On the hysteresis of wire cables in Stockbridge dampers

Stockbridge dampers are used e.g. for reducing wind-excited oscillations due to vortex shedding in conductors of overhead lines. In these dampers, mechanical energy is dissipated in wire cables (“damper cables”). The damping mechanism is due to statical hysteresis resulting from Coulomb (dry) friction between the individual wires of the cable undergoing bending deformation. Systems with statical hysteresis can be modelled by means of Jenkin elements arranged in parallel, consisting of linear springs and Coulomb friction elements. The damper cable is a continuous system and damping takes place throughout the whole length of the cable, so that distributed Jenkin elements are used. The local mechanical properties of the wire cable are identified experimentally in the time domain. In particular, the moment–curvature relation is determined experimentally at every location of the wire cable subjected to dynamic flexural deformations. Using such a model for the damper cables, the equations of motion can be formulated for a Stockbridge damper, and discretization of the damper cable leads to a system of non-linear ordinary differential equations. In order to test this dynamical model of a Stockbridge damper we compute impedance curves and compare them to experimental results.     

损伤因素对单层平面索网静力性能影响研究：有限元分析与试验验证

运用通用有限元软件ANSYS建立三维有限元模型,对横索与竖索连接节点失效、索预应力损失和锚固端失效这三种损伤因素的不同损伤工况下,单层平面索网结构的受力性能进行了非线性有限元分析,并与相应的试验结果进行了全面对比分析。结果表明：本文的有限元模型能够准确地分析计算上述三种损伤因素对单层平面索网结构受力性能的影响,包括结构...     

薄膜结构的几何非线性分析

使用动力松弛法对薄膜结构进行静载分析，并提出一种方法处理皱折单元以确保荷载分析的可靠性。薄膜结构如果在某膜单元的单向应力方向发生皱折，其单元本身仍然能够继续承受荷载，因此提出索松弛单元和膜皱折单元处理薄膜的索松弛和膜皱折问题。就索网结构和薄膜结构分类给出算例进行静载分析，算例表明本文的方法可以有效处理索松弛单元和膜皱折单元，确保荷载分析的准确性。     

Elastic cables–rigid body coupled dynamics: asymptotic modeling and analysis

An elastic cables–rigid body coupled model is proposed for investigating dynamic interactions between cables’ nonlinear transversal vibrations and boundary tower’s torsional dynamics, arising in large transmission line–tower systems and suspended cable–bridge tower systems. By introducing a weak torsion assumption and a large moment of inertia for the tower, an asymptotic expansion of cables–tower coupled dynamics is conducted in a weakly nonlinear framework, and a cables–tower reduced coupled model is eventually established. After model’s validations using direct numerical simulations, two distinct kinds of coupled dynamics are fully investigated. The first is that an external torque is applied to the tower and the two cables would both be indirectly excited, asymmetrically, by the torsional/oscillating tower. The two cables’ responses are the same in this case. The second is that only one of the two cables, i.e., the leader cable, is directly excited, and the other cable, i.e., the follower one, is only indirectly excited through cables–tower dynamic interactions. In such kind of leader–follower dynamics, the leader cable is quite different from the follower one. Nonlinear coupled frequency response diagrams for both systems are constructed using numerical continuation algorithms, mainly focused on the coupled steady solutions’ stabilities and bifurcations. Furthermore, the dynamic effects of tower’s moment of inertia, wing span and damping are thoroughly investigated.

     

冲击波荷载作用下拉线塔的非线性动力分析

拉线塔是一种含有柔索的非线性结构。在冲击波荷载作用下,拉线塔在三维空间内会产生大范围的非线性位移,用工程上常用的模型简化方法来分析大变形拉线塔的误差比较大。本文采用非线性有限元法编制的可在微机上运行的拉线塔非线性静、动力分析程序,计算了单根柔索的阶跃冲击响应与冲击波荷载作用下拉线塔的非线性几何大变形动力响应,计算结果与有关文献的计算结果以及试验结果非常吻合。     

斜拉桥索力优化的强次可行序列二次规划法

提出了一种斜拉桥索力优化的实用方法-强次可行序列二次规划法. 该方法通过建立斜拉 桥索力优化的非线性规划模型，以主梁和索塔的弯曲应变能为目标函数，斜拉索的索力为设 计变量，结构应力和索力为约束条件，计入大跨度斜拉桥各种几何非线性因素的影响，采用 强次可行序列二次规划算法进行优化求解，确定斜拉桥成桥合理状态的索力. 运用该方法对 某斜拉桥进行索力优化，结果表明该方法简单、有效.     

Large Amplitude Three-Dimensional Free Vibrations of Inclined Sagged Elastic Cables

The nonlinear characteristics in the large amplitude three-dimensionalfree vibrations of inclined sagged elastic cables are investigated. Amodel formulation which is not limited to cables having smallsag-to-span ratios and takes into account the axial deformation effectis considered. Based on a multi-degree-of-freedom cable model, a finitedifference discretization is employed within a numerical solution of thegoverning equations of three-dimensional coupled motion. Variousnumerical examples of arbitrarily inclined sagged cables with initialout-of-plane or in-plane motions are carried out for the case of aspecified end tension. The major findings consist of highlighting theextent of two-and three-dimensional nonlinear couplings, the occurrenceof nonlinear dynamic tensions, and the meaningfulness of modaltransition phenomena ensuing from the activation of various internalresonance conditions. The influence of cable inclination on thenonlinear dynamic behavior is also evaluated. Comprehensive discussionand comparison of large amplitude free vibrations of horizontal andinclined sagged cables are presented.     

Elastodynamic analysis of low tension cables using a new curved beam element

In this paper, we address and overcome the difficulties associated with the use of the classic cable theory to treat low tension cables by developing a new three-noded locking-free nonlinear curved beam element. Based upon nonlinear generalized curved beam theory, large deformations and rotations in the new element are formulated in terms of Updated Lagrangian framework. Consistently coupled polynomial displacement fields are used to satisfy the membrane locking-free condition and the requirement of being able to recover the inextensible bending modes. Quintic transverse displacement interpolation functions are used to represent the bending deformation of the beam, while the axial and torsional displacement fields are derived by integration of the presumably linear membrane and torsional shear strain fields, which are coupled with the transverse displacement fields. Numerical results are presented to demonstrate the superior accuracy and the high convergence rate of the newly developed curved beam element. The stability and accuracy of the new element are further validated by experiments of an instrumented free-swinging steel cable experiencing slack and low tension. Good agreements in cable position and tension are observed between the experimental results and the finite element predictions.     

Experimental and Analytical Investigation of Carbon Fiber Cable Vibration Damping

For structures deployed in space using cables where vibration damping is critical for structural stability, cable damping is significant to structural performance. To provide a better understanding of damping mechanism of carbon fiber cables, this paper describes the tests of cable damping under different experimental configurations (different cable length, tension and type), and presents an analytical method for modeling and therefore predicting cable damping. The method is developed using simplified but physically realistic assumptions on material constitutive properties and geometric compatibility conditions, and considered the contact forces and friction between helical wires. The results of the proposed method and several related issues are discussed and compared with those from experiments. These results show that the proposed method is useful and applicable for predicting cable damping value and its variation with cable tension, length and type of the cables.     

Cross validation of analytical and finite element models for Hydrodynamic Ram loads prediction in thin walled liquid filled containers

To reduce the vulnerability of both civilian and military aircraft, it is important to take the Hydrodynamic Ram pressure into account when designing their fuel tanks. Hydrodynamic Ram is especially dangerous for thin walled lightweight structures that cannot be armoured due to weight penalty reasons. Similarities in bubble behaviour between Hydrodynamic Ram and underwater explosion situations were observed in recent high-speed tank penetration/water entry experiments. A confined version of the Rayleigh–Plesset equation – which is classically used for incompressible bubble dynamics analysis (including underwater explosion) – was developed to simulate a bubble created by a Hydrodynamic Ram event induced by projectile penetration at ballistic speed in a confined geometry filled with a liquid. In the present work, the authors validate the proposed confined Rayleigh–Plesset equation for application on a spherical container thanks to quasi-incompressible ALE finite element simulation results. Then to determine the effect of liquid compressibility on confined bubble dynamics, the authors compare predictions of bubble radii obtained with the confined Rayleigh–Plesset equation with the prediction obtained using compressible finite element simulations. Eventually, the authors discuss differences in the bubble dynamics and hydrodynamic loads predictions obtained with the two approaches.     

斜拉桥合理成桥状态确定的一阶分析法

本文建立了斜拉桥索力优化的非线性规划模型，其中以斜拉桥主梁和索塔的弯曲应变能为目标函数，以各斜拉索的索力为设计变量，结构的应力及索力为约束条件，采用一阶分析法进行求解，用以确定成桥合理状态的索力。在计算中，考虑大跨度斜拉桥各种几何非线性因素的影响，并列出了优化模型的具体表达式及优化过程中的关键求解策略。应用该法和空间非线性有限元分析程序分析了某千米级斜拉桥方案的合理成桥状态，计算结果表明：该方法简单、有效。     

DYNAMIC CHARACTERISTICS OF VIBRATION ISOLATION SYSTEM WITH CUBIC STIFFNESS AND HYSTERESIS 1)

包含立方刚度和Bouc-Wen 型滞回的隔振系统具有复杂的非线性动力学特性。系统无阻尼响应模型可基于无滞回恢复力建立,利用谐波平衡法和泰勒展开求得近似解析解。系统有阻尼响应模型可利用解析/数值联合方法求解,该方法基于谐波平衡法和Levenberg-Marquardt 迭代算法,对于滞回产生的多值非光滑函数项,先计算时域响应再通过快速傅里叶变换求解谐波项系数。上述方法在含水平绞制梁的非线性隔振系统分析中得到有效应用。分析表明,在Bouc-Wen 型滞回和立方刚度的综合影响下,隔振系统呈现渐软–渐硬特性,滞回阻尼和线性阻尼都可以有效抑制共振,但前者高频隔振效果优于后者。     

Prediction of unwinding behaviors and problems of cables from inner-winding spool dispensers

Wire-guided control technologies are widely used to increase the targeting accuracy of advanced military weapons through the use of unwinding dispensers to guarantee that unwinding occurs without any problems, such as tangling or cutting. In this study, the transient behaviors of cables unwinding from inner-winding cylindrical spool dispensers are investigated. The cable is withdrawn from the spool dispenser at a constant velocity through a fixed point located along the axis of the spool dispenser. And when the cable is flown out of the dispenser, because several dynamic forces such as inertial forces, Coriolis forces, centrifugal forces, tensile forces, and fluid-resistance forces act on the cables, the cables exhibit highly nonlinear and complex unwinding behaviors which are called as unwinding balloons. For predicting these complex unwinding motions, the governing equations of motion for cables unwinding from a cylindrical spool dispenser of the inner-winding type are derived using the extended Hamilton’s principles for an open system in which mass can be transported at each boundary. Modified finite difference methods are used to discretize the spatial variables of the derived nonlinear partial differential equations. The time responses of the unwinding cables are calculated using Newmark time integration methods. Finally, in order to present numerical examples, an inner-winding spool dispenser that can be unwound up to a length of 50 km is designed by using simple geometrical relationships. The behaviors during unwinding from the designed inner spool dispenser are presented and modifications of the spool dispenser for avoiding unwinding problems are proposed by using the suggested numerical methods.     

In-plane non-linear dynamics of the stay cables

Stay cables used in cable-stayed bridge and cable-stayed arch bridge are prone to vibration due to their inherent susceptibility to external deflection. The present work is devoted to the mitigation of a stay cable from the point of view of its nonlinear dynamics. The Galerkin integral, multiple scales perturbation method, and numerical techniques are applied to analyze the primary and subharmonic resonances of the stay cable. The nonlinear dynamic response of the stay cable subjected to parametrical and forced excitations is investigated numerically. The effects of some key parameters of the stay cable, such as initial tension force, damping and inclination angle, and the excitation frequency and amplitude are discussed. The carbon fiber reinforced polymers (CFRP) cable is also studied to understand the effect of the material properties of cable. The results show that these parameters have a considerable effect on the dynamic behavior of the cable. In particular, unreasonable tension force and inclination angle of stay cable may cause excessive vibration. It is suggested that CFRP cable replaces steel cable, which can mitigate the vibration of a stay cable.     

Nonlinear transient response of stay cable with viscoelasticity damper in cable-stayed bridge

Taking the bending stiffness, static sag, and geometric non-linearity into consideration, the space nonlinear vibration partial differential equations were derived. The partical differential equations were discretized in space by finite center difference approximation, then the nonlinear ordinal differential equations were obtained. A hybrid method involving the combination of the Newmark method and the pseudo-force strategy was proposed to analyze the nonlinear transient response of the inclined cable-dampers system subjected to arbitrary dynamic loading. As an example, two typical stay cables were calculated by the present method. The results reveal both the validity and the deficiency of the viscoelasticity damper for vibration control of stay cables. The efficiency and accuracy of the proposed method is also verified by comparing the results with those obtained by using Runge-Kutta direct integration technique. A new time history analysis method is provided for the research on the stay cable vibration control.     

DYNAMICS OF MOORING CABLES IN RANDOM SEAS

The dynamic analysis of a catenary mooring cable due to random motion of an offshore platform is performed in the frequency domain. The nonlinear fluid-drag force is linearized using the statistical linearization technique. A previously developed numerical procedure based on converting a boundary value problem to an equivalent set of initial value problems is utilized to solve the problem, which avoids the need for modal analysis. The method is found to be versatile for the determination of spatially varying drag and the analysis of composite cables in a unified manner. The influence of current on drag damping has also been investigated. The effect of seabed friction damping has also been incorporated in the linearized analysis.     

悬索的变原长计算模式

本文从非线性弹性理论出发,采用泛函内积形式,建立了悬索非线性计算模式。提出了变原长迭代计算的基本思想,就一端固定、另一端张力已知的悬索模型,从Reissner变分理论出发,导出了该模式的非线性有限元的基本方程,使计算量大大减少。     

Experimental investigation of wind-induced vibrations of main cables for suspension bridges in construction phases

The main cables of suspension bridges show a changing cross-sectional shape with the evolution of construction phases, and they may suffer from severe wind-induced vibrations at certain conditions. The primary objective of this research was to examine the aerodynamic performance of the main cable in construction phases and to develop appropriate countermeasures to eliminate the potential wind-induced vibrations. Two cross-sections with different shapes of a main cable were chosen, and a series of wind tunnel tests were performed in a reduced wind velocity range of 32–366 using elastically mounted sectional models. Galloping occurred for the two cross-sections under certain wind incidence angles when a critical velocity was reached. No obvious hysteresis phenomenon of galloping was observed in the tests. The steady amplitude of galloping increased linearly with wind velocity and the increasing rate almost kept constant for different structural damping ratios. The aerodynamic nonlinearity, rather than the structural damping nonlinearity, is the main source leading to the limited amplitude oscillation. An empirical expression of galloping amplitudes for the two cross-sections was derived based on the test data. Meanwhile, the critical wind velocity was studied in a Scruton (Sc) number range of 108–4196 (as varied by changing the initial structural damping ratio between 0.093% and 3.62%). Results showed that the Den Hartog criterion was applicable to forecast the possibility of galloping, but not able to estimate the critical wind velocity for the main cable. Linear fitting method can be used to predict the critical velocity based on the experimental data. Finally, three vibration mitigation measures were studied, and a combination of structural and aerodynamic measures was recommended for galloping mitigation of main cables.     

考虑弯曲刚度斜拉索面内面外内共振分析

本文研究桥梁工程中含弯曲刚度斜拉索的面内面外内共振问题．描述了工程中斜拉索变形的三种状态,考虑弯曲刚度、大变形及垂度等因素,忽略斜拉索纵向惯性力的影响,运用Hamilton变分原理建立了含弯曲刚度的斜拉索面内面外耦合偏微分控制方程,采用Galerkin方法对偏微分方程离散,并运用多尺度摄动方法进行了求解,获得了斜拉索可能存在的内共振模式,以工程中一根斜拉索为例,运用有限元法对其进行动力特性分析,列出了斜拉索前10阶面内面外振动频率,找出面内面外可能产生内共振的模态,分别研究了主共振条件下斜拉索面内和面外1:1、2:1内共振情形,获得了有意义的结论．     

One-to-two global-local interaction in a cable-stayed beam observed through analytical, finite element and experimental models

The mechanism of cable end angle-variation induced oscillations in the non-linear interactions between beams and cables in stayed-systems is first explained by a proposed analytical model. It is then verified by both experimental and finite element models. The non-linear interaction maximizes its effects for cable oscillations when inherent quadratic coupling between local and global modes produces energy transfer from low to high frequency vibrations by means of a one-to-two global-local autoparametric resonance. The response of the analytical model is fully described using a continuation method applied directly to the reduced two degree of freedom discrete model showing that, for a selected one-to-two global-local resonant system, primary harmonic excitation of the global mode produces large oscillations of the local mode at twice the excitation frequency. Detailed comparisons between the responses of the analytical model, experimental results and finite element simulations show excellent agreement both in the qualitative behaviour and in the calculated/measured response amplitudes.