Propagation of a longitudinal pulse in wire ropes under axial loads

Measurements of the velocity of propagation of longitudinal pulses in wire ropes as a function of applied tension are reported. Twelve 3/8-in.-diam cables are investigated which differ in configuration, i.e., number of wires per strand and number of strands, and in the material from which the wires and the core are fabricated. The velocity of longitudinal waves is found to increase with increasing tension, approaching the velocity in a solid steel bar as the applied load is increased toward the failure load of the wire rope. The material from which the wires are fabricated and the number of strands, rather than the number of wires in a strand or its core material, appear to significantly affect the velocity of longitudinal pulses.     

Dynamic behavior of bridge-erecting machine subjected to moving mass suspended by wire ropes

The dynamic behavior of a bridge-erecting machine, carrying a moving mass suspended by a wire rope, is investigated. The bridge-erecting machine is modelled by a simply supported uniform beam, and a massless equivalent “spring-damper” system with an effective spring constant and an effective damping coefficient is used to model the moving mass suspended by the wire rope. The suddenly applied load is represented by a unitary Dirac Delta function. With the expansion method, a simple closed-form solution for the equation of motion with the replaced spring-damper-mass system is formulated. The characters of the rope are included in the derivation of the differential equation of motion for the system. The numerical examples show that the effects of the damping coefficient and the spring constant of the rope on the deflection have significant variations with the loading frequency. The effects of the damping coefficient and the spring constant under different beam lengths are also examined. The obtained results validate the presented approach, and provide significant references in the design process of bridgeerecting machines.     

Static lateral stiffness of wire rope isolators

This paper presents an analytical model for the static lateral stiffness of Wire Rope Isolators (WRI). The wire rope isolator, which is a passive isolation device, has been widely adopted as a shock and vibration isolation for many types of equipment and lightweight structures. The major advantage of the WRI is its ability to provide isolation in all three planes and in any orientation. The WRI in the lateral roll mode, is required to possess the required lateral stiffness to support and isolate the equipment effectively. The static lateral stiffness of WRI depends mainly on the geometrical characteristics and wire rope properties. The model developed in this paper is validated experimentally using a series of monotonic loading tests. The flexural rigidity of the wire ropes, which is required in the model, was determined from the transverse bending test on several wire rope cables. It was observed that the lateral stiffness is significantly influenced by the wire rope diameter and height of the isolator. The proposed analytical model can be used for the evaluation of lateral stiffness and in the preliminary design of the WRI.     

Parametric study of a two degree-of-freedom cylinder subject to vortex-induced vibrations

This numerical work is an attempt to build accurate and continuous response surfaces of two degree-of-freedom vortex-induced vibrations (VIV) of flexibly mounted cylinders for a wide range of transverse and in-line natural frequencies. We consider both the structure and the flow to be two-dimensional. The structure has a low mass damping, with the transverse and in-line mass ratios as well as the transverse and in-line damping coefficients being equal. The goal is to capture the sensitivity of the response to the change in the natural frequencies of the structure. The system is studied for a wide range of transverse natural frequency within the synchronization region. The extent of variation of the in-line natural frequency is chosen to be larger than the one of the transverse natural frequency in order to favor multi-modal responses. No preferred frequencies are emphasized within the intervals of study. The numerical technique uses a multi-element stochastic collocation method coupled to a spectral element based deterministic solver.     

A three dimensional approach to model steel wire ropes used in high energy absorber apparatus

The modeling method and dynamical characteristics of steel wire ropes has been researched for several decades. In the past, steel wire ropes were usually modeled as a two dimensional system, which was only suitable for the planar motion. Also, no kink-wave propagation was considered when steel wire ropes were used in relatively low speed engineering application areas. By contrast, a three dimensional approach to model steel wire ropes used in high energy absorber apparatus is presented in this paper. Three dimensional contacts between steel wire ropes and other objects and kink-wave propagation in steel wire ropes are taken into consideration when applying the new approach to model steel wire ropes. Compared to the two dimensional model of steel wire ropes, the proposed model regards steel wire ropes as a multi-body system consisting of identical cylindrical elements with 6 degrees of freedom connected by space constraints. Impact forces generated by three dimensional contacts between steel wire ropes and other objects are calculated and theories of elastic wave propagation are applied to analyze the kink-wave propagation when steel wire ropes are loaded with a sudden perpendicular impact by a high speed moving object. In addition, mathematical model of steel wire ropes is established and numerical simulation of the three dimensional model of steel wire ropes is implemented. By comparing the simulation results with the experimental data available, the model of steel wire ropes proposed in this paper is demonstrated to be valid and correct. Therefore, the proposed modeling method can be treated as a new approach in the research field of modeling steel wire ropes. The dynamical characteristics of the steel wire ropes based on this new modeling approach are addressed simultaneously and plots of the dynamics of steel wire ropes cannot only be regarded as a basis for the further comparative studies, but also can provide some significant and interesting results.     

三种典型轴向运动结构的振动特性对比

轴向运动结构的横向振动一直是动力学领域的研究热点之一.目前大多数的文献只涉及对一种模型的研究,而针对几种模型的对比分析较少.本文对3种典型轴向运动结构(Euler梁、窄板和对边简支对边自由的板)的振动特性进行了对比分析.针对工程中不同的结构参数,本文为其理论研究中选择更加合理的模型提供了参考.通过复模态方法求解了3种模型的控制方程,给出了其相应的固有频率及模态函数.对于板模型,同时考虑了其自由边界的两种刚体位移以及弯扭耦合振动3种情况.通过数值算例给出了3种模型的前四阶固有频率随轴速和长宽比的变化情况,并应用微分求积法对复模态方法得到的解析解进行验证.特别采用三维图的形式分析了不同的轴速、阻尼、刚度和长宽比等参数混合时对3种模型第一阶固有频率的影响,着重研究了窄板和梁的不同的长宽比和轴速混合时对两者的第一阶固有频率的相对误差的影响.结果表明:随着轴速的增大,3种模型的固有频率逐渐减小.窄板是板的一种简化模型.在各参数值发生变化时,阻尼对第一阶固有频率的影响最小.长宽比很大,轴速很小或为零时,复杂模型可以简化为简单模型.     

定、变载弯曲疲劳钢丝绳失效机理对比研究

为对比揭示定、变载弯曲疲劳钢丝绳断裂机理及磨损演化特性,运用自制钢丝绳弯曲疲劳试验机开展钢丝绳定载、变载弯曲疲劳试验,通过人工拆股统计法和VW-9000系列高速度数码显微系统对比研究钢丝绳断丝分布、断丝数、断口和磨痕形貌等断裂机理,对比分析钢丝绳未断钢丝和断丝的磨痕尺寸演化特性.结果表明:与钢丝绳定载弯曲疲劳相比,变载弯曲疲劳钢丝绳断丝出现较晚,芯股、螺旋股外层断丝数分别较多、较少,芯股外层钢丝断口挤压变形较大,芯股各层钢丝断口裂纹扩展区占比较低,芯股和螺旋股的各层钢丝磨痕尺寸总体较小,钢丝绳更易达到报废水平.     

Nonlocal Thermo-Electro-Mechanical coupling vibrations of axially moving piezoelectric nanobeams

This work is concerned with the thermo-electro-mechanical coupling transverse vibrations of axially moving piezoelectric nanobeams which reveal potential applications in self-powered components of biomedical nano-robot. The nonlocal theory and Euler piezoelectric beam model are employed to develop the governing partial differential equations of the mathematical model for axially moving piezoelectric nanobeams. The natural frequencies of nanobeams under simply supported and fully clamped boundary constraints are numerically determined based on the eigenvalue method. Subsequently, some detailed parametric studies are presented and it is shown that the nonlocal nanoscale effect and axial motion effect contribute to reduce the bending rigidity of axially moving piezoelectric nanobeam and hence its natural frequency decreases within the framework of nonlocal elasticity. Moreover, the natural frequency decreases with increasing the positive external voltage, axial compressive force and change of temperature, while increases with increasing the axial tensile force. The critical speed and critical axial compressive force are determined and the dynamical buckling behaviors of axially moving piezoelectric nanobeams are indicated. It is concluded the nonlocal nanoscale parameter plays a remarkable role in the size-dependent natural frequency, critical speed and critical axial compressive force.     

钢丝绳模型比较研究

将现有的各种钢丝绳计算模型进行比较研究，通过将数值结果与现有的实验数据进行比较可以看出，考虑绳芯变化并结合Love曲杆理论的JW和KC模型更适用于实际的钢丝绳结构。     

随机振动试验法测定钢丝绳的弹性模量

运用振动理论,将钢丝绳和下挂配重简化成单自由度弹簧质量系统,利用随机振动锤击法测量系统的频率,用于计算钢丝绳的弹性模量;同时应用弹性体的纵向波动理论,推导系统的固有频率,对比两者固有频率的表达式其结果一致. 随机振动试验法简单、实用,可用于测量钢丝绳的弹性模量,作为钢丝绳弹性模量测试方法的一种补充.     

弹性钢丝绳理论研究进展

对弹性钢丝绳理论的研究现状进行了较为全面、系统的介绍和总结,重点概述了离散模型的发展情况,对其它模型如半离散模型,则作了简要介绍;将几种离散模型的计算结果与实验情况进行了对照研究,提出并讨论了目前钢丝绳理论的某些不足之处及今后的研究方向．     

黏弹性阻尼作用下轴向运动Timoshenko梁振动特性的研究

黏弹性阻尼一直是轴向运动系统的研究热点之一.以往研究轴向运动系统大都没有考虑黏弹性阻尼的影响.但在工程实际中, 存在黏弹性阻尼的轴向运动体系更为普遍.本文研究了黏弹性阻尼作用下轴向运动Timoshenko梁的振动特性.首先, 采用广义Hamilton原理给出了轴向运动黏弹性Timoshenko梁的动力学方程组和相应的简支边界条件.其次, 应用直接多尺度法得到了轴速和相关参数的对应关系, 给出了前两阶固有频率和衰减系数在黏弹性作用下的近似解析解.最后, 采用微分求积法分析了在有无黏弹性作用下前两阶固有频率和衰减系数随轴速的变化; 给出了前两阶固有频率和衰减系数在黏弹性作用下的近似数值解, 验证了近似解析解的有效性.结果表明: 随着轴速的增大, 梁的固有频率逐渐减小.梁的固有频率和衰减系数随着黏弹性系数的增大而逐渐减小, 其中衰减系数与黏弹性系数成正比关系, 黏弹性系数对第一阶衰减系数和固有频率的影响很小, 对第二阶衰减系数和固有频率的影响较大.      

Coupled global dynamics of an axially moving viscoelastic beam

The nonlinear global forced dynamics of an axially moving viscoelastic beam, while both longitudinal and transverse displacements are taken into account, is examined employing a numerical technique. The equations of motion are derived using Newton′s second law of motion, resulting in two partial differential equations for the longitudinal and transverse motions. A two-parameter rheological Kelvin–Voigt energy dissipation mechanism is employed for the viscoelastic structural model, in which the material, not partial, time derivative is used in the viscoelastic constitutive relations; this gives additional terms due to the simultaneous presence of the material damping and the axial speed. The equations of motion for both longitudinal and transverse motions are then discretized via Galerkin’s method, in which the eigenfunctions for the transverse motion of a hinged-hinged linear stationary beam are chosen as the basis functions. The subsequent set of nonlinear ordinary equations is solved numerically by means of the direct time integration via modified Rosenbrock method, resulting in the bifurcation diagrams of Poincaré maps. The results are also presented in the form of time histories, phase-plane portraits, and fast Fourier transform (FFTs) for specific sets of parameters.     

横向载荷作用下轴向运动梁的屈曲失稳以及非线性振动特性

梁的轴向运动会诱发其产生横向振动并可能导致屈曲失稳,对结构的安全性和可靠性产生重大的影响。本文重点研究了横向载荷作用下轴向运动梁的屈曲失稳及横向非线性振动特性。基于Hamilton变分原理,建立了横向载荷作用下轴向运动梁的动力学方程,获得了梁的后屈曲构型。使用截断Galerkin法,将控制方程改写成Duffing方程的形式。用同伦分析方法确定载荷作用下轴向运动梁的非线性受迫振动的封闭形式的表达式。结果表明,后屈曲构型对轴向速度和初始轴向应力有明显的依赖性。通过同伦分析法得出非线性基频的显式表达式,获得了初始轴向力会影响非线性频率随初始振幅和轴向速度的线性关系。另外,轴向外激励的方向也会改变系统固有频率。     

轴向变速运动正交各向异性板的动态稳定性

研究面内载荷作用下轴向变速运动正交各向异性薄板的横向振动及其稳定性。利用Galerkin法与平均法,在激励频率为2倍固有频率或为两阶固有频率之和附近时得到自治的常微分方程组;在参数激励频率和激励振幅平面上,分析由共振引发的失稳区域。数值算例验证了面内载荷、轴向速度、加速度参数对失稳区域的影响。     

Natural frequencies of nonlinear vibration of axially moving beams

Axially moving beam-typed structures are of technical importance and present in a wide class of engineering problem. In the present paper, natural frequencies of nonlinear planar vibration of axially moving beams are numerically investigated via the fast Fourier transform (FFT). The FFT is a computational tool for efficiently calculating the discrete Fourier transform of a series of data samples by means of digital computers. The governing equations of coupled planar of an axially moving beam are reduced to two nonlinear models of transverse vibration. Numerical schemes are respectively presented for the governing equations via the finite difference method under the simple support boundary condition. In this paper, time series of the discrete Fourier transform is defined as numerically solutions of three nonlinear governing equations, respectively. The standard FFT scheme is used to investigate the natural frequencies of nonlinear free transverse vibration of axially moving beams. The numerical results are compared with the first two natural frequencies of linear free transverse vibration of an axially moving beam. And results indicate that the effect of the nonlinear coefficient on the first natural frequencies of nonlinear free transverse vibration of axially moving beams. The numerical results also illustrate the three models predict qualitatively the same tendencies of the natural frequencies with the changing parameters.     

轴向运动弦线横向振动的频域分析

轴向运动弦线是多种工程系统的模型。为明确轴向运动横向振动的频域特性，及探索频域方法的应用特点．本文用频域方法分析轴向运动弦线的横向振动。基于轴向运动弦线横向振动方程和边界条件．通过Laplace变换导出频率域中的控制方程，并将该控制方程和边界条件用状态变量表示。由状态空间中的控制方程导出特征方程，从而求出固有频率。由轴向运动弦线的矩阵函数计算得到系统的传递函数，然后用留数定理计算传递函数的Laplace逆变换．这样就可以得到时域响应。最后分析了轴向运动弦线的横向共振，若简谐外激励的频率与系统固有频率相同，系统响应将随时间无限增加。     

Nonlinear vibration suppression of composite laminated beam embedded with NiTiNOL-steel wire ropes

Nonlinear Dynamics - NiTiNOL-steel wire rope (NiTi-ST) is a new vibration absorber with nonlinear stiffness and hysteretic damping. Although there are many studies on NiTi-ST nonlinear...     

Dynamic design of a nonlinear energy sink with NiTiNOL-steel wire ropes based on nonlinear output frequency response functions

A novel vibration isolation device called the nonlinear energy sink(NES)with Ni Ti NOL-steel wire ropes(Ni Ti-ST) is applied to a whole-spacecraft system. The Ni Ti-ST is used to describe the damping of the NES, which is coupled with the modified Bouc-Wen model of hysteresis. The NES with Ni Ti-ST vibration reduction principle uses the irreversibility of targeted energy transfer(TET) to concentrate the energy locally on the nonlinear oscillator, and then dissipates it through damping in the NES with Ni Ti-ST.The generalized vibration transmissibility, obtained by the root mean square treatment of the harmonic response of the nonlinear output frequency response functions(NOFRFs),is first used as the evaluation index to analyze the whole-spacecraft system in the future.An optimization analysis of the impact of system responses is performed using different parameters of NES with Ni Ti-ST based on the transmissibility of NOFRFs. Finally, the effects of vibration suppression by varying the parameters of Ni Ti-ST are analyzed from the perspective of energy absorption. The results indicate that NES with Ni Ti-ST can reduce excessive vibration of the whole-spacecraft system, without changing its natural frequency. Moreover, the NES with Ni Ti-ST can be directly used in practical engineering applications.     

Effects of rotary inertia on sub- and super-critical free vibration of an axially moving beam

The most important issue in the vibration study of an engineering system is dynamics modeling. Axially moving continua is often discussed without the inertia produced by the rotation of the continua section. The main goal of this paper is to discover the effects of rotary inertia on the free vibration characteristics of an axially moving beam in the sub-critical and super-critical regime. Specifically, an integro-partial-differential nonlinear equation is modeled for the transverse vibration of the moving beam based on the generalized Hamilton principle. Then the effects of rotary inertia on the natural frequencies, the critical speed, post-buckling vibration frequencies are presented. Two kinds of boundary conditions are also compared. In super-critical speed range, the straight configuration of the axially moving beam loses its stability. The buckling configurations are derived from the corresponding nonlinear static equilibrium equation. Then the natural frequencies of the post-buckling vibration of the super-critical moving beam are calculated by using local linearization theory. By comparing the critical speed and the vibration frequencies in the sub-critical and super-critical regime, the effects of the inertia moment due to beam section rotation are investigated. Several interesting phenomena are disclosed. For examples, without rotary inertia, the study overestimates the stability of the axially moving beam. Moreover, the relative differences between the super-critical fundamental frequencies of the two theories may increase with an increasing beam length.