Model Of Flexible Beam Research Articles

SU‐FF‐T‐341: New BEAMnrc Tools for Photon and Electron Beam Model Analysis

Purpose: Accurate radiotherapy planning requires precise and adaptable beam models. A beam model must be able to reproduce the full range of output on a clinical accelerator if a 2%/2mm or better accuracy goal is to be met. Most beam models have not been able to consistently meet this goal. While beam models can be based largely on measurements, Monte Carlo calculations can also be useful for determining the needed parameters and the breadth of flexibility required. In particular, Monte Carlo calculations are critical for exploring the impact of asymmetries in the accelerator geometry. As part of an effort to develop flexible beam models meeting a 2%/2mm accuracy goal, we have developed new tools for use with BEAMnrc. Method and Materials: A version of beamnrc.mortran incorporating a lateral shift for each component module has been designed, allowing the impact of laterally offsetting electron beam and accelerator elements to be evaluated. The point source model has also been modified to permit a non‐normal beam angle to allow a sensitivity analysis to include an angular distribution at the focal spot with a tilted beam. In addition, we have developed a new component module RECT which includes a simple rectilinear phantom as part of BEAMnrc, removing the necessity of using DOSXYZnrc for simple geometries. Results: By bypassing the need for a phase space file, RECT can facilitate high‐statistic runs for large field configurations by eliminating restrictions on disk space. RECT can also take advantage of the homogeneity in a water phantom by allowing photon step sizes beyond individual voxel boundaries, speeding up the simulation. Conclusion: The inclusion of lateral offsets in Monte Carlo beam models has been demonstrated to reproduce asymmetries of several percent in large electron fields, and is being used to study the 1–2% asymmetries found in clinical photon fields.

SENSING IN THE NANO-ENVIRONMENT BASED ON HIGH ORDER HARMONIC MODES OF FLEXIBLE ARM

An Atomic Force Microscope (AFM) explores the topography of a sample surface using a micro-sized flexible cantilever, which works as a flexible robot arm. The flexible cantilever is controlled to keep vibrating when an AFM works in the tapping mode. The cantilever is modeled as a flexible beam instead of a point mass system in this paper. The nonlinear interaction force between the tip and sample surface is also modeled. A simulation environment is developed to simulate the dynamics of cantilevers using the flexible beam model. Simulation results confirm that the flexible beam model can represent the system more accurately than the point-mass model. It has been shown that lower modes are more sensitive to changes of surface topography or surface materials when the cantilever is driven to vibrate at a higher harmonic mode. At the same time, this simulation environment also provides a more accurate way to validate the design of a new AFM probe and AFM controller than simulation packages which use the point-mass model.

A comparison of methods for modelling the dynamics of a cricket bat

The dynamic characteristics of a cricket bat may be quantified using different modelling methods ranging from rigid-body models, flexible beam models, finite element (FE) models and modal models. This paper compares three models of a cricket bat. The first is an experimentally validated FE model. The validation of the FE model is described via correlation and mapping of results from experimental modal testing to FE calculated results via optimization procedures. Using the methodology described here, the actual bat dynamic characteristics can be identified to a reasonable level. The second and third models included a tapered and uniform beam model of the cricket bat. Although not predicting the frequencies of vibration of the higher modes as accurately as the FE model, the uniform beam model was useful as it provided a means for correlation of the taper model for the case when the condition of zero taper is approached. Results from parameter sensitivity analyses with each beam model were used to gain an insight into the influence of geometric and material properties on bat vibration characteristics. The combined use of beam model results and FE modelling was found to be an efficient means for quantifying the effect of material and geometric variations on bat dynamic characteristics. With the experimental, numerical and theoretical techniques presented in this paper, the aim of providing an informed choice for alternative bat designs was achieved.

129 パラメータ変動モデルを利用したスマート柔軟梁におけるヘルスモニタリンク

This paper describes a modeling of a smart flexible beam composed four piezoelectric materials due to detect the failure, for example, the damage of piezoelectric materials and the breaking wire. Model of the smart flexible beam in case of the failure is expressed by a linear parameter varying system. The output matrix of the object system is affected by damage of piezoelectric materials and breaking wire. Subspace state space identification is adopted in order to detect the failure. Numerical simulation indicates that the failure detection is possible by using proposed method.

VIBRATION OF A COMPLIANT TOWER IN THREE-DIMENSIONS

The three-dimensional motion of an offshore compliant tower using both rigid and flexible beam models is studied in this paper. The tower is modelled as a beam supported by a torsional spring at the base with a point mass at the free end. The torsional spring constant is the same in all directions. When the beam is considered rigid, the two-degree-of-freedom model is employed. The two degrees constitute the two angular degrees of spherical co-ordinates, and the resulting equations are coupled and non-linear. When the beam is considered as elastic, three displacements are obtained as functions of the axial co-ordinate and time; again with coupled and non-linear equations of motion. The free and the forced responses due to deterministic loads are presented. The free responses of the rigid and elastic beams show rotating elliptical paths when viewed from above. The rate at which the path rotates depends on the initial conditions. When a harmonic transverse loading is applied in one direction, the displacement in that direction shows subharmonic resonance of order 1/2 and 1/3 while the displacement in the perpendicular direction is affected minimally. Next, in addition to the harmonic load in one direction, a transverse load is applied in the perpendicular direction. The transverse load varies exponentially with depth but is constant with time. It is found that the transverse load affects the transverse displacements in the perpendicular direction minimally.

Nonlinear Vibration Control by Semi-active Piezo-actuator Damping.

A flexible beam model with bonded piezo-patches is taken as the study object. In order to suppress the disturbance vibration of the beam, the imposed voltage to the bonded piezoelectric elements is controlled. After the theoretical analysis for piezoelectric patches and beam structure, a bilinear form of the state space equation is derived. In this electromechanically coupled model, the imposed voltage control is related to the beam deformation state. Therefore, it is possible to realize the proposed semi-active control through a low cost approach. The concept of semi-active control comes from the fact of that only the gain of the imposed voltage is adjusted and the voltage direction is reverse to the deformation sensing. As a result, the control voltage is controlled only in two-phase planes. Here, nonlinear state feedback control theory is applied to design a controller and the proposed control approach is testified by numerical simulation.

Modeling of Flexible Beams for Robotic Manipulators

This work treats the problem of modeling robotic manipulators withstructural flexibility. A mathematical model of a planarmanipulator with a single flexible link is developed. This modelis capable of reproducing nonlinear dynamic effects, such as thebeam stiffening due to the centrifugal forces induced by therotation of the joints, giving it the capability to predictreliable dynamic behaviors for a wide range of applications. Onthe other hand, the model complexity is reduced, in order to keepit amenable for analysis and controller design. The models foundin current literature for control design of flexible manipulatorarms present dynamic limitations for the sake of real timeimplementation in a control scheme. These limitations are theresult of premature linearizations in the formulation of thedynamics equations. In this paper, these common linearizations arepresented and their dynamic limitations uncovered. An alternativereliable model is then presented. The model is founded on twobasic assumptions: inextensibility of the neutral fiber, andmoderate rotations of the cross sections in order to account forthe foreshortening of the beam due to bending. Simulation andexperimental results show that the proposed model has the closestdynamic behavior to the real beam.

Flexible beam analysis of the effects of string tension and frame stiffness on racket performance

It is generally accepted that a decrease in string tension leads to greater racket power and an increase in tension improves racket control. The increase in power at low string tension can be attributed partly to a decrease in energy loss in the ball and partly to a decrease in the vibrational energy transferred to the racket. Racket control is affected if the ball strikes the strings towards one edge of the frame, in which case the racket will rotate about the long axis through the handle. The angle of rotation is decreased when the string tension is increased. Quantitative estimates of the magnitude of these effects are presented, using a one dimensional flexible beam model to describe the racket and springs to model the ball and strings. For tensions in the range 50–60 lb (220–270 N), commonly used in tennis rackets, and for a ball incident at right angles to the string plane, changes in racket power and control are essentially negligible. However, a significant increase in racket power can be achieved by increasing the stiffness of the racket frame.

Static and dynamic stresses of practical thermowells

A flexible beam model is proposed for calculating the flow induced stresses and application limits of common thermowell designs. It is intended to replace traditional selection methods with one which emphasizes mechanical integrity and process containment.

Formulation of Flexible Beam with Large Rotation Using CMS.

This paper establishes a new formulation strategy of the flexible beam with large rotation motion. The finite element based formulation, that is previously presented for the analysis of the 'Spaghetti Problem' by authors, is extended to realize the low order and high accuracy beam model using a kind of Component Mode Synthesis Method. The deformation of the flexible beam is modeled by the combination of static mode represented by the shape function and the analytically evaluated both end clamed dynamic mode with respect to the local coordinate system. Body attached local coordinate system satisfies that x-axis of it connects both-ends of the beam. To demonstrate the efficiency and the validity of the flexible beam model in Multibody Dynamics, a 2-link flexible robot arm is modeled as the flexible multibody system consists of some rigid bodies and two flexible beams. The validity can be indicated by good agreements between the numerical simulation and the experimental results.

Symmetric dichotomy based inverse dynamic model of a high-speed flexible beam

The symmetric causal/acausal dichotomy based model is developed for the bounded noncausal internal dynamics of a high-speed flexible beam, and the resultant modeling redundancy is revealed. The efficient algorithm for computing the nominal torque as well as the state trajectories is proposed to relieve the redundant computational burden of the time-domain inverse dynamic solutions, and its implication to trajectory planning is also investigated.

Impact of a ball with a bat or racket

The collision of a ball with a baseball bat or a tennis racket is usually modeled in terms of rigid body dynamics, assuming that the hand exerts no impulsive reaction force on the handle during the collision. In this paper, a uniform aluminum beam was used as an idealized bat or racket, in order to examine both the rigid body approximation and the assumption that the hand force can be neglected. An aluminum beam was chosen so that its length and stiffness could easily be varied and so that the results could be compared with solutions for a flexible beam. It was found that rigid body models of beams, bats, or rackets are of limited use but the hand force can usually be neglected. The flexible beam model provides remarkably good agreement with experimental results and provides new insights into the dynamics of this type of collision, including the nature of the sweet spot.

Large amplitude vibration of a beam restrained by a non-linear sleeve joint

Abstract The damping characteristics of built-up structures damped predominantly by dry friction are studied. In particular, the influence of the fastening condition at the end of a beam on the nature and on the amount of passive damping is investigated. The fastening arrangement is modelled by a non-linear sleeve joint that includes the effects of dry friction, transverse and longitudinal restraint, clearance, and dissipation through impact. This sleeve joint model is combined with a large amplitude flexible beam model that accounts for beam extensibility and foreshortening. Time simulations of the free response are studied to determine the effect of various beam and joint parameters on the system vibratory characteristics. It is found that beam extensibility has a significant effect on the system’s damping characteristics, especially when the sleeve has a relatively stiff retaining spring. The findings are compared to the trends observed for simplified models in order to gain further insight.

Optimal mixed sensitivity for SISO-distributed plants

The authors extend previous results for the single-input/single-output (SISO) mixed sensitivity problem for distributed parameter systems to a more general setting in which the transfer function of the plant to be controlled has both irrational stable and irrational unstable parts. These developments were originally motivated by the computation of the infimal H/sup /spl infin//-norm of the weighted mixed sensitivity for the irrational transfer function model of a damped flexible beam. >

Some remarks on controllability and observability of a flexible beam model

Controllability and observability are discussed for a model of coupled bending torsional vibrations of a flexible beam. This model can be described by a second-order evolution equation on an appropriate Hilbert space. By using frequency-domain methods it is shown that controllability and observability of the flexible model can be checked by the conditions for the corresponding simplified first-order system.

Modeling of the slewing control of a flexible structure

This paper presents a formulation for the modeling of a single-link flexible beam that is undergoing slewing motion at an actively controlled pinned end, where the other end of the beam is free. This pinned end, or slewing axis, is of fixed orientation such that the beam rotates in the horizontal plane. A geared dc electric motor is connected to the beam at the slewing axis. A position and a velocity sensor are placed at this hinged location, and their proportional feedback provides a position control system about the slewing axis. The motor characteristics, gear ratio, and the position feedback constant determine an equivalent rotational spring constant, often called the servo stiffness. This paper generalizes the structure's boundary conditions at the slewing axis to include the effects of the servo system. It is shown that the clamped-free beam assumption for the dynamics of the structure is a valid assumption if the ratio of the servo stiffness to beam flexibility is high. However, for moderate or low values of this ratio, the clamped-free beam leads to erroneous system models so that it becomes necessary to consider the effects of the driving servo on the dynamics of the flexible beam.

Closed-Loop Behavior of a Feedback-Controlled Flexible Arm: A Comparative Study

The dynamics of mechanical systems with distributed flexi bility are described by infinite-dimensional mathematical models. In order to design afinite-dimensional controller, a finite-dimensional model of the system is needed. The con trol problem of a flexible beam is a typical example. The general practice in obtaining a finite-dimensional model is to use modal approximation for distributed flexibility, retain a finite number of modes, and truncate the rest. In this approx imation, the appropriate selection of the mode shape func tions and the number of modes is not clearly known. Mostly standard pinned-free and clamped-free mode shapes are used for the flexible beam model, retaining only two or three modes and truncating the rest. The actual system, on the other hand, is infinite-dimensional, and the modes describing its flexible behavior under feedback control would be neither pinned-free nor clamped-free boundary condition modes. Rather, the mode shapes themselves are a function of the feedback control. The infinite-dimensional transcendental transfer functions for a flexible beam are formulated without any modal ap proximation. Finite-dimensional transfer functions with different shapes and numbers of modes are formulated. The closed-loop performance predictions of different models under the same colocated and noncolocated controllers, which attempt to achieve high closed-loop bandwidth, are compared. Results are surprisingly consistent in all cases; the predictions of clamped-free mode shape models are much more accurate than the predictions of the pinned-free mode shape models.

Experimental Study on Feedback Control of Coupled Bending and Torsional Vibrations of Flexible Beams

Modeling and control of flexible beams has received a great deal of attention in recent years. When a tip-body of a flexible beam is a rigid body, not only bending vibration but also torsional vibration will occur. In this paper, we model the coupled bending and torsional vibrations as a set of decoupled partial differential equations with a set of coupled boundary conditions. The whole set of dynamic equations will be rewritten together as an evolution equation in a properly defined Hilbert space. It will be proven that a differential operator governing the system is selfadjoint and has a compact inverse. A stabilizing feedback control law of a rotation motor will be established on the basis of modal analysis. Experimental methods are discussed in detail, and the results demonstrate the effectiveness of the dynamic model and the proposed control law.

Distributed systems approach to the identification of flexible structures

This paper presents a distributed parameter estimation scheme and investigates its computational merit for three idealized examples of the identification of large flexible structures. The method retains the distributed nature of the structure throughout the development of the algorithm and a finite-element approximation is used only to implement the algorithm. This approach eliminates many problems associated with the model truncation used in other methods of identification. The identification problem is formulated in Hilbert spaces and an optimal control technique is used to minimize a weighted least squares of error between the actual and the model data. A variational approach is used to solve the problem. A costate equation, gradients of parameter variations and conditions for optimal estimates are obtained. Computer simulation studies are conducted using flexible beam models as examples. Numerical results show a close match between the estimated and true values of the parameters.