索膜结构自振特性的仿真分析

索膜结构属于风敏感结构,其在风荷载作用下的反应,与结构的自振特性密切相关.通过索膜结构的自振特性分析发现,索膜结构的自振频率较低且呈连续密集分布,振型也比较复杂;影响其自振特性的主要结构参数是膜中预应力和结构跨度,随着膜中预应力的增加,自振频率呈较大幅度提高,而随着结构跨度的增大,自振频率却大幅度降低;另外,加劲索的张拉刚度对自振频率特别是第一自振频率影响很小;运用有限元软件ANSYS模拟分析了一个实际算例,验证了以上结论.     

用能量法分析体外预压力对简支梁动力性能的二阶效应

精细地考虑了体外筋变形中的二阶项,用能量法推导了体外预应力梁的自振频率,阐明了体外预压力对梁自振频率的效应.计算结果表明:体外预压力压缩软化效应的影响系数,主要取决于转向座的数量.无转向座时,体外筋偏心距损失为最大,影响系数为1,体外预压力的效应与外轴力的效应相同.随着转向座数量的增加,偏心距损失减小,体外筋接近于无粘结筋,影响系数降低至接近于0,即接近于无粘结筋预压力的零效应.当梁转向座的数量≥2时,由于影响系数显著地小于1,可以忽略体外预压力的压缩软化效应.随着体外筋面积和偏心距的增加,梁的第1自振频率增大.不过,体外筋对其他阶自振频率的影响很小,可以忽略.     

耦合加载方式下复合材料叶片的预应力模态分析

针对大型风力机叶片在静止和变速运转工况下,振动模态计算分析方法和转速对频率的影响进行了研究.建立了叶片有限元模型,静力分析时采用耦合加载方式;采用分块Lanczos法分析了叶片的模态,考察了叶片固有频率对预应力效应的敏感程度及稳定性,探讨了转速对叶片频率的影响程度,分析了预应力效应产生的原因.结果表明:叶片主要以挥舞和摆阵振动形式为主;预应力效应对叶片的固有频率产生了较大影响,随转速的不断增大叶片的固有频率也随之增大,且预应力效应对叶片挥舞刚度的影响程度大于摆阵刚度的影响.     

悬浮隧道基于弹性边界的力学模型与移动荷载响应分析

悬浮隧道是一种创新型的水中交通结构,这种悬浮于水中的结构在考虑复杂边界条件下的力学建模及交通荷载引起的结构响应值得深入研究.本文将跨度范围内由多段锚索支撑的悬浮隧道视为弹性支撑梁,同时将两端的复杂边界条件考虑为具有不同约束刚度的竖向和转动弹性支撑,流体荷载由Morison方程考虑,建立了悬浮隧道在任意荷载作用下的动力学模型及考虑自振特性的特征方程.研究了跨内支撑刚度与边界约束参数多种组合条件下的频率、模态分布特征,得到了相应的敏感区间.同时,以某型号高铁列车为背景并将其考虑为一列移动集中力,研究了悬浮隧道结构关键位置的荷载响应与弹性支撑刚度之间的关系,结果表明跨内支撑刚度、边界约束刚度均对竖向位移存在显著影响,整体上约束刚度越大,相应的位移越小.     

T样条调配函数线性无关性的判定算法

针对T样条调配函数的公开问题——T样条曲面表达式中的调配函数是否具有线性无关性,提出一种T样条调配函数线性无关性的验证算法.首先分析了T样条调配函数的数学性质,给出T样条调配函数线性无关的充要条件和充分条件,通过充分条件可以较容易地对一些特殊的T样条调配函数的线性无关性进行判定;然后结合充要条件和充分条件给出一种T样条调配函数线性无关性的验证算法.最后通过实例验证了该算法的有效性.文中结果对于开展T样条造型算法方面的研究有重要意义.     

函数拟合法力数字传感器的非线性和温度补偿

针对力数字传感器存在的分散性、非线性和温度特性问题,通过软件进行补偿.分析了力数字传感器的非线性特性,采用三次样条插值获得被测重力和输出频率的函数关系,将测量得到的输出频率通过三次样条插值计算得到被测重力.对于力数字传感器的温度特性,建立了分段三次插值函数,利用反函数得到不同温度下输出频率与被测重力的函数关系.将温度和频率量作为自变量,通过分段三次插值函数计算得到被测重力.函数拟合法实现力数字传感器的非线性和温度补偿使所需数据量减少.实测表明:该方法的测量精度高,非线性和温度补偿后的最大引用误差为0. 5%,满足实际工程的需要.     

连续等距区间上积分值的二次样条插值

目的 在现实中,某些插值问题结点处的函数值往往是未知的,而仅仅已知一些区间上的积分值。为此提出一种给定已知函数在连续等距区间上的积分值构造二次样条插值函数的方法。方法 首先,利用二次B样条基函数的线性组合去满足给定的积分值和两个端点插值条件,该插值问题等价于求解n+2个方程带宽为3的线性方程组。然后,运用算子理论给出二次样条插值函数的误差估计,继而得到二次样条函数逼近结点处的函数值时具有超收敛性。最后,通过等距区间上积分值的线性组合逼近两个端点的函数值方法实现了不带任何边界条件的积分型二次样条插值问题。结果 选取低频率函数,对积分型二次样条插值方法和改进方法分别进行数值测试,发现这两种方法逼近效果都是良好的。同样,选取高频率函数对积分型二次样条插值方法进行数值实验,得到数值收敛阶与理论值相一致。结论 实验结果表明,本文算法相比已有的方法更简单有效,对改进前后的二次样条插值函数在逼近结点处的函数值时的超收敛性得到了验证。该方法对连续等距区间上积分值的函数重构具有普适性。     

中心B样条二进小波多尺度边缘提取

分析了截尾的Canny算子在多尺度边缘提取时对运算速度造成的影响,提出了中心B样条二进小波多尺度边缘提取,详尽地研究了Canny算子与中心B样条函数的若干性质,中心B样条函数具有紧支集,以极快的速度逼近高斯函数,四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器.四阶中心B样条函数是二阶平滑问题的唯一最优解,并且它的时频测不准关系值非常接近时频测不准关系下界.从对计算结果的讨论中也得出中心B样条二进小波优于Canny算子的结论.     

基于遗传算法的三次样条函数拟合

介绍了遗传算法（ＧＡ）的一种新应用－三次样条函数拟合中的参数估计问题。三次样条函数拟合是曲线拟合的一个认的较好方法,它具有很好的分段光滑性,但三次样条函数拟合涉及到矩阵求逆,离散样本点越多,矩阵就越大,求逆就越繁琐。文中将用ＧＡ用于三次样条函数拟合的系数求解,避开了矩阵求逆的繁琐问题,结合具体例子作了一些探索。文中还对标准遗传算法进行了适当的改进,实验结果说明遗传算法是用于参数估计、优化的有力工具     

小波方法光顺的B样条模糊系统及其应用

为了减少不准确数据对模糊系统的影响, 本文利用准均匀B样条小波方法光顺了B样条模糊系统. 首先将B样条模糊系统的多分辨率表示转化为准均匀B样条函数的多分辨率表示, 接着利用准均匀B样条小波分解方法对相应的准均匀B样条函数进行分解就得到了一系列光顺性逐渐增强、规则个数逐渐减少的模糊系统, 即基于小波方法的光顺B样条模糊系统. 最后, 仿真结果表明, 小波方法光顺的B样条模糊系统构造的模糊控制器在改善原来B样条模糊系统构造的模糊控制器性能的同时, 大大提高了原来控制器的运行效率.     

多跨下承式拱桥面内全局动力学理论与自由振动研究

为弥补高维工程结构有限元分析对结构参数优化设计等的局限,本文基于欧拉伯努利梁理论与传递矩阵法,研究大跨度拱桥面内自由振动问题.首先,基于多跨拱桥的刚度分析,建立系统的全局动力学模型.其次,基于传递矩阵法建立系统的全局动力学理论,最后,以一座四跨下承式拱桥的平面力学模型,求解其面内自由振动时的固有频率与振型,并将所得结果与用同样参数建模的有限元分析结果对比,证明本文所建理论对求解该类问题的有效性与精确性.此外,通过整桥各跨矢跨比、吊杆截面面积、拱肋惯性矩等的多组参数组合分析了该系统面内自振频率的分布规律.结果表明：随着拱桥矢高增大,系统固有频率减小,因拱桥质量的快速增加,对整桥面内刚度影响显著;增大吊杆截面面积可在一定程度内增大拱桥的面内刚度,导致系统频率在一定范围内增大,且观察到Veering现象.     

An analytical solution for in-plane free vibration and stability of loaded elliptic arches

In-plane free vibration and stability analyses of elliptic arches subjected to a uniformly distributed vertical static loading are performed here. A variational principle is applied to derive the governing equations for free vibration and stability of preloaded arches, considering the effect of the extensibility of the arch centerline but neglecting the effect of shear deformation. Particular attention is given to present a general procedure for combining series solutions with stiffness matrixes to construct an analytical solution for free vibration and stability of loaded arches with varying curvature. The correctness of the proposed solution is verified through a convergence study on the vibration frequencies of a loaded circular arch and by comparing the results with published data. The solution is further applied to investigate the behaviors of clamped or fixed-free elliptic arches.     

In-plane vibration of plates by continuous mass matrix method

The continuous mass matrix method derived for frameworks is extended to the analysis of in-plane vibration of plates. A continuous mass distribution which is the same as the actual mass distribution of the plate is considered over each rectangular finite element. Taking into account that the rigid body movement produces inertial forces in dynamic analysis for a rectangular plate element eight independent conditions are provided to satisfy eight independent freedoms. Each condition is obtained from an independent displacement distribution satisfying the equations of motion at any point of the element and not only at the nodes of the rectangle. The dynamic element stiffness matrix thus obtained is a function of the natural circular frequency. The limit of the dynamic element stiffness matrix when the value of the natural circular frequency tends to zero is the static, stress compatible element stiffness matrix. The analysis of plates under forcing forces is performed by modal analysis after the natural circular frequencies and the corresponding modal shapes have been obtained from the free vibrations, for all the forcing forces are assumed to be function of the same time variation. Otherwise one must recur to a numerical analysis. The effect of the sizes, number of the meshes, the additional static load on the plate and the rigidity of the boundaries on the vibration of the plate is discussed. Few example problems are solved in order to illustrate the above mentioned effects. The numerical results obtained by continuous mass matrix method are compared with those of consistent mass matrix method. The convergence in terms of the sizes of meshes and the limit of convergence are examined.     

Stability and load-carrying capacity of three-dimensional long-span steel arch bridges

The behavior of several models of three-dimensional long-span steel arch bridges is investigated for evaluating the effects of various design parameters on both the strength and stability of these special structures. The major concerns in the design of a long-span steel arch bridge, from the structural safety point of view, are the yield and buckling failures. Different design parameters may affect the failure load for either type of failure in various ways. This study investigates how changes in certain design parameters would affect the behavior of steel arch bridges, which could lead to an optimum design of this type of bridge structures. The effects of the plate girder stiffness and arch bracing stiffness as well as the rise-to-span ratio and inclination of the arches towards each other are examined in this study. Both critical buckling load and the load-carrying capacity of each design alternative are investigated using the finite element method. All design alternatives are based on the latest AASHTO code for highway bridge design. It is concluded from this study that the inclined arch bridge using the maximum practical rise-to-span ratio (which is about 0.25) is the most favorable design. In addition, the increase in the stiffness of the plate girder does not reduce the bending moments in the arch ribs. However, providing a lateral bracing system with sufficient stiffness greatly reduces the out-of-plane bending moments and increases the load-carrying capacity and the critical buckling load of a long-span arch bridge.     

Optimal topology design of internal stiffeners for machine pedestal structures using biological branching phenomena

Naturally evolved biological structures exhibit the optimal characteristics of light weight, high stiffness, and high strength. Based on the growth mechanism of biological branch systems in nature, an optimization method for internal stiffener plate distribution in box structures is suggested. Under the given load and support conditions, the internal stiffener plates of machine pedestal structures grow, bifurcate, and degenerate towards the direction of maximum overall structural stiffness in accordance with the adaptive growth law. The optimal and distinct distribution of internal stiffener plates with the most effective load path is thus obtained. Based on this, a size optimization for lightweight design is conducted, in which the self-weight of the structures is taken as the design objective, and the natural vibration frequency and static stiffness in the direction that is sensitive to machining accuracy are set as constraints. Finally, an optimized structure is obtained. The effectiveness of the proposed method is verified by using a precision grinder bed as an example. The results of numerical simulation and 3D–printed model experiment indicate that both the dynamic and the static performance of the optimized structure are improved, while the structural weight is reduced by compared with the initial structure. The suggested design method provides a new solution approach for the design optimization of machine pedestal structures.     

隔振对象重量变化对准零刚度隔振器隔振性能的影响

本文主要研究隔振对象重量变化对一类准零刚度隔振器隔振性能的影响,并给出了新的研究结果.文中使用欧拉屈曲梁构建负刚度调节结构并设计了隔振系统的平衡位置可调机构.假设系统有轻微的过载和超载,推导了系统的动力学方程并进行求解,定义了非线性隔振系统的力传递率及位移传递率来评价系统的隔振性能.对线性隔振系统,超载会让隔振频率略微降低,共振放大峰略微增大.对于准零刚度隔振系统,力传递率和线性系统类似,但是对于位移传递率,过载会导致系统固有频率和共振放大峰均升高,反而不利于隔振.研究结果可以对此类隔振系统的使用场合以及对过载和轻载的选择有工程指导意义.     

带质量块微型双稳态压电板的动力学分析

本文对带质量块的微型双稳态压电板进行动力学分析.以中心固支四边自由的带质量块微型压电层合板为研究对象,应用应变梯度理论考虑尺寸效应,综合考虑力、电、热耦合作用,采用Von Karman大变形理论,运用Hamilton原理建立非线性动力学方程.利用特征值法探究不同内禀长度和不同压电铺设面积的情况下,温度和电压对其固有频率和稳定性的影响.其次研究了不同外激励下系统的非线性动力学响应.通过本文的研究发现,随着压电铺设面积的增大,力、电、热耦合效应增强,对系统的稳定性影响越显著;通过研究温度和电压对系统振动幅值的影响为振动控制提供了理论依据.同时发现尺寸效应对结构刚度影响较大,验证了微型结构考虑尺度效应的必要性.本文的研究结果会为今后的工程实际应用提供一定的理论参考价值.     

A dynamic stiffness element for free vibration analysis of composite beams and its application to aircraft wings

The dynamic stiffness matrix of a composite beam that exhibits both geometric and material coupling between bending and torsional motions is developed and subsequently used to investigate its free vibration characteristics. The formulation is based on Hamilton’s principle leading to the governing differential equations of motion in free vibration, which are solved in closed analytical form for harmonic oscillation. By applying the boundary conditions the frequency dependent dynamic stiffness matrix that relates the amplitudes of loads to those of responses is then derived. Finally the Wittrick-Williams algorithm is applied to the resulting dynamic stiffness matrix to compute the natural frequencies and mode shapes of an illustrative example. The results are discussed and some conclusions are drawn. The theory can be applied for modal analysis of high aspect ratio composite wings and can be further extended to aeroelastic studies.     

Free and forced vibration analysis of viscoelastic damped FG-CNT reinforced micro composite beams

In this paper, free and forced vibration analysis of viscoelastic microcomposite beam reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) is studied using the modified couple stress theory (MCST). The material properties of micro composite beam by generalized rule of mixtures carbon nanotubes are estimated. In addition, these properties are stated as uniform, and functionally graded (FG) distributions in the thickness direction. Energy method and Hamilton’s principle are employed to establish the governing equations of motion for the vibration of viscoelastic damped micro composite beam reinforced by SWCNTs based on the Kelvin–Voigt model. The influences of material length scale parameter, structural damping coefficient and different distributions of SWCNTs on non-dimensional complex natural frequency and amplitude vibration of the viscoelastic micro composite beam are investigated. The results reveal that the lowest vibration amplitude of FG microcomposite beam by the FG-X and the highest occurs by FG-◊. Moreover, in the presence of external periodic load and the absence of structural damping coefficient, the vibration amplitude increases and FG microcomposite beam becomes unstable, even though the amplitude of vibration decreases with increasing structural damping coefficient. It is shown that the natural frequency of SWCNT reinforced composite is more than the frequency of multi-walled carbon nanotubes because SWCNT have more stiffness. In addition, the results illustrate that the experimental data by Lei et al. agree well with those predicted by the MCST in the present work.