Tip Of Beam Research Articles

Vibration attenuation of a flexible beam mounted on a rotating compliant hub

This study considers the problem of attenuating the vibration of a slender flexible beam mounted on a compliant rotating hub without the need for sensor(s) placement at the beam. A modal state-space model of the beam-hub system dynamics is constructed from the first ten modes of vibration of the system. A reduced-order optimal observer is utilized to estimate the deflection of the beam tip from measurements of the horizontal and vertical deflections of the hub. Two orthogonal actuators are used to manipulate the hub such that the relative motion between the hub and the tip of the beam is minimized. Hence, the demand on the control effort is to force the beam tip and the hub to vibrate as a rigid body. The horizontal control effort is a function of the difference between the measured horizontal hub deflection and the estimated horizontal tip deflection, and the same is true for the vertical control effort. Simulation of the proposed control strategy is carried out and the results are presented.

The finite element analysis and experimental study of beams with active constrained layer damping treatments

Vibration control of structures is confronted with many problems like the proper selection of modelling methods, controllability and observability of models, model size and model reduction methods. In this paper a practical procedure is proposed to overcome technical problems of structure control due to a large model size. Firstly, an accurate numerical model is derived by using the finite element method. This model is verified by modal analysis experiments. Secondly, a new model reduction procedure is proposed to reduce considerably the full order model. This reduction makes the reduced order model controllable and observable. In a further step, a controller is designed based on the verified reduced order model. Finally, a real-time control system is set up. The controlled and uncontrolled impulse responses at the free tip of the cantilever beam with active constrained layer damping treatments are compared both in time domain and frequency domain. The results clearly show the efficiency of the proposed procedure. The procedure proposed in this paper can be extended towards more complex structures.

Electromagnets calibration utilizing the pull-in instability

Precise determination of electromagnetic characteristics is crucial for many applications employing magnetic actuators such as magnetic bearings and precision machine controls. Traditionally, this task is achieved by the constant air gap type of calibration. Although this method can achieve high accuracy, the requirements for dedicated instrumentation and precise machining impose limitations to most users. In this article, an alternative approach utilizing pull-in instability to calibrate electromagnets is presented. The electromagnet to be calibrated exerts a force on the tip of a cantilever beam and causes deflection. The deflection-current curve is recorded to obtain the exact pull-in current. Finally, the electromagnetic force constant can be derived from the pull-in current, the initial air gap, and the equivalent stiffness of the cantilever beam. Experimental results showed that the calibrated force coefficients agreed with those obtained from the standard constant air gap method within 3–10% accuracy. In comparison with the constant air gap method, this approach is potentially cheaper and can achieve an accuracy level sufficient for subsequent robust control purpose.

Modeling and bending vibration control of nonuniform thin-walled rotating beams incorporating adaptive capabilities

This paper addresses the problems of modeling and bending vibration control of tapered rotating blades modeled as nonuniform thin-walled beams and incorporating adaptive capabilities. The blade model incorporates non-classical features such as transverse shear, secondary warping and includes the centrifugal and Coriolis force fields. For the non-adaptive system, an assessment of a number of non-classical features including the taper characteristics is accomplished. The adaptive capabilities are provided by a system of piezoactuators bonded to the structure surface and spread over the entire span of the beam. Based on the converse piezoelectric effect and on the out-of-phase actuation, the piezoactuators produce a localized strain field in response to the applied voltage, and consequently, a change of the dynamic response characteristics is induced. A combined feedback control law relating the piezoelectrically induced transversal bending moment at the beam tip with the kinematical response quantities appropriately selected is used, and the beneficial effects upon the closed-loop dynamic characteristics of the blade are highlighted.

Dynamic analysis and optimal design of a piezoelectric motor.

This article presents the dynamic modeling of a bimodal piezoelectric ceramic motor by use of the finite element method. The extended Hamilton's principle is utilized for formulating dynamic equation of motion, and the Lagrange multiplier method is used to model the contact dynamics between the resonator beam tip and the rotor. The numerical simulation result is approximate to the practical experimental data, which indicates that the modeling and the experiment are fairly accurate. The Taguchi experimental design method is applied to decrease the experimental effort and find the optimal design. This approach shows that the shape of the output head of the motor determines the output performance significantly. The modified shapes of output head also are carried out with a practical experiment to verify the outcomes based on the Taguchi experimental design method.

Dynamic plastic behavior of a free–free beam striking the mid-span of a clamped beam with shear and membrane effects considered

Recently Yu et al. (Int. J. Solids Struct. 38 (2001) 261) made a study on the dynamic behavior of a flying free–free beam striking the tip of a cantilever beam using the rigid, perfectly plastic (r-p-p) material model. Later, also based on the r-p-p material model Yang and Yu (Mech. Struct. Mach. 29 (2001) 391) analyzed another impact problem of a free rotating hinge beam striking a cantilever beam. Both of these studies ignored the finite deflection effects on the plastic behavior of the colliding beams. However if the free–free beam strikes a clamped beam, the influence of finite-deflections, or, geometric changes, must be retained in the governing equation if the maximum permanent transverse displacement of the clamped beam exceeds the corresponding beam thickness. The problem becomes more interesting since the deformation mechanisms of the beam system and the partitioning of energy dissipation in the beams are significantly different from those predicted by ignoring the influence of membrane forces. Accordingly the failure modes of the structure are different. In the present paper, a theoretical model based on the r-p-p material idealization is proposed to simulate the dynamic behavior when the mid-point of a translating free–free beam impinging on the mid-span of a clamped beam with the beam axes perpendicular to each other. The plastic behavior of the beam system is explored with shear sliding and finite deflection effects taken into account. The final deflection, the dissipation of energy within the two beams after impact and the influence of the structural and material parameters are discussed. It is shown that membrane force plays an important role during the response process, especially when the deflection is of the same order as the thickness of the clamped beam.

Plastic modal approximations in analyzing beam-on-beam collisions

Dynamic behavior of a moving free–free beam striking the tip of a cantilever beam, as a typical example of collision between two deformable structures, is analysed by employing modal approximation techniques. The applicability of both rigid-plastic and elastic–plastic mode approximations is examined in predicting the energy partitioning between the two colliding beams. Three rigid-plastic modes (RP-Modes) are considered and the Lee’s functional is applied to select the appropriate mode. It is found that one of the beams would absorb all the initial kinetic energy, unless a higher-order RP-mode is adopted. To incorporate the effect of elastic deformation into the modal solution, an elastic, perfectly plastic mode (EP-Mode) approximation for the same problem is proposed. By replacing each of the plastic hinges in the RP-Mode with a nature hinge and an elastic–plastic rotational spring, the fundamental features of the dynamic elastic–plastic behavior of the two colliding beams are revealed. Both beams participate in energy dissipation, while the structural and geometrical parameters greatly influence the energy partitioning. It is shown from numerical examples that the EP-Mode solution provides a fairly good approximation compared with the RP complete solution and finite element simulation.

Genetic fuzzy system for damage detection in beams and helicopter rotor blades

Structural damage detection is an inverse problem of structural engineering having three main parts: finding the existence, location and extent of damage. In this study, a genetic fuzzy system is used to find the location and extent of damage. A finite element model of a cantilever beam is used to calculate the change in beam frequencies because of structural damage. Using these changes in frequencies, a fuzzy system is generated and the rule-base and membership functions optimized by genetic algorithm. The output faults of the fuzzy system are four levels of damage (undamaged, slight, moderate, and severe) at five locations along the beam (root, inboard, center, outboard and tip). The genetic fuzzy system developed for a noise level of 0.20 in the data gives a fault isolation success rate of 99.81% when the first eight natural frequencies are used. With noise level of 0.15 and 0.10, accuracy rates of 100% are obtained even when only the first four natural frequencies are used. The fuzzy system also shows excellent robustness with missing measurements and degrades gradually in the presence of faulty sensors/measurements. The genetic fuzzy system allows easy rule generation for different structures and when the number of inputs and outputs increase, thereby avoiding the ‘curse of dimensionality’ that plagues fuzzy systems. Results with a non-uniform beam and a finer output set of damage at 10 locations in the beam also show excellent results. The genetic fuzzy system also gives very good results for BO-105 hingeless helicopter rotor blade for frequency as well as mode shape-based data. The genetic fuzzy logic system in this study is proposed as a method for automatic rule generation in fuzzy systems for structural damage detection.

Modeling and vibration feedback control of rotating tapered composite thin-walled blade

This paper addresses the problem of the modeling and vibration control of tapered rotating blade modeled as thin-walled beams and incorporating damping capabilities. The blade model incorporates non-classical features such as anisotropy, transverse shear, secondary warping and includes the centrifugal and Coriolis force fields. For the rotating blade system, a thorough validation and assessment of a number of non-classical features including the taper characteristics is accomplished. The damping capabilities are provided by a system of piezoactuators bonded or embedded into the structure and spread over the entire span of the beam. Based on the converse piezoelectric effect, the piezoactuators produce a localized strain field in response to a voltage and consequently, a change of the dynamic response characteristics is induced. A velocity feedback control law relating the piezoelectrically induced transversal bending moment at the beam tip with the appropriately selected kinematical response quantity is used and the beneficial effects upon the closed-loop dynamic characteristics of the blade are highlighted.

Closed-form analysis of thin-walled composite I-beams considering non-classical effects

In this work, a closed-form analysis of thin-walled open profile composite beams such as I-beam has been performed. The analysis includes the effects of elastic couplings, shell wall thickness, transverse shear deformation, torsion warping, and constrained warping. A mixed beam approach based on Reissner’s semi-complementary energy functional is used to derive the beam force–displacement relations. A closed-form solution for the static response of both symmetric and anti-symmetric layup beams with transverse shear couplings is derived. The beams considered have the boundary condition of one end fixed and the other end warping restrained and are subjected to unit bending or torque load at the beam tip. The shear flow distribution related with the applied forces and moments along the contour of the beam is also identified. The static results of composite I-beams have been validated against those of detailed two-dimensional finite element analysis. The effects of warping restraint and transverse shear deformation on the static behavior of open-section composite beams are investigated in the analysis.

OPTIMAL VIBRATION ESTIMATION OF A NON-LINEAR FLEXIBLE BEAM MOUNTED ON A ROTATING COMPLIANT HUB

To eliminate the need for sensor placement on rotating flexible beams such as turbine blades, helicopter rotors and like applications, a new approach has been developed based on the linear quadratic estimator (LQE) technique for estimating the vibration of any point on the span of a rotating flexible beam mounted on a compliant hub ( plant) in the presence of process and measurements noise. A non-linear model of the plant is utilized in this study to mimic the actual plant behavior. The corresponding plant dynamics of the LQE are in the form of a reduced order linear model constructed from the eigenvalues and eigenfuctions of a finite element dynamic model of the plant formulated in the state space. A virtual hub deflection (that mimics the actual measurement of the vertical hub deflection needed by the estimation process) is generated by the non-linear model of the plant. The LQE reconstructs the states of the plant, including transverse deflection of the beam at any point, from the measurements of the vertical deflection of the hub, assuming that it is the most accessible state for measurement. Estimated beam tip deflection obtained by the proposed technique is then compared to the tip deflection generated by the non-linear model and the results show good agreement.

Vibration and stability control of robotic manipulator systems consisting of a thin‐walled beam and a spinning tip rotor

AbstractVibration and stability feedback control of a robotic manipulator modeled as a cantilevered thin‐walled beam carrying a spinning rotor at its tip is investigated. The control is achieved via incorporation of adaptive capabilities that are provided by a system of piezoactuators, bonded or embedded into the host structure. Based on converse piezoelectric effect, the piezoactuators produce a localized strain field in response to an applied voltage, and as a result, an adaptive change of vibrational and stability response characteristics is obtained. A feedback control law relating the piezoelectrically induced bending moments at the beam tip with the appropriately selected kinematical response quantities is used, and the beneficial effects of this control methodology upon the closed‐loop eigenvibration characteristics and stability boundaries are highlighted. The cantilevered structure modeled as a thin‐walled beam, and built from a composite material, encompasses non‐classical features, such as anisotropy, transverse shear, and secondary warping, and in this context, a special ply‐angle configuration inducing a structural coupling between flapping‐lagging and transverse shear is implemented. It is also shown that the directionality property of the material of the host structure used in conjunction with piezoelectric strain actuation capability, yields a dramatic enhancement of both the vibrational and stability behavior of the considered structural system. © 2002 Wiley Periodicals, Inc.

DYNAMIC CHARACTERISTICS OF STEPPED CANTILEVER BEAMS CONNECTED WITH A RIGID BODY

The object of this work is to analyze the dynamic characteristics of the portal frame which consists of two stepped beams including a thin plate and a torsional spring at the discontinuous point and a rigid body connecting each beam tip. This structure is available in a lot of cases that need higher stiffness and linear motion of the tip mass. For example, it might be used for an optical pick-up actuator, using piezoelectric materials, for the high area density CD, DVD or the next generation of optical memory devices, which require superrigidity and linear motion in focusing. The mathematical modelling and the derivation of the equation of motion are given for the cantilevers with identically paralleled and stepped beams. The equation of motion and the associated boundary and the continuous conditions are analytically obtained by using Hamilton's variational principle. The exact solutions are presented and compared with the results obtained by FEM Tool (IDEAS).

Modeling of Flexural Beams Subjected to Arbitrary End Loads

The analysis of compliant mechanisms is often complicated due to the geometric nonlinearities which become significant with large elastic deflections. Pseudo rigid body models (PRBM) may be used to accurately and efficiently model such large elastic deflections. Previously published models have only considered end forces with no end moment or end moment acting only in the same direction as the force. In this paper, we present a model for a cantilever beam with end moment acting in the opposite direction as the end force, which may or may not cause an inflection point. Two pivot points are used, thereby increasing the model’s accuracy when an inflection point exists. The Bernoulli-Euler beam equation is solved for large deflections with elliptic integrals, and the elliptic integral solutions are used to determine when an inflection point will exist. The beam tip deflections are then parameterized using a different parameterization from previous models, which renders the deflection paths easier to model with a single degree of freedom system. Optimization is used to find the pseudo rigid body model which best approximates the beam deflection and stiffness. This model, combined with those models developed for other loading conditions, may be used to efficiently analyze compliant mechansims subjected to any loading condition.

Shear strengthening of beam-column joints

Shear failure of beam-column joints is identified as the principal cause of collapse of many moment-resisting frame buildings during recent earthquakes. Effective and economical rehabilitation techniques for the upgrade of the joint shear-resistance capacity in existing structures are needed. The objective of this research is to develop effective selective rehabilitation schemes for reinforced concrete beam-column joints using advanced composite materials. Several reinforced concrete beam-column joints were constructed. The joints were designed to simulate nonductile detailing characteristics of pre-seismic code construction. The control specimens showed joint shear failure when subjected to cyclic loading at the beam tip. Different fibre-wrap rehabilitation schemes were applied to the joint panel with the objective of upgrading the shear strength of the joint. The tested rehabilitation techniques were successful in improving the shear resistance of the joint and in eliminating or delaying the shear mode of failure.

Dynamic Behavior of Elastically Tailored Rotating Blades Modeled as Pretwisted Thin‐Walled Beamsand Incorporating Adaptive Capabilities

A number of issues related with the vibrational behavior of rotating blades modeled as pretwisted thin-walled anisotropic beams, incorporating adaptive capabilities are addressed. The adaptive capabilities are provided by a system of piezoactuators bonded or embedded into the structure. Based on the converse piezoelectric e€ect and on the out-of-phase activation, boundary control moments are piezoelectrically induced at the beam tip. A feedback control law relating the induced bending moments with the kinematical response quantities appropriately selected is used, and its bene®cial e€ects, considered in conjunction with that of the beam anisotropy and structural pretwist upon the closed/open loop eigenvibration characteristics are highlighted.

A bidirectional magnetic microactuator using electroplated permanent magnet arrays

A novel bidirectional magnetic microactuator using electroplated permanent magnet arrays has been designed, fabricated and characterized. To realize a bidirectional microactuator, CoNiMnP-based permanent magnet arrays have been fabricated first on a silicon cantilever beam using a new electroplating technique. In the fabricated permanent magnets, the vertical coercivity and retentivity have been achieved up to 87.6 kA/m (1100 Oe) and 190 mT (1900 G), respectively by applying magnetic field during electroplating. A prototype bidirectional magnetic microactuator has been realized by integrating an electromagnet with a silicon cantilever beam, which has permanent magnet arrays on its tip. By applying a do current of 100 mA and altering its polarity, bidirectional motion on the tip of the cantilever beam has been successfully achieved in the deflection range of /spl plusmn/80 /spl mu/m.

3219 皮膚表面粗さ・硬さ計測用センサシステムの開発

This paper is a study on the development of a haptic sensor system for monitoring skin conditions. The base of the sensor is a copper shell, around which a rubber sponge layer, PVDF film, a protective layer of acetate film and gauze are applied in sequence. The sensor is attached to the tip of an elastic cantilevered beam and pressed against an area of skin. It is then slide over the skin to collect surface morphological features. Through the fundamental experiment using the artificial objects, the surface roughness and softness are evaluated visually by using Symmetrized Dot Pattern. The sensor system is then applied to the clinical test. Results show that the sensor output well describes the skin conditions.

Tactile Differentiator.

This paper proposes the Tactile Differentiator that can enhance the edge of polygonal surface through tracing motion. It is composed of a flexible beam anchored at the base with a moment sensor, and an actuator for moving the whole system. When the beam tip passes over the edge where two different planes are intersected with an arbitrary angle, the Tactile Differentiator provides a step change of output, as if it were just like a differentiator. The edge enhancement factor of sensor is introduced with the shape of beam, the intersection angle of environment, and the contact friction. By using the factor, the design orientation of the sensor is discussed. Experimental results are also shown to verify the basic idea.

W-1-3-4 STABILITY PROPERTIES OF CONTROLLED FLEXIBLE ARM : THEORETICAL AND EXPERIMENTAL ASPECTS

For vision-based controlled flexible arm, the accuracy of the finite dimensional dynamic models and stability become very important for controller design. This paper designs suitable controller for a flexible arm with vision-based control. Input of the controller is the measured position error of the beam tip, which can be directly obtained by camera. In spite of the observed differences of results between actual system and simulated system, the results are good enough to validate the arm model. Simulation and experimental results show that the PID controller is acceptable. It is also stressed that two limiting factors, which are the camera sampling rate and a dead band in the velocity command, will influence the properties of the control system for vision-based controlled flexible arm.