Flexible Truss Research Articles

Virtual Dynamic Vibration Absorber Trap Fusion Active Vibration Suppression Algorithm Based on Inertial Actuators for Large Flexible Space Trusses

This paper presents a virtual dynamic vibration absorber (DVA) trap fusion active vibration suppression algorithm based on inertial actuators as a solution to the harmonic vibration control problem of large flexible space trusses. Firstly, the mechanism of the inertial actuator is analyzed, and the relationship between the bandwidth of the algorithm and the intrinsic frequency of the inertial actuator is derived. Secondly, a dynamic model of the space truss is constructed. Subsequently, an analysis is conducted to determine the manner in which the virtual DVA exerts influence on the system’s dynamic characteristics. Based on this analysis, a virtual DVA trap fusion active vibration suppression algorithm is designed. Finally, the efficacy of the proposed algorithm in suppressing vibration is demonstrated through experimentation. The algorithm was demonstrated to be effective in suppressing both single-frequency harmonic vibration and multi-frequency harmonic vibration under the working conditions of single-degree-of-freedom and multi-degree-of-freedom of a flexible truss. The vibration suppression efficiency was found to be greater than 60%. It is therefore evident that the proposed algorithm has the potential to be applied to the vibration suppression of telescopes assembled in orbit in the future.

Finite element dynamic modeling and attitude control for a slender flexible spacecraft

This paper aims to study the dynamic modeling and attitude control of a kind of slender flexible spacecraft. The basic structure of this kind of spacecraft is different from the traditional structure of a center rigid body with flexible appendages, but rigid bodies at both ends, which are connected by a flexible truss structure. Firstly, the finite element modeling method is adopted to establish the dynamic model of this kind of spacecraft, and the vibration frequency and damping of the flexible structure are obtained. The unconstrained modes of the flexible spacecraft are obtained through mathematical analysis, finite element analysis and frequency domain analysis. In addition, a nonlinear sliding surface with angular velocity constraint is designed. On this basis, an adaptive sliding mode (ASM) controller is proposed, stability of the close-loop system under the controller is proved, and the dynamic model is verified through mathematical simulation.

Thermal design optimization method of mesh reflector antennas considering the interaction between cable net and flexible truss

Thermal design optimization method of mesh reflector antennas considering the interaction between cable net and flexible truss

3D-printed, electrically conductive structures for magnetic attitude control

The use of embedded current loops for the attitude control of large, flexible spacecraft is investigated. Length-scaling laws are derived by determining what fraction of a planar spacecraft’s mass would need to be allocated to the conductive current loops in order to produce a torque at least as large as the gravity gradient torque. Simulations are then performed of a flexible truss structure, modelled as a spring–mass system, for a range of structural flexibilities and a variety of current loop geometries. Simulations demonstrate rotation of the structure via the electromagnetic force on the current carrying elements, and are also used to characterise the structural deformations caused by the various current loop geometries. An attitude control simulation is performed, demonstrating a 90∘ slew manoeuvre of a 250 × 250 m flexible structure through the use of three orthogonal sets of current loops embedded within the spacecraft.

Form Finding of Asymmetric Cable Network Reflector with Flexible Ring Truss

In this work, the form finding of an asymmetric cable network reflector is considered by taking into account the elastic deformation of the flexible ring truss. Firstly, by treating the boundary nodes as fixed nodes, the balance equations of the structure are transformed into linear equations using the force density method (FDM). Next, the genetic algorithm (GA) is used to find the force density values that satisfy the surface accuracy required to complete the form finding of a cable network reflector. Secondly, a design procedure is presented by incorporating the elastic deformation of the ring truss. Finally, using an iterative process, the coordinates of the boundary nodes are modified to repeat the first step to obtain better surface accuracy. Numerical experiments are presented to demonstrate the effectiveness of the proposed method in comparison with the conventional method.

Composite Control of Attitude Tracking and Vibration Suppression of a Rigid–Flexible Coupled System

AbstractThis paper presents a composite control approach that facilitates both stable attitude tracking and vibration suppression of a space flexible slewing truss. An improved proportional-differe...

Application of Magneto Rheological Damper System In Warren Truss Bridge Structure

This paper considers the application of magnetorheological (MR) damper, RD-8040-1, for attenuation vibration in flexible truss bridge deck structures. The modeling and identification of the damper property by using SAP2000 analysis software from an experimental data set generated by dynamic tests of the MR damper mounted in a testing machine where velocity and current are used as input, and the force as output. Theoretical investigations and in-site experiments are carried out in Chamran’s laboratory, Ahvaz, Iran. Truss bridges are an innovative structure that shall be studied in their systems and connections to earn stability and damping in related to certain lateral loads such as seismic load's post-earthquake load. The issue of damping is the cooperation between elements in the truss bridge of deck systems. Significantly, MR damper among components based on their reaction can be defined in the form of a percentage of control of loads in the structure of deck in a bridge system. This article proposes the application of damper at interconnecting of bridge deck through minimizing vibration force by using the Bouc-wen model. In summary, this paper is understood the effect of damping application on overall formation nonlinear analysis Models at this major element.

Fuzzy PD hybrid control of low frequency vibration of annular antenna

The annular antenna is a typical large flexible space truss structure featured by small damping and low modal frequencies. The external disturbances, e.g. impulse load resulting from satellite attitude adjusting, may induce the low frequency large amplitude vibrations of annular antenna for a long time and thus reduce working precision and cause even its damage. The active control of vibration of annular antenna under impulse excitation is investigated in the paper. The voice coil actuator instead of piezoelectric stack actuator is used in order to meet the demand of large output displacement. The governing equation of active vibration control system is established by use of finite element method. The proportional differential (PD) control and fuzzy control algorithms are firstly studied in the active control. The results show that the fuzzy control exhibits worse control performance than PD control due to weak control function near structural equilibrium position. To circumvent the drawback of fuzzy control, a fuzzy PD hybrid control strategy is proposed which can combine the merits of both control methods. The simulated and experimental results show that the fuzzy PD hybrid control can yield the best control effect under impulse excitation comparing with the PD control and ordinary fuzzy control. The work provides a promising control way for active control of low frequency and large displacement vibration of annular antenna in satellite engineering.

Design and performance assessment of a distributed vibration suppression system of a large flexible antenna during attitude manoeuvres

One of the major needs of future Earth Observation satellites is to fulfil high demanding pointing requirements when using instrumentations supported by or mounted at the end of very large flexible truss structures. Those spacecraft often call for the capacity of performing fast and precise manoeuvres without exceeding deformation requirements related to their flexible parts. On-board mechanical disturbances can be generated by an attitude control equipment and pointing mechanisms. In this perspective, a network of smart actuators/sensors can be mounted on a passive structure to counteract undesired elastic vibrations. In this paper, the problem of micro-vibration control for a spacecraft equipped with a very large flexible antenna is addressed. The instrument is sustained by an active frame hosting an optimally distributed network of actuators and sensors dedicated to vibrations suppression. The fully coupled 3-D equations for a flexible spacecraft subjected to forces of the orbital environment are derived taking the presence of the smart materials into account. The 3-D flexible structure model is developed and validated via FEM formulation by using commercial codes. The model is then reduced to obtain a system to be easily handled by control systems algorithms. A placement strategy to identify the best location for vibration control devices is carried out by using Gramian-based techniques. Typical profiles of attitude manoeuvres are then simulated by applying a control torque while simultaneously suppressing unwanted vibrations. To achieve a high performance, feedback methods are implemented to coordinate the actuators and ensure that maximum tip displacement requirements are satisfied during operations.

Application of Similarity Theory for Dynamic Characteristics Prediction of Crane Flexible Truss Boom

The aim of this study is to explore the similarity relations of dynamic characteristics of crane flexible truss boom. Combining perturbation theory with vibration analysis, a calculation method of the flexible boom natural frequency undergoing large overall rotary motion was proposed. According to the similarity theory, in terms of the geometrically similar truss boom, the similarity relations of their natural frequency and other parameters were derived. Taking the slenderness ratio of the actual product as the reference standard, two groups of scale-down crane truss boom experiments were designed. The results showed that, in aspect of the boom section size and the boom length, by using the similarity relations of the flexible boom, the dynamic characteristics can be predicted well.

Integrated power and vibration control of gyroelastic body with variable-speed control moment gyros

The gyroelastic body refers to a flexible structure with distributed angular momentum exchange devices (AMEDs), such as the momentum wheels (MWs) or the control moment gyros (CMGs). The amplitude or the direction of the angular momentum of the rotors in the AMEDs can be changed to produce torques for vibration suppression of the flexible structure. In order to take full advantage of the AMEDs on the flexible structure, the AMEDs are also used for energy storage in this study, thus, an integrated power and vibration control system (IPVCS) is obtained. In this paper, the single-gimbal variable speeds control momentum gyros (VSCMGs) are chosen as the distributed AMEDs mounting on a constrained flexible structure. It can work in a “CMG & MW” mode and a “VSCMG” mode for simultaneous vibration suppression and energy storage. First, the dynamics of a constrained gyroelastic body is established, whereas the power equation of the rotors is deduced. Second, the feedback control laws are designed when the VSCMGs work in the CMG & MW mode and the VSCMG mode, respectively. Finally, numerical examples are presented for a flexible truss with distributed VSCMGs to verify the effectiveness of the proposed feedback control strategies.

Dynamic Analysis of the Deployment for Mesh Reflector Antennas Driven With Variable Length Cables

Abstract This paper addresses the deployment dynamic analysis of antennas mainly composing of deployable truss and cable net. The antennas are deployed by retracting driving cables, which pass through pulleys fixed on the deployable truss successively. An analytical model is first proposed for the driving cable system where the nodal position and the transmission lengths of the cable segment between two adjacent pulleys are selected as the generalized coordinates. This model could simulate the dynamics of the driving cables with time-varying length. Then, the flexible multibody dynamic model of the deployable antenna including the flexible deployable truss and cable net is established. The absolute nodal coordinate formulation is employed to model the flexible deformation of the truss and the tension of the cable net. The method is demonstrated by analyzing the deployment of a cylindrical mesh antenna. The deployment experiment of the antenna shows that the proposed method can correctly predict the driving force and length variation of the driving cables, the bending deformation of the flexible truss, and the deployment process.

Integrated form finding method for mesh reflector antennas considering the flexible truss and hinges

Form finding plays an essential role in the design of deployable mesh reflectors (DMRs), and it concerns their electromagnetic performance. However, classic form finding methods ignore the compatible deformation between cable networks and supporting structures. Even though the finite element method can be adopted to compensate the deviations caused by the compatible deformation, many iterations have to be involved and the effects are usually not satisfied. In this paper, an integrated form finding method considering the flexibility of the truss and hinges is proposed. Firstly, the rod of the truss is modeled by Euler–Bernoulli beam and the hinge is described by the flexible joint with six degree of freedoms (DOFs) to form the integrated element. These elements are assembled according to the topology of the truss to obtain the equilibrium equation of the truss. Secondly, the boundary conditions are applied to condense the DOFs of beam nodes, so that the rods, hinges and cable networks can be combined by adopting the corresponding consistency conditions, and then the equilibrium equation of the coupled model is established. Finally, the integrated form finding method is formed by incorporating the gradient based optimization method into the coupled model. This method is further applied to the form finding of the ring truss DMR, and the corresponding case studies are provided. The stiffness coefficients of three kinds of hinges in six DOFs are measured and utilized. The obtained design parameters are imported into ABAQUS to calculate the actually formed reflective surface, so as to verify the result. The form finding results are also compared with those in previous literature. The proposed method is proved to be effective in the form finding of DMRs, and the deviations of the form and force distribution of reflective surfaces caused by the compatible deformation are totally avoided.

Deployment analysis of deployable antennas considering cable net and truss flexibility

Dynamic analysis of antennas during the deployment is very important. Several successful methods have been demonstrated. However, few studies have been conducted on the deployment analysis of antennas with cable net and flexible truss. This paper presents an analysis method of the deployment of antennas consisting of cable net and flexible truss. First, a beam element is used to model the flexible truss and a cable element with a transition function is used to model the cable net from slack to tension state. Then, the deployment of the antenna is planned and the corresponding variation of the length of the driving cable is obtained. Due to the fact that antennas deploy very slowly in space, the mechanism analysis problem for the antenna during deployment is discretized to several quasi-static configuration analysis problems. By using the principle of minimum potential energy, the equilibrium state of the quasi-static configuration at an instant of the deployment is computed. Numerical simulation of 2 m aperture mesh reflector antenna was performed. The numerical results are compared with previous works, and the validity of the method is demonstrated.

Dynamic analysis of suspension cable based on vector form intrinsic finite element method

A vector finite element method is presented for the dynamic analysis of cable structures based on the vector form intrinsic finite element (VFIFE) and mechanical properties of suspension cable. Firstly, the suspension cable is discretized into different elements by space points, the mass and external forces of suspension cable are transformed into space points. The structural form of cable is described by the space points at different time. The equations of motion for the space points are established according to the Newton’s second law. Then, the element internal forces between the space points are derived from the flexible truss structure. Finally, the motion equations of space points are solved by the central difference method with reasonable time integration step. The tangential tension of the bearing rope in a test ropeway with the moving concentrated loads is calculated and compared with the experimental data. The results show that the tangential tension of suspension cable with moving loads is consistent with the experimental data. This method has high calculated precision and meets the requirements of engineering application.

Active vibration control of large space flexible slewing truss using cable actuator with input saturation

SummaryThis paper proposes a composite approach to implementing attitude tracking and active vibration control of a large space flexible truss system. The system dynamic model is based on Hamilton's principle and discretized using the finite difference method. A nonlinear attitude controller for position tracking is developed based on the input‐output linearization of the discretized system, which can effectively improve system performance compared with a traditional proportional‐differential feedback controller. A taut cable actuator scheme is presented to suppress tip vibration because the mechanical model is a large large‐span spatial structure; furthermore, because the cable has the feature of unilateral input saturation constraint, which can provide only a pulling force, a nonlinear quadratic regulator controller is developed by introducing a piecewise nonquadratic cost function to suppress the vibration of the flexible structure. To investigate the factors that influence the damping effects of the cable, the parametrically excited instability of a cable under 2 supports is analyzed. Simulation results illustrate that the proposed attitude controller can implement the task of position tracking, and the vibration suppression control law is shown to be optimal for functional performance with input saturation.

Identification of Vibrating Structures under Stochastic Loading Conditions

A stochastic identification technique is proposed to estimate both the order and parameters of multi- inputs multi-outputs vibrating structural systems. A time-series model of an over-specified order is considered. The extraneous modes associated with the over-specified order model are distinguished from system modes by applying a backwards approach. The poles of the extraneous modes have been shown to be canceled by the extra zeroes. These poles are found to be generally inside the unit circle. Simulation examples have been presented to illustrate the effectiveness of the present proposed identification approach. Experimental runs on the vibration of a flexible truss, representing the tower of an overhead tower cranes, is carried out, the data of which was used to identify the system order and parameters.

The Analysis of Stiffness and Stability of Luffing Jib Cranes Based on Theory of Second Order

Luffing jib cranes are large flexible complex truss structure, and their mechanical property is nonlinearity. So the Precise analysis method for the stiffness and stability problem has been paid attention to by the researchers. To solve this problem, the equivalent mechanical model of luffing jib crane was established by taking the lifting load, counter weight and dead weight into consideration. The stiffness and stability of luffing jib crane was analyzed by using the differential equation of deflection based on second-order effect. The calculating formulas of lateral deflection, amplification factor of deflection and stability was derived. Taking a luffing jib tower crane for example, the lateral stiffness was calculated respectively by the formula given by this paper, the traditional linear method and the finite element method, and show that the result calculated by the formula given by this paper is identical to that by finite element software ANSYS, the error is 1.8%. and the error of traditional method is 7.6%, It is clear that calculation expression of lateral deflection, deflection amplification factor and the stability in this paper are accuracy. This method can be applied to the analysis of calculation of luffing jib tower crane stiffness and stability.

Optimum placement of actuators in structural and control design using Stackelberg games

Actuator placement has a significant impact on the dynamic response of actively controlled structures. Misplaced actuators and sensors often lead to controllability and observability problems, and the desired system performance may not be achieved with any choice of control law. This paper addresses the design of actively controlled structures wherein both the actuator placement and controller design aspects are addressed simultaneously. It is assumed that a hierarchical structure exists between the actuator placement and controller design objective functions with the actuator placement problem considered as being more important. The resulting multiobjective design problem is solved as a bi-level Stackelberg game. A computational procedure based on variable updating using response surface methods is developed for exchanging information between the two levels (leader and follower). The optimization problem has mixed discrete-continuous variables with discrete variables corresponding to actuator placement and continuous variables associated with the controller design problem. The solution approach includes a blend of genetic algorithms and sequential quadratic programming techniques and is applied to the design of a flexible truss structure. The proposed approach successfully designed an optimum controller while minimizing the weight of the structure and simultaneously maximizing the energy dissipated by the controller to bring the structure to its equilibrium position when subjected to an external disturbance.

Design of Viscous Dampers in Seismically Excited Flexible Truss Towers

In the present article, the gain matrix for active devices placed directly between masses on a truss tower is transformed for devices placed at multiple levels between masses. The transformed gains are then used with the single-mode approach to determine the damper coefficients. Numerical validation of the proposed method is provided for a 3D truss tower with a single damper installed at each level, and alternate damper configurations are investigated. Damper configurations in which at least one damper is located at a level between concentrated masses result in a tower response that is comparable to that of the optimal configuration.