Thermo-mechanical vibration analysis of nonlocal temperature-dependent FG nanobeams with various boundary conditions

In this paper, the thermal effect on free vibration characteristics of functionally graded (FG) size-dependent nanobeams subjected to an in-plane thermal loading are investigated by presenting a Navier type solution and employing a semi analytical differential transform method (DTM) for the first time. Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton's principle and they are solved applying DTM. According to the numerical results, it is revealed that the proposed modeling and semi analytical approach can provide accurate frequency results of the FG nanobeams as compared to analytical results and also some cases in the literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as thermal effect, material distribution profile, small scale effects, mode number and boundary conditions on the normalized natural frequencies of the temperature-dependent FG nanobeams in detail. It is explicitly shown that the vibration behavior of an FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.     

Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method

In this paper nonlocal Euler–Bernoulli beam theory is employed for vibration analysis of functionally graded (FG) size-dependent nanobeams by using Navier-based analytical method and a semi analytical differential transform method. Two kinds of mathematical models, namely, power law and Mori-Tanaka models are considered. The nonlocal Eringen theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. Governing equations are derived through Hamilton's principle and they are solved applying semi analytical differential transform method (DTM). It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of FG nanobeams. The good agreement between the results of this article and those available in literature validated the presented approach. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as small scale effects, different material compositions, mode number and thickness ratio on the normalized natural frequencies of the FG nanobeams in detail. It is explicitly shown that the vibration of a FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.     

大扁平比胎侧解析刚度建模及轮胎动力学分析EI北大核心CSCD

针对重载轮胎大扁平比结构建模问题,从动力学建模、实验模态分析、结构参数辨识等方面,基于解析弹性基础的欧拉梁模型,对重载轮胎的柔性胎体和大扁平比胎侧曲梁的低频动力学特性开展研究,建立了考虑充气预紧力的欧拉梁胎体模型,利用实验模态方法,探究了不同充气压力下的柔性胎体振动特性;考虑胎侧曲梁预紧力弦效应和结构弯曲效应,建立了大扁平比胎侧曲梁解析刚度模型;基于模态测试结果,进行柔性胎体与解析胎侧结构参数辨识。研究结果表明:在0~180 Hz频率范围内,重载轮胎以结构周向弯曲振动为主,可利用基于弹性基础的柔性梁模型表征;大扁平比胎侧曲梁的解析刚度与胎侧的几何、结构和充气压力参数直接相关;轮胎充气压力影响柔性胎体梁的轴向预紧力和胎侧的弦刚度,进而影响轮胎弯曲振动特性。     

On sixfold coupled vibrations of thin-walled composite box beams

This paper presents a general analytical model for free vibration of thin-walled composite beams with arbitrary laminate stacking sequences and studies the effects of shear deformation over the natural frequencies. This model is based on the first-order shear-deformable beam theory and accounts for all the structural coupling coming from the material anisotropy. The seven governing differential equations for coupled flexural–torsional–shearing vibration are derived from the Hamilton’s principle. The resulting coupling is referred to as sixfold coupled vibration. Numerical results are obtained to investigate the effects of fiber angle, span-to-height ratio, modulus ratio, and boundary conditions on the natural frequencies as well as corresponding mode shapes of thin-walled composite box beams.     

Exact determinant for infinite order FEM representation of a Timoshenko beam–column via improved transcendental member stiffness matrices

Transcendental stiffness matrices for vibration (or buckling) have been derived from exact analytical solutions of the governing differential equations for many structural members without recourse to the discretization of conventional finite element methods (FEM). Their assembly into the overall dynamic structural stiffness matrix gives a transcendental eigenproblem, whose eigenvalues (natural frequencies or critical load factors) can be found with certainty using the Wittrick–Williams algorithm. A very recently discovered analytical property is the member stiffness determinant, which equals the FEM stiffness matrix determinant of a clamped ended member modelled by infinitely many elements, normalized by dividing by its value at zero frequency (or load factor). Curve following convergence methods for transcendental eigenproblems are greatly simplified by multiplying the transcendental overall stiffness matrix determinant by all the member stiffness determinants to remove its poles. In this paper, the transcendental stiffness matrix for a vibrating, axially loaded, Timoshenko member is expressed in a new, convenient notation, enabling the first ever derivation of its member stiffness determinant to be obtained. Further expressions are derived, also for the first time, for unloaded and for static, loaded Timoshenko members. These new expressions have the advantage that they readily reduce to corresponding expressions for Bernoulli–Euler members when shear rigidity and rotatory inertia are neglected. Additionally, the total equivalence of the normalized transcendental determinant with that of an infinite order FEM formulation aids understanding and evaluation of conventional FEM results. Examples are presented to illustrate the use of the member stiffness determinant. Copyright © 2004 John Wiley & Sons, Ltd.     

Propagation of a partially coherent higher-order cosh-Gaussian beam through a paraxial ABCD optical system

Based on the generalized Huygens–Fresnel integral, analytical expressions for the mutual coherence function, the spatial complex degree of coherence, and the effective size of a partially coherent higher-order cosh-Gaussian beam through a paraxial ABCD optical system have been derived. As a numerical example, the propagation of a partially coherent higher-order cosh-Gaussian beam through an optical Fourier-transforming system with a limiting aperture is illustrated. The normalized intensity distribution, the spatial complex degree of coherence, and the effective beam size for the partially coherent higher-order cosh-Gaussian beam are numerically demonstrated in the observation plane. The influences of the spatial coherence length and the limiting aperture on the normalized intensity distribution, the spatial complex degree of coherence, and the effective beam size are also examined in detail.     

简谐激励下阻尼复合结构多尺度拓扑优化设计

目的 为得到抗振性能良好的板壳结构,保证设备的正常工作,文中提出一种板壳阻尼复合结构多尺度优化设计方法。方法 以动柔度为目标,建立频域激励下和固定频率点激励下板壳阻尼复合结构中阻尼材料宏观分布和微结构协同设计的多尺度问题的数学模型,推导目标函数和约束条件对设计变量的灵敏度,并基于移动渐近线法求解优化数学模型。结果 所提多尺度设计方法可以有效获得板壳结构最优阻尼材料宏观布局和最优阻尼复合材料微结构构型,提高了结构的动力学性能,同时结果也表明涂敷阻尼复合材料结构的振动响应相较于仅涂敷单一阻尼材料的振动响应大幅减小。结论 研究表明,不同激励频率下阻尼材料的宏观分布形态不同,阻尼材料主要分布于结构模态振型位移的最大处和支撑端,通过加强结构的刚度,抑制了结构变形,减小了振动响应。微结构构型基本类似,其基本形态都是低刚度、高阻尼材料呈条状分布,条状分布的阻尼复合材料微结构在受弯方向上的刚度较大,可以有效抵制结构的弯曲变形。     

土-结构相互作用对结构主动控制的影响研究

利用弹性半空间假定,推导了结构考虑土与结构相互作用(SSI)体系的主动控制方程.分析了土与结构相互作用对结构主动控制的影响.并分析研究了土及结构各种主要参数对结构控制效果的影响.研究结果表明,土与结构相互作用对结构主动控制效果有一定影响;地基土的性质、结构刚度、基础埋深等在一定范围内对结构的主动控制有着显著的影响.     

多加筋圆柱壳体振动特性的导纳法研究

弹性多加筋圆柱壳体由于其结构的特点，广泛应用于工程实际，因此对其进行振动研究具有重要的工程价值和应用意义。文章利用薄板和梁的导纳公式推导了多加筋圆柱壳体在任意位置简谐力激励下的弯曲振动响应，并对特定参数的多加筋圆柱壳体的振动能量分布进行了数值仿真，结果表明振动能量在加筋处呈现急剧衰减。还对不加筋圆柱壳以及加不同数目筋的圆柱壳的振动响应进行了对比，得到了加筋和加不同叛目的筋对结构振动能量分布和传播的影响。     

Invariant error metrics for image reconstruction

Expressions are derived for the normalized root-mean-square error of an image relative to a reference image. Different versions of the error metric are invariant to different combinations of effects, including the image's (a) being multiplied by a real or complex-valued constant, (b) having a constant added to its phase, (c) being translated, or (d) being complex conjugated and rotated 180 degrees . Invariance to these effects is particularly important for the phase-retrieval problem. One can also estimate the parameters of those effects. Similarly, two wave fronts can be compared, allowing for arbitrary constant (piston) and linear (tilt) phase terms. One can also include a weighting function. The relation between the error metric and other quality measures is derived.     

含焊接残余应力薄圆板结构自由振动近似解

研究焊接残余应力对薄圆板结构振动特性的影响,解决薄圆板结构振动中存在非均匀分布预应力问题。根据含预应力结构的应变-应力方程,建立含预应力薄圆板结构的运动控制方程。基于Rayleigh-Ritz法构造Lagrange能量泛函方程。将预应力和位移试函数展开成三角级数形式,对含预应力薄圆板结构的自由振动问题进行求解。以周边简支边界薄圆板结构为例,对比焊接残余应力的不同分布形式对薄圆板结构固有频率及振型的影响。数值计算结果验证了所提方法的有效性,可应用于解决任意分布预应力问题。     

热-力-粘弹耦合多孔FGVM梁的动力学特性

研究了初始轴向机械力作用下三参数Winkler-Pasternak粘弹性地基上多孔功能梯度粘弹性材料(FGVM)梁在热环境中的自由振动特性。考虑满足热传导方程的稳态温度分布以及材料性质的温度相关性,采用Kelvin-Voigt模型并由含孔隙率修正的混合幂率梯度分布来表征内含均匀孔隙FGVM梁的材料属性。基于n阶广义梁理论,在Hamilton体系下建立该系统动力学模型的控制方程;应用扩展型广义Navier法得到固支-固支、固支-简支、简支-简支这3种边界FGVM梁耦合振动输出响应的精确解;通过算例主要探究了梁理论、边界条件、热-力耦合效应、粘弹性地基系数、结构内阻尼系数、孔隙率、材料梯度指标、跨厚比以及振型阶次等诸多参数对FGVM梁动力学特性的影响。     

管道结构振动有限元法分析及减振研究

 对管道振动机理进行了分析，运用弹性力学理论，建立了管道系统结构振动数学模型，并采用有限元方法，通过计算机仿真，分析了管道系统的结构振动，得出了管道系统结构振动固有频率和振型分布，掌握了结构参数对结构振动的影响规律，并进行了实验验证．     

On the size-dependent behavior of functionally graded micro-beams

In this paper, the size-dependent static and vibration behavior of micro-beams made of functionally graded materials (FGMs) are analytically investigated on the basis of the modified couple stress theory in the elastic range. Functionally graded beams can be considered as inhomogeneous composite structures, with continuously compositional variation from usually a ceramic at the bottom to a metal at the top. The governing equations of motion and boundary conditions are derived on the basis of Hamilton principle. Closed-form solutions for the normalized static deflection and natural frequencies are obtained as a function of the ratio of the beam characteristic size to the internal material length scale parameter and FGM distribution functions of properties. The results show that the static deflection and natural frequencies developed by the modified couple stress theory have a significant difference with those obtained by the classical beam theory when the ratio of the beam characteristic size to the internal material length scale parameter is small.     

汽轮发电机定子端区汇水管的磁弹性耦合振动方程与固有特性

依据Love曲梁理论,推得了大型汽轮发电机运行时,定子端区圆形汇水管非线性磁弹性耦合振动的一般方程。根据麦克斯威尔方程,并采用分离变量法对向量磁位满足的泊松方程进行求解,给出了圆形汇水管所处的磁场强度分布情况,在此基础上推得了汇水管所受电磁力的解析表达式。通过对汇水管固有振动特性的分析计算,并与有限元计算结果和实验值的比较,证实了本文求解过程的正确性。同时,本文的研究方法和计算结果,也为工程实际中对大型汽轮发电机定子端区汇水管的设计与振动分析提供了理论依据,具有一定的实际指导价值。     

振动压路机作业引起地基振动的解析法研究

利用Shah函数和Heaviside阶跃函数描述振动压路机在时间和空间上的间隔冲击作用,并将荷载函数代入弹性半空间的动力控制方程进行联立求解.利用三重Fourier变换推导出频率-波数域的解析解,然后反演到时间-空间域.通过数值算例,研究了振动压路机引起地基振动的衰减规律和频谱特征,并考察了压路机激振频率、名义振幅和行...     

湿-热-机耦合作用下多孔功能梯度梁的振动及屈曲特性

采用一种拓展的n阶广义梁理论（GBT）,研究了轴向机械载荷作用下多孔功能梯度材料（FGM）梁在湿热环境中的振动及屈曲特性。考虑了材料的物性随温度变化,湿-热沿梁厚按三种不同类型分布,采用含孔隙率的修正Voigt混合率模型描述多孔功能梯度梁的材料属性,在宏-细观力学模型框架下应用Hamilton原理统一建立了系统的自由振动及屈曲方程,采用Navier法求解FGM简支梁的静动态响应。通过算例验证并讨论了GBT阶数n的理想取值,可用于丰富梁理论。探讨了湿热效应、湿-热-机耦合、孔隙率、材料梯度指标、跨厚比对FGM梁振动及屈曲特性的影响。结果表明:湿-热加剧降低了FGM梁的频率和临界载荷,且不同类型的湿热分布对其减小程度有显著差异;随着孔隙率增大,梁结构的整体刚度虽有所弱化,但在湿热环境中频率反而增大,稳定性增强;湿-热效应对多孔FGM细长梁频率和稳定性影响十分显著,但对短粗梁的影响比较有限。      

经典边界条件黏弹性Pasternak地基上Bernoulli-Euler梁横向自振特性分析

自振特性在结构的动力分析中具有重要的意义。将回传射线矩阵法(MRRM)推广到地基梁自振特性的研究中,通过节点力平衡和位移协调方程及对偶局部坐标系下单元相位关系,建立两端简支、两端自由、两端固支、简支-自由、简支-固支及固支-自由这六种边界条件下黏弹性Pasternak地基上的Bernoulli-Euler梁的回传射线矩阵,进而得到其频率方程。根据单一局部坐标系下的边界条件,推导出模态函数解析表达式,进一步根据正交归一化条件求解模态函数表达式中的未知参数。通过具体算例验证了回传射线矩阵法求解的正确性,并对不同边界条件下的自振频率、衰减系数及模态函数进行了分析。为黏弹性地基梁的振动特性研究提供理论基础。     

基于有限元的有限板面导纳的数值计算

利用有限元方法对有限薄板结构在均布力作用下的二维面导纳进行数值计算的方法。根据有限元模型的特点,利用有效点导纳的原理,推导出均布力作用下面导纳的计算方法。并将通过有限元方法获得的计算结果与同样模型条件下根据理论公式计算获得的结果进行比较,证明有限元方法简单可行。还研究有限元计算中一些主要参数对计算结果的影响,为今后进行同类有限元计算提供参数设置的参考依据。     

运行列车对高层建筑结构的振动影响

建立了一种列车-轨道-路基解析分析模型,将钢轨视为竖直平面内支承在Winkler弹性基础上的一根连续的Euler-Bernoulli梁,考虑轮轨接触的影响,推导出单个轮对荷载对地基的作用力,通过迭加方式得到整列车对路基产生的动荷载;在此基础上,选取铁路线附近的某高层建筑,用有限元分析的方法计算了该高层建筑所受到的振动影响;研究了不同车速下不同距离建筑物中不同楼层的振动规律:振动随楼层高度增加具有不同程度增大的趋势;车速越大,建筑物的振动响应也越大;随着到轨道中心线距离的增加,建筑结构的振动逐渐减小。