicated plate was depicted by unit dish region. The coefficient of ftmdamental frequency was calculated. Whilst, taking simple-supported elastic rectangle-plates with arc radius as an example, the effects on fundamental frequency caused by the concentrated mass and position, the ratio of the length to width of rectangle, as well as the coefficient of constant in-plane stress were analyzed respectively.

Analytical and Experimental Study of Free Vibration of Beams Carrying Multiple Masses and Springs

The structures in engineering can be simplified into elastic beams with concentrated masses and elastic spring supports. Studying the law of vibration of the beams can be a help in guiding its design and avoiding resonance. Based on the Laplace transform method, the mode shape functions and the frequency equations of the beams in the typical boundary conditions are derived. A cantilever beam with a lumped mass and a spring is selected to obtain its natural frequencies and mode shape functions. An experiment was conducted in order to get the modal parameters of the beam based on the NExT-ERA method. By comparing the analytical and experimental results, the effects of the locations of the mass and spring on the modal parameter are discussed. The variation of the natural frequencies was obtained with the changing stiffness coefficient and mass coefficient, respectively. The findings provide a reference for the vibration analysis methods and the lumped parameters layout design of elastic beams used in engineering.

一种机构刚度分布方法及在Stewart机构中的应用

并联机构(PKM)通常用于工业加工中的切削或装配,其优良的刚度特性和动态特性对机器人末端精度有了很好的保障。以机构低频共振的振幅为中间量,在机构固有频率振动分析的基础上,采用一阶共振能量分析法,计算机构各连杆刚度分布的比例,建立了一类新的机构刚度(变形能)分布评价指标。该方法用在方案设计阶段,可得到机构的整体刚体分布情况,从而获得了理论层面上的动力学性能依据。最后,以两类典型的Stewart并联机构作为案例,证明了该方法的有效性。

弹磁强化非线性能量阱的吸振性能研究

在纯立方非线性能量阱(Nonlinear Energy Sink,NES)的基础上引入弹磁元件,构成新型的弹磁强化非线性能量阱。建立含线性主振子和该非线性能量阱组成的系统的动力学方程,运用龙格库塔法对该非线性能量阱的动力学特征进行分析,并对比弹磁强化非线性能量阱和纯立方刚度非线性能量阱的吸振性能,研究弹磁强化非线性能量阱参数对其吸振性能的影响。分析结果表明,弹磁强化非线性能量阱具有较好的减振效果;通过增大弹磁元件中永磁铁质量、半径以及线性弹簧的刚度系数,减小永磁铁初始间距,都可以优化其减振效果。但激励幅值较大时,振幅会在共振频率附近出现不稳定响应或者出现双峰现象。

航空弹性并车机匣模态分析与结构参数优化

针对某型航空并车机匣的模态共振问题,考虑航空机架弹性支承刚度,采用有限元法进行典型工况下约束模态分析,研究了并车薄壁机匣结构参数对约束模态固有频率的影响规律。结果表明优化支承位置是大幅度改变固有频率最有效的方式;当固有频率处在共振区间边缘时,可通过优化壁厚、筋板的方法小幅度调整。当2个支承位置位于机匣平面对称轴线时,固有频率最小且随支承距离减小而减小。随着薄壁厚度增大,1、3、5、6阶模态频率减小,2、4阶增大。1、3阶模态频率基本不受筋板参数的影响;2、4阶模态频率随筋板宽度、高度增大和宽高比减小而增大且4阶频率随筋板角度增大而增大;5、6阶模态频率随筋板角度增大、筋板宽度减小而增大。在此基础上,对弹性并车机匣的结构参数进行优化使固有频率避开共振区间,提高了机匣的抗振能力。

弹性地基上非对称多孔功能梯度材料夹层板的自由振动

基于精细剪切变形理论研究了弹性地基上的非对称孔隙功能梯度材料(functionally graded material, FGM)夹层板的自由振动。结合该理论提出了一种新的非对称多孔FGM夹层板在弹性地基上的自由振动模型,且该模型只包含四个未知变量。控制方程是通过Hamilton原理建立的,并通过Navier法获得了其在四边简支下的固有频率。将模型退化为无弹性地基的非对称FGM夹层板以验证模型的准确性。最后详细讨论了参数变化对弹性地基上的非对称多孔FGM夹层板的自由振动行为的影响。研究发现,在不同的弹性系数下,非对称多孔FGM夹层板的固有频率会随着边厚比的增加而增加,而体积分数指数的增加对于不同弹性系数下的非对称多孔FGM夹层板的固有频率有不一样的变化。

弹性轨枕与道砟垫组合有砟轨道结构减振效果分析

以西安地铁16号线一期工程沙河滩车辆段规划上盖小学建筑区域为工程背景,开展不同车速下轨道结构减振响应现场测试,并与普通碎石道床进行对比,利用分频振级和最大Z振级两种评价指标研究弹性轨枕与道砟垫有砟轨道结构的组合减振效果。结果表明:采用弹性轨枕减振垫碎石道床时,曲线地段钢轨和轨枕的垂向加速度比直线地段有明显增大,而地表加速度差别不大;随着列车速度增大,钢轨、轨枕和地表的垂向加速度总体呈增大趋势,曲线地段加速度变化波动明显,建议该曲线地段列车运行速度小于15 km/h;弹性轨枕减振垫碎石道床减振频段为4~100 Hz,与普通碎石道床相比,两种减振指标条件下弹性轨枕减振垫碎石道床的减振效果均达12 dB以上,减振效果良好。

弹性联轴器对车辆动力传动系统扭振特性影响研究

车辆动力传动系统属于多自由度扭转振动系统 ,其轴系的扭转振动是影响其系统安全的重要因素之一。文中通过建立某车辆动力传动系统的多自由度质量—弹性—阻尼动力学模型 ,根据振动理论并依托系统扭振实验研究了3种弹性联轴器对该系统扭振特性的影响规律 ,着重分析联轴器刚度和阻尼对系统固有频率、固有振型、强迫振动响应等模态参数的影响。通过对比研究获得如下结论 ,匹配的弹性联轴器可以调整系统的低阶固有频率、避免系统发生共振、衰减共振振幅和发动机输出力矩的幅值不均匀性 ,即改善动力传动系统的扭振特性。

声学超材料在低频减振降噪中的应用评述

低频机械波在传播过程中穿透力强,难以衰减,特别是次声频段的机械波易与机体器官发生共振,对身体造成危害。为了实现对低频机械波的有效控制,解决现代工业生产和生活中普遍存在的噪声污染问题,结合最近十几年发展起来的声子晶体和声学超材料,系统地总结和论述通过声子晶体和声学超材料解决低频振动噪声问题的新方法。归纳和总结典型的低频振动噪声来源和对其进行控制方面存在的一些困难,介绍低频振动噪声的危害。重点概括基于声子晶体禁带特性实现低频振动噪声被动控制的相关研究工作,主要介绍通过亚波长尺寸特征的杆、薄板和薄膜类结构来实现低频振动和噪声衰减的具体方法和效果。在声学超材料的理论框架下,讨论薄膜类结构在低频振动噪声衰减中的应用及其优缺点。通过结合实际工程需要和最新研究动态,对这一领域存在的问题和后续发展趋势进行总结。研究对推动声子晶体和声学超材料在工程实践中的应用具有一定的引导意义。

动态弹性模量用于评估不同等级规格材的研究

参照加拿大锯材目测分等规则,将人工林杉木(Cunninghamia lanceolata(Lamb.)Hook.)足尺规格材(45 mm×90 mm×3 700 mm)分成精选级(SS)及Ⅰ、Ⅱ、Ⅲ4个等级,利用纵向基频振动无损检测法获得动态弹性模量,同时参照ASTM D198—99标准测试了其静态抗弯弹性模量。探讨不同等级的动态与静态抗弯弹性模量之间的相互关系,并比较不同等级静态抗弯弹性模量发现:不同等级动静态弹性模量的相互关系不同,其决定系数(R2)依次分别是0.761(Ⅱ)、0.715(SS)、0.703(Ⅰ)和0.356(Ⅲ),即Ⅱ等级以上的动静态弹性模量的相关性很好,可以通过动态弹性模量预测规格材的静态弹性模量;Ⅲ等级的相关性稍差一点,但都在0.01水平上具有显著的相关性;不同等级的静态抗弯弹性模量不等,Ⅱ等级的静态抗弯弹性模量值最大10.701 GPa,其次分别是SS、Ⅰ、Ⅲ,依次分别为:10.359、9.840、9.554 GPa。

三维振动强化抛光振动台变刚度弹性支承调谐固频的探讨

振动强化、抛光技术用于对复杂异型曲面工件进行表面强化、抛光处理。对三维强化、抛光振动台变刚度弹性支承调谐固频的问题进行了探讨。理论分析计算与实验研究表明 :这种调谐方式是有效的。

机车驱动系统弹性架悬的机理与应用研究

机车驱动系统弹性架悬有利于机车的横向动力学性能。为了阐明其机理并据此优化驱动系统悬挂参数,建立10自由度的驱动系统弹性架悬机车单转向架横向动力学模型,比较不同的驱动系统悬挂参数对机车横向动力学性能的影响,从动力吸振角度解释其机理并提出最佳悬挂频率选取的原则;针对两种结构形式驱动系统的机车,对整车多体动力学模型进行仿真,对理论分析结果进行验证。结果表明:当驱动系统悬挂频率接近于轮对蛇行运动频率时,机车动力学性能最佳,驱动系统相对构架横向和摇头运动吸收了构架的振动能量,减小了构架的蛇行运动幅值,从而提高了机车横向动力学性能;摆杆位于电机侧时,机车动力学性能明显改善,相对驱动系统非弹性悬挂,摆杆位于电机侧和非电机侧对机车最大轮轴横向力分别减小了45%和34%;摆杆长度大于100mm时,驱动系统悬挂频率小于3Hz;理论上驱动系统最佳悬挂阻尼比为0.1～0.3,但为了减小驱动系统相对构架的横向位移,需要提高悬挂阻尼。

振动频率对饱和黏土动力特性的影响

为了了解振动频率对饱和黏土动力特性的影响,针对天津临港工业区典型黏土做了一系列原状土与重塑土的动力试验.结果表明,随着频率的增加,原状土变形曲线由破坏型向发展型再向渐稳型过渡,重塑土变形曲线多为直线型.对4种动变形曲线定义了不同的破坏标准,发现随着振动频率的增加,软黏土动强度的变化趋势为先提高,之后增长幅度减小.频率越低,原状土的孔压升高越快;但振动频率对于重塑土孔压发展影响较小,原状土的界限孔压比低于重塑土.振动频率越低,原状土的动弹性模量软化指数下降得越快,并最终稳定在界限软化指数;不同振动频率下,重塑土软化指数的发展较为一致.

低频脉冲振动条件下金属成形的体积效应分析

将一定频率和振幅的脉冲振动信号施加到金属成形系统中,并对脉冲振动信号进行傅立叶变换,建立了振动拉伸的一维弹塑性本构模型和粘弹塑性本构模型。在计算瞬时应变的大小与屈服极限的基础上建立判断准则,并利用MATLAB对本构方程进行求解,从而确定了脉冲振动拉伸在材料变形时的动态应力和平均应力。按照所给定的振型参数和材料机械性能参数,结合特定的脉冲振动拉伸实例,分别绘制了两种模型的动态应力-时间曲线、动态应力-应变曲线和平均应力-应变率曲线。实验分析表明,在低频振动作用下,金属材料变形可以按照粘弹塑性模型来描述,且实验结果与理论计算结果比较一致,从而实现低频脉冲振动塑性成形粘弹塑性模型和弹塑性模型的体积效应分析。