Flexible Beam Structure Research Articles

Vibration Control of a Structural System Using Magneto-Rheological Fluid Mount

In this work, a mixed mode-type magneto-rheological fluid mount (MR mount in short) is devised by considering the nondimensional formulation of Bingham plastic flow, and applied to vibration control of a structural system subjected to external excitations. The structural system consists of a vibrating mass, semi-active MR fluid mount, and passive rubber mounts. The MR mount is installed on the beam structure as a semi-active actuator and supports the vibrating mass, while the flexible beam structure is supported by two passive rubber mounts. After verifying the field-dependent damping force characteristics of the MR mount, the governing equation of the structural system is derived in the modal coordinate and rewritten as a state space control model. The linear quadratic Gaussian (LQG) controller is then formulated in order to attenuate vibration of the structural system. The LQG controller is experimentally realized and control responses such as accelerations and transmitted forces of the structural system are presented in the frequency domain.

Displacement Control of a Beam using Photostrictive Optical Actuators

Photostrictive materials are emerging as a new actuation medium. In contrast to the traditional transducers, photostrictive materials can produce actuation strains as a result of irradiation from incident light, having neither electric lead wires nor electric circuits. In this study, a static analytical model is derived for a flexural beam with surface bonded photostrictive optical actuators. An analysis of the proposed model is carried out by considering the induced force and bending moment produced on the beam by the patched actuator. Analytical solutions of the transverse deflection, induced by the photostrictive actuators, are derived for different boundary conditions. Those solutions are explicitly expressed in terms of the geometry and position of the actuators patched on the beam. To support the validity of the developed model, a finite element verification is presented. This research work investigates the application of photostrictive actuators for optimum displacement control of a flexible beam structure. Studies are performed to examine the effects of various actuator locations and lengths on photostrictive actuation.

Vibration control of a flexible structure using a hybrid mount

This paper presents vibration control of a flexible beam structure using a hybrid mount which consists of elastic rubber and piezoelectric stack actuator. After identifying stiffness and damping properties of the rubber and piezoelectric elements, a mechanical model of the hybrid mount is established. The mount model is then incorporated with the beam structure, and the governing equation of motion is obtained in a state space. A sliding mode controller is designed in order to actively attenuate the vibration of the beam structure subjected to high-frequency and small magnitude excitations. The controller is experimentally realized and measured control responses such as acceleration of the beam structure and force transmission through the hybrid mount are evaluated and presented in both frequency and time domains.

Vibration control of a flexible beam structure using squeeze-mode ER mount

This paper presents vibration control of a flexible beam structure supported by squeeze-mode electro-rheological (ER) mounts. After devising an appropriate size of the squeeze-mode ER mount, its field-dependent damping forces are evaluated at various exciting frequencies. The damping force controllability of the ER mount is also demonstrated by implementing a proportional integral derivative (PID) controller. The ER mounts are then incorporated with a flexible beam structure subjected to external excitations. The governing equation of the structural system is obtained and an optimal controller which consists of the position and velocity components of the beam structure as feedback signals is designed to attenuate the imposed vibrations. The controller is empirically realized and control responses such as beam acceleration are evaluated in time and frequency domains. In addition, the forces transmitted from the input point (exciting position) to the base plate (mount position) are investigated by applying control voltage and constant voltage.

207 柔軟多体構造の座屈を考慮した構造解析

The buckling analysis method based on Corotational formulated FEM for complex flexible multibody beam structures is proposed. This method makes it possible to analyze light weight deployable beam structures that may be subjected to buckling taking into account the geometric nonlinearity stemming from large rotations. The mechanical motion, elastic deformation and buckling can be handled by the consolidated mathematical treatment and computational algorithm presented in this paper. This paper especially focuses on a buckling mode injection method while a concerned structure undergoes mechanical motion. A buckling mode is estimated even though a bifurcation point is not accurately obtained. The validity of this method is confirmed in a numerical examination.

Vibration Isolation of Structural Systems Using Squeeze Mode ER Mounts

This paper presents vibration control of flexible structures using squeeze mode ER mounts. After devising the squeeze mode ER mount, its field-dependent damping forces are evaluated at various exciting frequencies. The ER mounts are then incorporated with a flexible beam structure. The governing equation of motion is obtained and an optimal controller which represents controllable damping force is designed to attenuate unwanted structural vibration. The controller is experimentally realized and control responses are presented in the frequency domain. In addition, vibration control responses of a flexible frame structure integrating with the proposed ER mounts are investigated by experiment.

Damage identification of flexible beam structures using large displacements

In previous works we have proposed a damage location strategy for flexible beam structures where non-linear displacements are observed. The present paper deals with the computation of physical characteristics associated with detected damages. Even using a preliminary location stage allowing to reduce the set of parameters, the problem of their evaluation is made difficult because of the non-linearities. There is a strongly non-linear ill-posed problem to solve. For correlating measured data with the given modelling, a measure of the error on the constitutive relation is written. The computation of the damages is made in a very general development within the framework of the continuum media mechanics and can be applied using different numerical approaches. The introduction of supplementary experimental information such as the measured strain helps the strategy. To illustrate the method, we choose a finite element discretization. The ability to quantify single and multiple damage events is investigated through a set of numerical examples.

Vibration Control of a Flexible Structure Using ER Dampers

This technical brief addresses the vibration control of a flexible beam structure using ER (electro-rheological) dampers. A clamped-clamped flexible beam system supported by two short columns is considered. An ER damper which is operated in shear mode is designed on the basis of Bingham model of the ER fluid, and attached to the flexible beam. After deriving the governing equation of motion and associated boundary conditions, a sliding mode controller is formulated to effectively suppress the vibration of the beam caused by external forces. In the formulation of the controller, parameter variations such as frequency deviation are treated to take into account the robustness of control system. The effectiveness of the proposed control system is confirmed by both simulation and experimental results.

Analysis of flexible multibody systems with spatial beams using mixed variational principles

A general finite element formulation is presented for dynamic analysis of spatial elastic beams, for small strains, in a multi-body configuration. The tangent maps associated to the finite rotation vector are used to compute the tangent matrices used to integrate implicitly the equations of motion in descriptor form. A corotational method and a mixed variational method are used to compute the tangent stiffness matrix. The tangent constraint matrices are obtained using consistent linearization of the constraint equations. The tangent inertia matrices, including the gyroscopic and centrifugal terms, are also obtained by using the tangent maps of rotation. The numerical examples analyzed in this paper include: dynamic analysis of flexible beam structures and multi-flexible body systems with open and closed kinematic loops. A comparison with the previous results in the literature shows a very good performance in terms of time integration step and number of elements used. © 1998 John Wiley & Sons, Ltd.

Analysis of flexible multibody systems with spatial beams using mixed variational principles

A general finite element formulation is presented for dynamic analysis of spatial elastic beams, for small strains, in a multi-body configuration. The tangent maps associated to the finite rotation vector are used to compute the tangent matrices used to integrate implicitly the equations of motion in descriptor form. A corotational method and a mixed variational method are used to compute the tangent stiffness matrix. The tangent constraint matrices are obtained using consistent linearization of the constraint equations. The tangent inertia matrices, including the gyroscopic and centrifugal terms, are also obtained by using the tangent maps of rotation. The numerical examples analyzed in this paper include: dynamic analysis of flexible beam structures and multi-flexible body systems with open and closed kinematic loops. A comparison with the previous results in the literature shows a very good performance in terms of time integration step and number of elements used. © 1998 John Wiley & Sons, Ltd.

Nonlinear Decentralized Control of a Flexible Cable-stayed Beam Structure

A decentralized controller that suppresses the vibrations of a flexible cable-stayed beam structure induced by an external random disturbance is presented. The controller is designed based on a lumped-mass model representation of the distributed parameter flexible beam structure. It contains a linear part and a nonlinear part. The linear part is used to introduce damping into the beam structure and the nonlinear part is used to further reduce the vibrations caused by the external disturbance. Its performance is assessed via digital computer simulation.

Evolutionary adaptive active vibration control

This paper presents an investigation into the development of an adaptive active control mechanism for vibration suppression using genetic algorithms (GAs). GAs are used to estimate the adaptive controller characteristics, where the controller is designed on the basis of optimal vibration suppression using the plant model. This is realized by minimizing the prediction error of the actual plant output and the model output. A MATLAB GA toolbox is used to identify the controller parameters. A comparative performance of the conventional recursive least-squares (RLS) scheme and the GA is presented. The active vibration control system is implemented with both the GA and the RLS schemes, and its performance assessed in the suppression of vibration along a flexible beam structure in each case.

Elastic Finite Element Analysis for a Flexible Beam Structure.

A finite element anlaysis is performed for large deformations of a felxible beam. The total Lagrangian formulation for a general large deformation, which involves finite rotations, is chosen and the exponential map is used to treat finite rotations from the Eulerian point of view. The finite elements results are confirmed for several cases of deformations through comparison to a first order elasticity solution obtained by numerical integration, and the agreement between the two is found to be excellent. For lateral buckling, the point of vanishing determinant of the resulting unsymmetric tangent stiffness is traced to examine its relationship to bifurcation points. It is found that the points of vanishing determinant is not corresponding to bifurcation points for large deformation in general, which suggests that the present unsymmetric tangent stiffness is not an exact first derivative of internal forces with respect to displacement.

Motion Control of a Variable-Geometry Flexible Structure using Neural-Network Inverse Model and Fuzzy-Set Theory.

This paper presents a numerical method for motion control of a variable-geometry flexible beam structure. The transient response of the structure is calculated using updated nodal coordinates and internal forces, and the stiffness matrix for the beam elements in a finite element model. Using the results of various quasi-static finite element analyses, the neural-network feedforward controller learns an inverse model of the controlled flexible structure. To minimize the tracking error and to damp the vibration, the fuzzy feedback controller is combined with feedforward controller, which uses the above inverse model to estimate the sensitivity of the controlled structure. As an example, this method is applied to an arm-like flexible, lightweight beam structure which has 21 elements including two variable links, and the motion is analyzed.

Heterogeneous and homogeneous parallel architectures for real-time active vibration control

The paper presents an investigation into parallel processing techniques for real-time adaptive control of a flexible beam structure. Three different algorithms, namely simulation, control and identification are involved in the adaptive control algorithm. These are implemented on a number of uniprocessor and multiprocessor, homogeneous and heterogeneous, computing platforms involving transputers, digital signal processing devices and several general purpose sequential processors. The partitioning and mapping of the algorithms on the homogeneous and heterogeneous architectures is also explored. The interprocessor communication speed is investigated to establish the real-time performance aspects of the processors on the basis of the nature of the algorithms involved. A close investigation into the performance of several compilers is made and discussed within the context of real-time implementations. Finally, a comparison of the results of the implementations is made.

Self-Tuning Active Vibration Control in Flexible Beam Structures

This paper presents the design and performance evaluation of an adaptive active control mechanism for vibration suppression inflexible beam structures. A cantilever beam system in transverse vibration is considered. First-order central finite difference methods are used to study the behaviour of the beam and develop a suitable test and verification platform. An active vibration control algorithm is developed within an adaptive control framework for broadband cancellation of vibration along the beam using a single-input multi-output (SIMO) control structure. The algorithm is implemented on a digital processor incorporating a digital signal processing (DSP) and transputer system. Simulation results verifying the performance of the algorithm in the suppression of vibration along the beam, using single-input single-output and SIMO control structures, are presented and discussed.

Geometric nonlinear analysis of flexible spatial beam structures

An updated Lagrangian formulation of the spatial beam element is presented for a purely geometric nonlinear analysis in which the geometric stiffness matrix is expressed either by a one-dimensional integration of the stress resultants or by a closed form of element-end forces. A computer code, NACS, is developed based on this formulation which has a number of facilities to meet the special requirements for the analysis of suspension and cable-stayed bridges. Several example problems are reported.