A procedure for the static analysis of cable structures following elastic catenary theory

The paper proposes an unitary strategy for the static analysis of general cable nets under conservative loads. A form-finding is first performed in order to initialize the successive non linear analysis. The numerical procedures carried on in both steps, form finding and structural analysis of the net, employ a three dimensional elastic catenary element. Equilibrium conditions at internal nodes and kinematic compatibility at the end nodes of each cable are used to derive the global equations of the net. When the pre-stresses are high and the topology of the net is involved, an accurate initializing solution is essential for the convergence of the successive numeric non linear structural analysis (performed by Newton method). The numerical applications highlight the capability of the proposed procedure to solve three dimensional problems with taut and slack cables, out of plane distributed forces (modeling wind loads), point loads along the cables. The contemporary presence of cables and compression truss elements is also considered testing the effectiveness of the method in the analysis of tensegrity structures.     

Analysis for the optimal location of cable damping systems on stayed bridges

Computational models are increasingly being used for the dynamic analysis of structures with nonlinear or uncertain behavior, such as cables in stayed bridges, which nowadays are progressively more used as an alternative for long span and slim structures. In this work, a 3D nonlinear model is described to evaluate the wind dynamic effects on cables for this type of bridges under different scenarios, but also for health monitoring and structural simulation to guarantee performance, evaluate load capacity and estimate life prediction. Fatigue is one of the most relevant and complex failure causes in highway bridges, particularly on the anchorage elements of the cables in stayed bridges; where dampers may be used to minimize the dynamic behavior of the structure and reduce fatigue damage. With this nonlinear simulation model, different damper locations and configurations are evaluated to find the optimal position. A feasibility function is used as a weighting function to take into account the damper’s size and design. Analysis is particularly focused for a real cable stayed bridge in the state of Veracruz in México. Although the geometry, the forces and the stresses on cable structures are a challenge, even for structural specialists, the results from this work using the proposed 3D nonlinear model showed to be accurate for the simulation of many different wind scenarios, and damper’s location and orientations. Finally, the feasibility weighting function enabled the geometrical limitations to estimate the best location of a damper system to minimize the risk for fatigue failure.     

PI force feedback control for large flexible structure vibration with active tendons

Active tendon, consisting of a displacement actuator and a collocated force sensor, was first presented by Preumont and his co-workers to attenuate the vibration of large flexible space structures, and the control algorithm adopted by them was integral force feedback. This paper presents a new proportional-integral （PI） force feedback algorithm to achieve larger damping ratios for the structure without the requirement of structure model. Stability of the control system is shown, and simulations of a structure similar to JPL-MPI demonstrate the effectiveness of the proposed algorithm for vibration control of space structures.     

REDUCTION APPROACHES FOR VIBRATION CONTROL OF REPETITIVE STRUCTURES

The reduction approaches are presented for vibration control of symmetric, cyclic periodic and linking structures. The condensation of generalized coordinates, the locations of sensors and actuators, and the relation between system inputs and control forces are assumed to be set in a symmetric way so that the control system posses the same repetition as the structure considered. By employing proper transformations of condensed generalized coordinates and the system inputs, the vibration control of an entire system can be implemented by carrying out the control of a number of sub-structures, and thus the dimension of the control problem can be significantly reduced.     

Non-probabilistic reliability method and reliability-based optimal LQR design for vibration control of structures with uncertain-but-bounded parameters

Uncertainty is inherent and unavoidable in almost all engineering systems. It is of essential significance to deal with uncertainties by means of reliability approach and to achieve a reasonable balance between reliability against uncertainties and system performance in the control design of uncertain systems. Nevertheless, reliability methods which can be used directly for analysis and synthesis of active control of structures in the presence of uncertainties remain to be developed, especially in non-probabilistic uncertainty situations. In the present paper, the issue of vibration con- trol of uncertain structures using linear quadratic regulator （LQR） approach is studied from the viewpoint of reliabil- ity. An efficient non-probabilistic robust reliability method for LQR-based static output feedback robust control of un- certain structures is presented by treating bounded uncertain parameters as interval variables. The optimal vibration con- troller design for uncertain structures is carried out by solv- ing a robust reliability-based optimization problem with the objective to minimize the quadratic performance index. The controller obtained may possess optimum performance un- der the condition that the controlled structure is robustly re- liable with respect to admissible uncertainties. The proposed method provides an essential basis for achieving a balance between robustness and performance in controller design ot uncertain structures. The presented formulations are in the framework of linear matrix inequality and can be carried out conveniently. Two numerical examples are provided to illustrate the effectiveness and feasibility of the present method.     

单层平面索网幕墙结构的几何非线性问题研究

单层平面索网支承式玻璃幕墙结构是近年来在国内外应用较为广泛的一种新型幕墙结构形式,由于单层平面索网不具有负高斯曲面形式,结构在平面外方向的刚度偏柔,表现出较明显的几何非线性特征.本文采用连续化方法建立了单层平面索网结构考虑几何非线性影响的静力平衡方程和振动方程,得到了结构刚度的解析表达式,并采用谐波平衡法求得非线性频率的简化解析表达式,以此为基础研究了单层平面索网结构的静力非线性和动力非线性问题.研究结果表明:结构的非线性和结构的初始位置密切相关;结构的非线性频率主要取决于索的初始应变、结构振动幅值与跨度的比值,几何非线性对于结构动力性能的影响要小于对结构静力性能的影响;本文得到的结构在地震荷载和平均风荷载作用下的非线性振动方程和非线性频率为结构在地震荷载和脉动风荷载作用下动力响应的求解奠定了基础.     

Stochastic optimal control of cable vibration in plane by using axial support motion

A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is proposed.The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of cable vibration by using the Galerkin method.The partially averaged Ito equation for controlled system energy is further derived by applying the stochastic averaging method for quasi-non-integrable Hamiltonian systems.The dynamical programming equation for the controlled system energy with a performance index is established by applying the stochastic dynamical programming principle and a stochastic optimal control law is obtained through solving the dynamical programming equation.A bilinear controller by using the direct method of Lyapunov is introduced.The comparison between the two controllers shows that the proposed stochastic optimal control strategy is superior to the bilinear control strategy in terms of higher control effectiveness and efficiency.     

Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network

In this paper a new approach is presented to reduce vibrations for one- and two-dimensional mechanical structures, as beam or thin plates, by means of several piezoelectric transducers shunted with a proper electric network system. The governing equations of the whole system are coupled to each other through the direct and converse piezoelectric effect. More in detail, the mechanical equations are expressed in accordance with the modal theory considering n vibration modes and the electrical equations reduce to the one-dimensional charge equation of electrostatics for each of n considered piezoelectric transducers. In this electromechanical system, a shunting electric device forms an electric subsystem working as multi degrees of freedom (dof’s) damped vibration absorber for the mechanical subsystem. Herein, it is introduced a proper transformation of the electric coordinates in order to approximate the governing equations for the whole shunted system with n uncoupled, single mode piezoelectric shunting systems that can be readily damped by the methods reported in literature. A further numerical optimisation problem on the spatial distribution of the piezoelectric elements allows to achieve a better performance. Numerical case studies of two relevant systems, a double clamped beam and a fully clamped plate, allow to take into account issues relative to the proposed approach. Laboratory experiments carried out in real time on a beam clamped at both ends consent to validate the proposed technique.     

大型网架式可展开空间结构的非线性动力学与控制

我国航天工业迫切需要掌握可入轨后展开的大型网架式空间结构技术,以便研制口径十几米、乃至数十米的大型星载天线。该技术的主要科学基础是这类空间结构展开和服役过程的非线性动力学建模、分析和控制。本文综述了与上述科学基础相关的研究进展,提出应重点关注的三个科学问题：一是大型网架式空间结构展开过程的多柔体系统动力学,尤其是如何对微重力环境下索网的接触和缠绕、运动副内碰撞、结构展开与航天器本体间的耦合等导致的非线性动力学进行建模和分析;二是大型网架式空间结构展开锁定后服役的动力学分析,尤其是如何揭示结构柔性、众多运动副间隙、交变热载荷等因素引起的复杂非线性振动机理;三是大型网架式空间结构展开锁定后服役的动力学控制,尤其是如何在欠驱动、低能耗条件下对非线性振动和波动传播提出有效的控制方法。     

Active vibration control and suppression for integrated structures

Spacesmictures,aircraftstrUctures,satellitesandsoonarerequiredtobelightinweightduetotherequirementofoperation.TheyarealsolightlydampedbecauseofthelowinternaldampingofthematerialsusedintheirconstrUction.Thus,theywillgeneraiClargeamplitudevibration,whichmayreducetheprecisionofoperationandaffectthePerformanceofoperation.Itisessentialtousesuitablecontrolsystemtocontrolthevibrationofsimctures.Sincethesesmicturesaredistributedparametersystemshavinganinfinitesetofvibrationmodes,thecontrolsystemwith…     

Optimal placement of piezoelectric active bars in vibration control by topological optimization

A continuous variable optimization method and a topological optimization method are proposed for the vibration control of piezoelectric truss structures by means of the optimal placements of active bars. In this optimization model, a zero-one discrete variable is defined in order to solve the optimal placement of piezoelectric active bars. At the same time, the feedback gains are also optimized as continuous design variables. A two-phase procedure is proposed to solve the optimization problem. The sequential linear programming algorithm is used to solve optimization problem and the sensitivity analysis is carried out for objective and constraint functions to make linear approximations. On the basis of the Newmark time integration of structural transient dynamic responses, a new sensitivity analysis method is developed in this paper for the vibration control problem of piezoelectric truss structures with respect to various kinds of design variables. Numerical examples are given in the paper to demonstrate the effectiveness of the methods.     

Combined control of fast attitude maneuver and stabilization for large complex spacecraft

In remote sensing or laser communication space missions, spacecraft need fast maneuver and fast stabilization in order to accomplish agile imaging and attitude tracking tasks. However, fast attitude maneuvers can easily cause elastic deformations and vibrations in flexible appendages of the spacecraft. This paper focuses on this problem and deals with the combined control of fast attitude maneuver and sta- bilization for large complex spacecraft. The mathematical model of complex spacecraft with flexible appendages and momentum bias actuators on board is presented. Based on the plant model and combined with the feedback controller, modal parameters of the closed-loop system are calculated, and a multiple mode input shaper utilizing the modal information is designed to suppress vibrations. Aiming at reducing vibrations excited by attitude maneuver, a quintic polynomial form rotation path planning is proposed with constraints on the actuators and the angular velocity taken into account. Attitude maneuver simulation results of the control systems with input shaper or path planning in loop are sepa- rately analyzed, and based on the analysis, a combined control strategy is presented with both path planning and input shaper in loop. Simulation results show that the combined control strategy satisfies the complex spacecraft＇s require- ment of fast maneuver and stabilization with the actuators＇ torque limitation satisfied at the same time.     

The identification of the vibration control system parameters designed for continuous miner machines

The Continuous Miner machines are exposed to time dependent loads during normal operation of the rock cutting process. These loads cause vibrations, which have a negative influence on the whole structure of the machine. This phenomenon can be eliminated by applying passive or active vibration control systems (VCS). Generally these systems are coupled with additional elements, which provide dispersion or transfer energy. The energy thus acquired can also reinforce the intended function such as rock cutting operation in the case of mining machines. The objective of this paper is to present the method of numerical identification of VCS parameters for Continuous Miner machines. The main function of the presented system is to reduce displacement of cutting drum by using elastic element joined to machine chassis and applying appropriate algorithm of control of the angular velocity of cutting drum. The method described improves efficiency of mining and increases durability of machine. In order to determine mechanical and control parameters of VCS the genetic algorithm optimisation method conjugated with numerical modal analysis was used. Finally the transient dynamic analysis was performed for the full-scale model of Continuous Miner in order to verify VCS in normal working condition.     

Nonlinear dynamic response and active vibration control of the viscoelastic cable with small sag

IntroductionCablesareveryefficientstructuralmembersandhencehavebeenwidelyusedinmanylong_spanstructures,includingcable_supportbridges,guyedtowersandcable_supportroofs.Sincecablesarelight,veryflexibleandlightlydamped ,structuresutilizingcables,i.e .,cable_structuresystems,usuallyhavevariousdynamicproblems.Theirmodelsarethereforeverimportantinpredictingandcontrollingtheirresponses.Inthelastdecade,thenonlineardynamicvibrationandstabilitybehaviorofcablesandcable_structureshavedrawntheattentionofman…     

阻尼网络作为干扰项的指北方位惯导统一控制方程

为更加简捷高效地实现惯导计算机的程序编排,提出了一种新的指北方位惯导系统统一控制方程.通过改变系统控制方块图的结构,将无阻尼惯导系统和阻尼网络人为分离,阻尼网络的输出可视为系统的干扰项.系统控制方程始终采用无阻尼条件下的表达式,惯导系统控制方程和阻尼网络可以实现模块化设计,使控制方程的实现形式和推导过程大为简化.无阻尼...     

Sliding mode maneuvering control and active vibration damping of three-axis stabilized flexible spacecraft with actuator dynamics

This paper presents a dual-stage control system design method for the three-axis-rotational maneuver control and vibration stabilization of a spacecraft with flexible appendages embedded with piezoceramics as sensor and actuator. In this design approach, the attitude control system and vibration suppression were designed separately using a lower order model. Based on the sliding mode control (SMC) theory, a discontinuous attitude control law in the form of the input voltage of the reaction wheel is derived to control the orientation of the spacecraft actuated by the reaction wheel, in which the reaction wheel dynamics is also considered from the real applications point of view. The asymptotic stability is shown using Lyapunov analysis. Furthermore, an adaptive version of the proposed attitude control law is also designed for adapting the unknown upper bounds of the lumped disturbance so that the limitation of knowing the bound of the disturbance in advance is released. In addition, the concept of varying the width of boundary layer instead of a fixed one is also employed to eliminate the chattering and improve the pointing precision as well. For actively suppressing the induced vibration, modal velocity feedback and strain rate feedback control methods are presented and compared by using piezoelectric materials as additional sensors and actuators bonded on the surface of the flexible appendages. Numerical simulations are performed to show that rotational maneuver and vibration suppression are accomplished in spite of the presence of disturbance torque and parameter uncertainty.     

Eigenfrequency analysis of cable structures with inclined cables

The approximate eigenfrequencies for the in-plane vibrations of a cable struc- ture consisting of inclined cables,together with point masses at various points were com- puted.It was discovered that the classical transfer matrix method was inadequate for this task,and hence the larger exterior matrices were used to determine the eigenfrequency equation.Then predictions of the dynamics of the general cable structure based on the asymptotic estimates of the exterior matrices were made.     

Dynamic modelling and active vibration control of a submerged rectangular plate equipped with piezoelectric sensors and actuators

The active vibration control of a rectangular plate either partially or fully submerged in a fluid was investigated. Piezoelectric sensors and actuators were bonded to the plate, and the assumed mode method was used to derive a dynamic model for the submerged plate. The properties of the piezoelectric actuators and sensors, as well as their coupling to the structure, were used to derive the corresponding equations of their behaviour. The fluid effect was modelled according to the added virtual mass obtained by solving the Laplace equation. The natural vibration characteristics of the plate both in air and in water were obtained theoretically and were found to be consistent with the experimental results, and the changes in the natural frequencies resulting from submersion in fluid can be accurately predicted. A multi-input, multi-output positive position feedback controller was designed by taking the natural vibration characteristics into account and was then implemented by using a digital controller. The experimental results show that piezoelectric sensors and actuators along with the control algorithm can effectively suppress the vibration of a rectangular plate both in air and submerged in a fluid.     

Autoresonant homeostat concept for engineering application of nonlinear vibration modes

Analysis of strongly nonlinear (vibro-impact) systems revealed an existence of nonlinear modes of vibration with spatial and temporal concentration of energy. The modes can be realised, for example, through intensification of the vibration process by condensing the vibration into a sequence of collisions for impulsive action of the tools to the media being treated or can be as a result of some discontinuity (slackening of a contact, arrival of crack, etc.) in the structure. The use of the nonlinear modes to develop useful mechanical work leads to necessity of excitation and control of resonance in ill-defined dynamical systems. This is due to the poorly predictable response of the media being treated. Excitation, stabilisation and control of a nonlinear mode at the top intensity in such systems is an engineering challenge and needs a new method of adaptive control for its realisation. Such a control technique was developed with the use of self-exciting mechatronic systems. The excitation of the nonlinear mode in such systems is a result of artificial instability of mechanical system conducted by positive electronic feedback. The instability is controlled by intelligent identification of the mode and active tracing of the optimal relationship between phase shifting and limitation in the feedback circuitry. This method of control is known as autoresonance. Applications of autoresonant control for development of the new machines are described. The paper is a revised and extended version of authors’ presentation at ASME 2004 International Mechanical Engineering Congress, Anaheim, CA, USA. An erratum to this article can be found at     

绳驱桁架结构伸展臂的主动振动控制

伸展臂由于受到空间温度变化和卫星机动动作的影响,不可避免地会产生振动。在阻尼较低的空间环境中,这种振动衰减较慢,影响伸展臂的正常工作。因此,合适的振动控制方法对于伸展臂的正常工作至关重要。本文采用拉绳作为作动器的空间桁架结构伸展臂,研究其作动绳上铰链串联顺序的优化和模型预测控制律的设计,这两部分内容均考虑了作动绳的单边约束和饱和约束。首先,通过ANSYS软件获取结构的模态信息;然后结合系统可控性原理和遗传算法计算出作动绳上铰链串联最优顺序;最后,在数值仿真中,通过设计的控制率对一个由四个单元组成的桁架结构伸展臂的振动控制过程进行仿真分析。结果表明,提出的作动绳串联铰链的方式能够有效抑制伸展臂的振动。