Model Of Flexible Beam Research Articles

Preliminary design and structural analyses of DEMO bioshield roof

Abstract The bioshield is a reinforced concrete structure encasing the cryostat that fulfils three main functions: reduce the gamma radiation level to allow man access to external areas, provide access to the cryostat, and – as part of the tokamak building structure – provide support to the equipment and building structures on top of the bioshield roof. The bioshield roof may or may not have the additional function of supporting the cryostat top lid against external or internal pressure loads. Both the cryostat top lid as well as the bioshield roof must provide access to the vertical ports, i.e. large trapezoidal openings that are closed during plasma operation. Bioshield plugs must be inserted to maintain the bioshield’s function to protect the area above against radiation exposure. In addition, in case of a major failure in the early operational phase the bioshield roof shall be removable to allow full access to the tokamak via the overhead crane. The paper presents the results of the first ever design study of the DEMO bioshield roof. The circular symmetry roof construction that is a steel structure with concrete inserts arranged in three peripheral rows to allow full access to the tokamak via the overhead crane has been proposed. Using a flexible beam model, a number of options for the structural concept of the bioshield roof have been assessed. It has been proven that concepts with 16 innermost shield plugs as well as one innermost opening/plug are structurally feasible. The importance of the upper and lower toroidal girders of the steel load bearing structure has been identified. A mass assessment has shown that the weights of all parts of the bioshield roof are well within the lifting capacity of the overhead crane.

Diagnosis of EMD645 diesel engine connection rod failure through modal testing and finite element modeling

Abstract Connection rods are best known through their use in internal combustion piston engines. GM-GT26 locomotive uses a 3300 horse power V type engine with 16 cylinders that works at maximum crank speed of 900 RPM. The present study is concerned with the failure of a 645E3B engine connection rod with a reported catastrophic deformation due to unknown reasons. This rod has suffered from simultaneous bends in two surfaces with obvious marks of failure. A theoretical procedure, an experimental modal analysis technique and simulation by using finite element engineering softwares are used for this study. It includes finding the natural frequencies and the corresponding mode shapes for a new connection rod. This is then used to validate the FEM simulated model. The critical loads and the buckling forces on the connection rod are then calculated. The maximum loads are calculated by using the classical approaches and are verified by simulation in ADAMS-Engine software. The dynamic modeling includes rigid and flexible beam models and the torsional modes of vibrations are also considered. It is concluded that the connection rod failure is due to buckling at the presence of hydrolock phenomenon. The outcome of this research provides vital information for the proper operation and maintenance of heavy duty Diesel engines.

A novel fractional-order model and controller for vibration suppression in flexible smart beam

Vibration suppression represents an important research topic due to the occurrence of this phenomenon in multiple domains of life. In airplane wings, vibration can cause discomfort and can even lead to system failure. One of the most frequently used means of studying vibrations in airplane wings is through the use of dedicated flexible beams, equipped with sensing and actuating mechanisms powered by suitable control algorithms. In order to optimally reject these vibrations by means of closed-loop control strategies, the availability of a model is required. So far, the modeling of these smart flexible beams has been limited to deliver integer order transfer functions models. This paper, however, describes the mathematical framework used to derive a fractional-order impedance lumped model for capturing frequency response of a flexible beam system exposed to a multisine excitation. The theoretical foundation stems from fractional calculus applied in combination with transmission line theory and wave equations. The simplified model reduces to a minimal number of parameters when converging to a limit value. It is shown that the fractional-order model outperforms an integer order model of the smart beam. Based on this novel fractional-order model, a fractional-order $$\hbox {PD}^\mu $$ controller is then tuned. The controller design is based on shaping the frequency response of the closed-loop system such that the resonant peak is reduced in comparison to the uncompensated smart beam system and disturbances are rejected. Experimental results, considering a custom-built smart beam system, are provided, considering both passive and active control situations, showing that a significant improvement in the closed-loop behavior is obtained using the proposed controller. Comparisons with a fractional-order $$\hbox {PD}^\mu $$ controller, tuned according to classical open-loop frequency domain design specifications, are provided. The experimental results show that the proposed tuning technique leads to similar results as the classical approach. Thus, the proposed method is a viable alternative, being based on closed-loop specifications, which is more intuitive for practitioners.

Kinematic and dynamic analysis of compliant mechanisms considering both lateral and axial deformations of flexural beams

The kinematic and dynamic analysis of compliant mechanisms is investigated comprehensively in this work. Based on the pseudo-rigid-body model, a new PR model is proposed to simulate both the lateral and axial deformations of flexural beams in compliant mechanisms. An optimization for the characteristic factors and a linear regression for the stiffness coefficients of PR pseudo-rigid-body model are presented. Compared with the 1R and 2R pseudo-rigid-body model, the advantage of the PR model is well illustrated. The dynamic modeling of flexible beams in compliant mechanisms is then developed based on the PR pseudo-rigid-body model. The dynamic equation of a PR pseudo-rigid-body dynamic model is derived and the dynamic responses are then presented. The kinematic and dynamic analysis of a compliant slider-crank mechanism is presented by the 1R, 2R and PR model, respectively. The effectiveness of pseudo-rigid-body models and the superiorities of the PR pseudo-rigid-body model and PR pseudo-rigid-body dynamic model are shown clearly in the numerical example.

Coupling dynamic behaviors of spatial flexible beam with weak damping

SummaryAs a typical high‐dimensional nonlinear dynamic problem, the difficulties of the dynamic analysis on the spatial flexible damping beam mostly result from the coupling between the spatial motion and the transverse vibration. Considering the coupling effect and the weak structure damping, the dynamic behaviors of the spatial flexible beam are investigated by a complex structure‐preserving method in this paper. Based on the variational principle, the dynamic model of the spatial flexible damping beam is established, which can be decoupled into two parts approximately, one controls the spatial motion and another mainly controls the transverse vibration. For the first part, the classic fourth‐order Runge–Kutta method can be used to discrete it expediently. For the latter part, based on the generalized multi‐symplectic idea, the approximate symmetric form as well as the generalized multi‐symplectic conservation law is formulated, and a 15‐point scheme equivalent to the Preissmann scheme is constructed. Numerical iterations are performed for six typical initial cases between the two parts to study the dynamic behaviors of the spatial flexible beam. In the numerical experiments, the effects of the damping factor and the initial conditions (including the initial radial velocity and the initial attitude angle) on the dynamic behaviors of the spatial flexible beam are investigated in detail. From the numerical results, it can be concluded that the damping effect on the long‐time dynamic behaviors of the spatial flexible beam could not be neglected even if it is weak; the numerical method proposed in this paper owns the tiny numerical dissipation as well as the excellent long‐time numerical stability. Copyright © 2016 John Wiley & Sons, Ltd.

Active Vibration Control of a Flexible Beam Structure Using Chaotic Fractal Search Algorithm

Abstract The performance of lightweight and flexible systems such as beam, plate and shell structures are vulnerable to excessive vibration level. Thus, many vibration control techniques have been developed in the past two decades in order to overcome this problem. In this paper, the development of active vibration control to suppress the unwanted vibration from a flexible beam structure is presented. The objective of this work was to evaluate the performance of chaos-enhanced Stochastic Fractal Search (CFS) optimization algorithm in modeling and vibration control of flexible beam system. Parametric modeling of the system was developed using auto-regressive exogenous (ARX) model structure based on the input-output data from previous experimental finding. The first two resonance frequencies of flexible beam structure was found at 3.418 Hz and 21 Hz. The accuracy of generated flexible beam model was validated using correlation and system stability tests. A PID controller incorporated with CFS optimization algorithm was employed to attenuate the unwanted vibration from the flexible beam system. Based on the proposed method, about 83.95% of the initial vibration disturbance successfully been suppressed with the mean-squared error value of 1.5178 x 10 -4 been achieved. In conclusion, the simulation study indicates that the CFS algorithm possess capability to extract an adequate and stable model of the flexible beam structure, hence a better performance of control strategy can be achieved.

Implementation of swarm algorithm in modeling a flexible beam structure

The application of System Identification techniques for modeling a flexible beam structure are presented in this paper. The flexible beam has been widely applied in various fields engineering and industrial. However, the flexible structure is easily influenced by unwanted vibration which may lead to fatigue, performance reduction and structure damage. Thus, the unwanted vibration must be controlled and reduced. In order to have a good controller performance for vibration suppression, an appropriate model of flexible beam is required. Hence, to obtain a model of the flexible beam structure, Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC) are implemented in this study as System Identification techniques. The implementation of PSO and ABC requires experimental data input and output retrieved from data acquisition from a well-developed experimental test rig via MATLAB Simulink platform. Results obtained are displayed in graphical plots and numerical values. The predicted model is validated via mean square error (MSE) and correlation tests. To represent the dynamic model of the flexible beam structure, model with minimum MSE value and correlation test within 95 % confidence interval is selected as the best fit model. The result shows that PSO algorithm produces better performance compared to ABC algorithm with a 3rd order predicted model that has lowest MSE value and correlation tests within 95 % confidence interval for the beam system.

DEVELOPMENT OF DYNAMIC MODEL FOR VIBRATION CONTROL OF FLEXIBLE BEAM

The present study aims at developing a new dynamic model for vibration control of a composite carbon cantilever beam. The finite element method (FEM) is used to derive the introduced model. Modal analysis is performed on the cantilever beam using ANSYS software package and results were compared with similar published work using ABAQUS software package to validate the results obtained from ANSYS. The theory behind the extraction of flexible beam model from the finite element model is introduced. The eigenvalues and eigenvectors resulting from this analysis are integrated into MATLAB, which is used to derive the state space model of the system. Through MATLAB/ SIMULINK tools a PID controller was designed and controlled system performance under different system inputs is studied to test the efficiency of the controller. The results show similar responses and similar error percentage signals to various step input angles. In addition, the system shows a good performance to sine wave input signal despite the presence of a minor lag.

Large deflections and vibrations of a tip pulled beam with variable transversal section

Abstract The use of long flexible probes in outdoors exploration vehicles, as opposed to short and rigid arms, is a convenient way to grant easier access to regions of scientific interest such as terrain slopes and cliff sides. Longer and taller arms can also provide information from a wider exploration horizon. The drawback of employing long and flexible exploration probes is the fact that its vibration is not easily controlled in real time operation by means of a simple analytic linear dynamic model. The numerical model required to describe the dynamics of a very long and flexible structure is often very large and of slow computational convergence. The present work proposes a simplified numerical model of a long flexible beam with variable cross section, which is statically deflected by a pulling cable. The paper compares the proposed simplified model with experimental data regarding the static and dynamic characteristics of a beam with variable cross section. The simulations show the effectiveness of the simplified dynamic model employed in an active control loop to suppress tip vibrations of the beam.

On prediction of torque in flexible pipe reeling operations using a Lagrangian–Eulerian FE framework

Abstract In this paper a new framework for FE simulation of reeling operations that utilizes a Lagrangian–Eulerian description of the beam kinematics is proposed. In contrast to the conventional Lagrangian approach, the material is enabled to flow with an axial velocity through a nearly space-fixed beam mesh. This gives far more effective and robust simulations since the length of the beam model reduces significantly and because the contact geometry undergoes less changes. The main ingredients of the Lagrangian–Eulerian framework and a flexible pipe beam model are presented. An idealized spoolbase-vessel load-out operation is considered in order to gain insight into the torsional failures experienced by subsea contractors in recent years. Here, three different mechanisms were found to provoke torsional failure of the pipe. Strategies to avoid the torsional failures and FE modeling remarks are provided.

Effect of geometrical and environmental parameters on vibration of multi-layered piezoelectric microcantilever in amplitude mode

In this paper, the vibration motions of multi-layered piezoelectric microcantilevers (MCs) are analyzed in which these MCs are able to perform both actuating and sensing of tip deflection simultaneously. With respect to the presence of piezoelectric layers, these MCs modeled in several structures such as two layers and two segments. The governing equations of motion for these MCs are obtained using Hamilton’s principle. It should be noted that the microcantilever (MC) is modeled as a continuous beam based on Euler–Bernoulli beam theory. Then, the obtained differential equation is solved by finite element method and the time response is obtained using Newmark method. In simulation of the vibrating behavior of MCs in contact mode, the flexible beam model includes attractive, adhesive and repulsive forces, as well as the interaction of the capillary fluid layers. In order to study vibrating motion of MC, the effect of air moisture and the tip–sample equilibrium distance as environmental parameters on the amplitude and current output are investigated, and also, a sensitivity analyses are conducted on the amplitude and current output of sensor in terms of the geometrical parameters of the MC layers and the results are analyzed.

A boundary control for motion synchronization of a two-manipulator system with a flexible beam

A novel synchronization motion control method is proposed in this paper for the system in which two manipulators are constrained by a flexible beam. Different from the general synchronization control method, the coupling dynamics among various actuators is considered as the shear force, which results from the synchronization errors. Then a simple boundary control is introduced to realize the synchronization motion of actuators by suppressing the shear force. In order to avoid the drawbacks of assumed modes model, the dynamic model of flexible beam is described by a distributed parameter model in this paper. A Riesz basis method is used to prove that the proposed control law can guarantee the synchronization system to be exponential stability. Simulation results demonstrate that the proposed method can effectively improve the performance of synchronization motion compared with other methods.

Modal Analysis of a Flexible Beam Attaching Multiple Absorbers

Structural wave propagation in beam structures can lead to unwanted noise transmission and radiation. Dissipation effects of the multiple absorbers have been proved. This paper presents a model of flexible beam with complex boundary conditions and this model with multiple attaching absorbers which are used to dissipate energy of main structure. The beam model are formulated by linear Lagrange equation and discretized by the Ritz method and the model with multiple absorbers is introduced by substructure method. Consequently, the mass matrix and stiffness matrix are obtained and numerical simulation is processed. Natural frequencies with corresponding modal mode of are obtained. Comparing the results between two models, the absorbers can enhance the natural frequencies effectively and the quantities of absorbers agree with the orders of frequencies and corresponding modes.

Complete dynamic modeling and approximate state space equations of the flexible link manipulator

This work treats the problem of dynamic modeling and state space approximation for robotic manipulators with flexibility. Case studies are planar manipulators with a single flexible link together with clamped-free ends and tip mass conditions. In this paper, complete dynamic modeling of the flexible beam without premature linearization in the formulation of the dynamics equations is developed, whereby this model is capable of reproducing nonlinear dynamic effects, such as the beam stiffening due to the centrifugal and the Coriolis forces induced by rotation of the joints, giving it the capability to predict reliable dynamic behavior. On the other hand, in order to show the joint flexibility effects on the model dynamic behaviors, manipulator with structural and joint flexibility is considered. Thus, a reliable model for flexible beam is then presented. The model is founded on two basic assumptions: inextensibility of the neutral fiber and moderate rotations of the cross sections in order to account for the foreshortening of the beam due to bending. To achieve flexible manipulator control, the standard form of state space equations for a flexible manipulator system (flexible link and actuator) is very important. In this study, finite difference method for discretization of the dynamic equations is used and the state space equations of the flexible link with tip mass considering complete dynamic of the system are obtained. Simulation results indicated substantial improvements on dynamic behavior and it is shown that the joint flexibility has a considerable effect on the dynamic behavior of rotating flexible arm that should not be simply neglected. The effects of tip mass is proved to be increasing the elastic deformations’ amplitudes and increasing stability.

Modeling of a Nonlinear Euler-Bernoulli Flexible Beam Actuated by Two Active Shape Memory Alloy Actuators

There are two different ways of using shape memory alloy (SMA) wire as an actuator for shape control of flexible structures: it can be either embedded within the composite laminate or externally attached to the structure. As the actuator can be placed at different offset distances from the beam, external actuators produce more bending moment and, consequently, considerabnle shape changes with the same magnitude of actuation force compared with the embedded type. Such a configuration also provides faster heat transfer rate owing to convection, which is very important in shape control applications that require a highfrequency response of SMA actuators. Although combination and physics-based modeling of externally attached SMA actuator wires and strips have been considered by many researchers, these studies have some drawbacks, which, if neglected, result in a number of errors in the theoretical results compared with experimental results. These shortcomings are considering the linear Euler-Bernoulli beam theory, not deriving the actuation force of the SMA from the constitutive equations, and taking into account the effect of only one SMA wire actuation force on, for example, the structure. These assumptions may lead to erroneous theoretical modeling results compared with experimental results. In this study, the aforementioned difficulties of attaching SMA actuators to the smart structures have been addressed. In other words, instead of linear beam theory, nonlinear beam theory is used in system modeling and, therefore, the proposed method and results are valid in large deflection and rotation behavior of beam. Also, in comparison to many other analyses that the effect of only one SMA wire is investigated, in the present research the effect of all active and inactive SMA wires is considered. Accordingly, the result of this paper can easily be generalized to the structure with several SMA wire actuations. Moreover, with the purpose of having practical applications in modeling and control, the heat transfer equations of all SMA wires are considered in the analysis and, as a result, the control inputs of the presented model are SMA wire electric currents rather than SMA temperatures. First, a flexible beam actuated by two active SMA actuators is modeled. Then, the Brinson constitutive equations and thermoelectric equations for SMA materials are coupled with the nonlinear beam behavior, and the coupled system of equations is numerically solved for some particular practical cases. Finally, the numerical results of the model simulation are verified against the experimental results using a test setup to validate the proposed model prediction. The implemented method used in this paper can be easily extended to the more complex smart structure with numerous externally attached SMA wires.

Dynamic analysis of tapping-mode AFM considering capillary force interactions

Abstract The Atomic Force Microscope (AFM) scans the topography of a sample surface using a micro-sized flexible cantilever. In tapping-mode AFM, the tip–surface interactions are strongly nonlinear, rapidly changing and hysteretic. This paper explores, numerically, a flexible beam model that includes attractive, adhesive and repulsive contributions, as well as the interaction of the capillary fluid layers that cover both the tip and the sample in ambient conditions common in experiments. Forward-time simulation has been applied with an event handling numerical technique for dynamic analysis, and the Amplitude–Phase–Distance (APD) curves have been extracted. The branches of periodic solutions are found to end precisely where the cantilever comes into grazing contact with event surfaces in state space, corresponding to the onset of capillary interactions and the onset of repulsive forces associated with surface contact. The dissipated power, in the presence of conservative tip–sample interaction forces where the source of hysteresis is the formation and rupture of a liquid bridge between the tip and the sample, has been measured too. This simulation provides a more accurate way to validate the design of a new AFM probe and AFM controller than simulations which use the lumped-mass model.

Dynamic modeling of flexible beam with considering shear deformation in non-inertial reference frame

In this paper, the effect of shear deformation is considered into flexural deflection of the geometrically nonlinear deformation of a flexible beam. Then, considering the coupling effect of deformation in to the extensional and flexural deflection, the second-order coupling terms of deformation in two displacement fields are developed and the axial inertial force and transverse distributed force are considered. The finite element method is used for the system discretization and the coupling dynamic equations of flexible beam are obtained by Lagrange’s equations. In this way, the new governing differential equations of the beam in the geometrically non-linear kinematics of deformation are derived. Numerical examples of a flexible beam are studied to analyze the effect of shear deformation on the dynamic character and to investigate the coupling effect. Furthermore, from this present method, a moving Timoshenko beam can also produce the dynamic stiffening phenomenon and some new properties can be shown.

Impact forces and torques transmitted to the hand by tennis racquets

When a tennis racquet is used to strike a ball, impulsive and vibration forces are transmitted to the hand and arm. Measurements are presented showing that the dynamics of the collision can be described by replacing the hand and arm with a mass of about 200 g attached rigidly to the end of the handle. This information was combined with a flexible beam model of a racquet to calculate the impulsive and vibration forces on the hand as functions of various physical properties of the racquet, for impacts along the longitudinal axis of the racquet face. The force on the hand is largest for impacts near the tip or throat of the racquet and is a smallest for impacts near the middle of the strings. It is shown that the force can be reduced by using a heavier or stiffer racquet, by increasing the mass of the head rather than the handle, or by using softer strings or softer balls.

Exact dynamic modeling of a spatial flexible beam with large overall motion and nonlinear deformation

In this paper, the dynamic modeling theory of a spatial flexible beam, which undergoes large overall motion and nonlinear deformation, is investigated. As we know, in spacecraft and space station, there are a lot of flexible appendices so the dynamic modeling of a flexible beam is essential. Yet the existing models, in our opinion, lack several important coupling terms. This paper supplies these important coupling terms. Based on the new approach of deformation of fully geometrically nonlinear beam model developed，the finite element method is used for the system discretization and the coupling dynamic equations of flexible beam are obtained by Lagrange’s equations. The complete expression of stiffness matrix and all coupling terms are included in the dynamic equations. The second order coupling terms between rigid large overall motion, arc length stretch, lateral flexible deformation kinematics and torsional deformation terms are included in the present exact coupling model to expand the theory of one-order coupling model. The dynamic modeling method in this paper is of theoretical significance and has reference value for the rigid-flexible coupling system dynamic investigation .

Finite Element Modeling of a Slewing Non-linear Flexible Beam for Active Vibration Control with Arrays of Sensors and Actuators

In this article, a new finite element model (FEM) of an Euler—Bernoulli beam, developed through an absolute nodal coordinate formulation (ANCF), is presented for simulation and analysis of the performance of surface-bonded piezoelectric actuators in suppressing non-linear transverse vibrations that are induced by very fast slewing. The elastic deformations experienced are an order of magnitude larger than cases considered to date, and the model employs a unique cubic spline approximation to the beam’s deformed elastic line that is in terms of node positions and curvatures. To ensure relevant commentary on the vibration suppression properties of the distributed piezoelectric actuators, a material damping model was introduced in the continuum equations to capture the non-linear damping of the very slender beam that is observed in experiments. Following the ANCF methodology, the constitutive damping moment is formulated in terms of the absolute nodal coordinates with care taken to ensure the calculation is singularity free. Galerkin’s method of weighted residuals is applied to discretize the revised equations of motion derived for the beam continuum. The FE beam model exploits a synergy between the twisted spline geometry and the lumped mass approximation to halve the size of the matrix equations that must be solved on each time step. However, this condensation of the matrix equations requires the use of interelement boundaries at the edges of the surface-bonded piezos. Using a single-link flexible manipulator as an example, a number of static and dynamic simulation examples that illustrate the validity of our FEM are presented, including comparisons to theoretical and other existing numerical solutions in literature. In addition, active vibration control examples are presented using proportional- and derivative-based hub motion and piezoelectric actuator controls in suppressing dramatic vibrations induced by fast slewing.