• Journal of the Korean Society for Precision Engineering
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• v.13 no.11
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• pp.132-142
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• 1996

This paper presents a technique to model and control a manipulator which has a flexible link and moves in a vertical plane. The flexible link is modeled as an Euler-Bernoulli Beam. Elastic deformation of the flexible link is represented using the assumed modes method. A comparison function which satisfies all geometric and natural boundary conditions of a cantilever beam with an end mass is used as an assumed mode shape. Lagrange's equation is utilized for the development of a discretized model. This paper presents a simple technique to improve the correctness of the developed model. The final model including the shortening effect due to elastic deformation correlates very well with experimental results. The free body motion simulation shows that two assumed modes for the representation of the elastic deformation is proper in terms of the model size and correctness. A control algorithm is developed using PID control technique. The proportional, integral and derivative control gains are determined based on dominant pole placement method with a rigid one-link manipulator. A position control simulation shows that the control algorithm can be used to control the position and residual oscillation of the flexible one-link manipulator effectively.

• Steel and Composite Structures
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• v.42 no.1
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• pp.75-90
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• 2022

The pointwise equilibrium polynomial (PEP) element considering local second-order effect has been widely used in direct analysis of many practical engineering structures. However, it was derived according to Euler-Bernoulli beam theory and therefore it cannot consider shear deformation, which may lead to inaccurate prediction for deep beams. In this paper, a novel beam-column element based on Timoshenko beam theory is proposed to overcome the drawback of PEP element. A fifth-order polynomial is adopted for the lateral deflection of the proposed element, while a quadric shear strain field based on equilibrium equation is assumed for transverse shear deformation. Further, an additional quadric function is adopted in this new element to account for member initial geometrical imperfection. In conjunction with a reliable and effective three-dimensional (3D) co-rotational technique, the proposed element can consider both member initial imperfection and transverse shear deformation for second-order direct analysis of frame structures. Some benchmark problems are provided to demonstrate the accuracy and high performance of the proposed element. The significant adverse influence on structural behaviors due to shear deformation and initial imperfection is also discussed.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.12
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• pp.143-152
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• 1997

The deflection of an end mill is very important in machining process and cutting simulation because it affects directly workpiece accuracy, cutting force, and chattering. In this study, the deflection of the end mill was studied both experimentally and by using finite element analysis. And the moment of inertia of cross sections of the helical end mill is calculated for the determination of the relation between geometry of radial cross section and rigidity of the tools. Using the Bernoulli-Euler beam theory and the concept of equivalent diameter, a deflection model is established, which includes most influences from tool geomety parameters. It was found that helix angle attenuates the rigidity of the end mill by the finite element analysis. As a result, the equivalent diameter is determined by tooth number, inscribed diameter ratio, cross sectional geometry and helix angle. Because the relation betweem equivalent diameter and each factor is nonlinear, neural network is used to decide the equivalent diameter. Input patterns and desired outputs for the neural network are obtained by FEM analysis in several case of end milling operations.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.11
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• pp.34-41
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• 1997

This paper presents a technique to control a very flexible robot moving in a vertical plane. The flexible robot is modeled as an Euler-Bernoulli beam. Elastic deformation is approximated using the assmed modes method. A comparison function which satisfies all geometric and natural boundary conditions of a cantilever beam with an end mass is used as an assumed mode shape. Lagrange's equation is utilized for the development of a discretized model. A control algorithm is developed using a simple PID cnotrol tech- nique. The proportional, integral and deivative control gains are determined based on the dominant pole placement method and tuned to show no overshoot and no steady state error, and short settling time. The effectiveness of the developed control scheme is showed in the hub angular diaplacement control experiment. Three different end masses are uned in the experiment. The experimental results show that developed control algorithm is very effective showing little overshoot, no steady state error, and less than 2.5 second settl- ing time in case of having an end mass which is equivalent to 45% of the manipulator mass. Also the experimental results show that the residual vibration fo the end point is effectively controlled.

• Smart Structures and Systems
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• v.29 no.5
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• pp.705-714
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• 2022

In this paper, the effect of magnetic field on the vibration behavior of a Magnetorheological elastomer (MRE) sandwich MEMS actuated by electrostatic actuation with conductive skins are examined within the multiple scales (MMS) perturbation method. Magnetorheological smart materials have been widely used in vibration control of various systems due to their mechanical properties change under the influence of different magnetic fields. To investigate the vibrational behavior of the movable electrode, the Euler-Bernoulli beam theory, as well as Hamilton's principle is used to derive the equations and the related boundary conditions governing the dynamic behavior of the system are applied. The results of this study show that by placing the Magnetorheological elastomer core in the movable electrode and applying different magnetic fields on it, its natural vibrational frequency can be affected so that by increasing the applied magnetic field, the system's natural frequency increases. Also, the effect of various factors such as the electric potential difference between two electrodes, changes in the thickness of the core and the skins, electrode length, the distance between two electrodes and also change in vibration modes of the system on natural frequencies have been investigated.

• Advances in aircraft and spacecraft science
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• v.10 no.3
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• pp.257-279
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• 2023

This manuscript is dedicated to deriving the closed form solutions of free vibration of viscoelastic nanobeam embedded in an elastic medium using nonlocal differential Eringen elasticity theory that not considered before. The kinematic displacements of Euler-Bernoulli and Timoshenko theories are developed to consider the thin nanobeam structure (i.e., zero shear strain/stress) and moderated thick nanobeam (with constant shear strain/stress). To consider the internal damping viscoelastic effect of the structure, Kelvin/Voigt constitutive relation is proposed. The perforation geometry is intended by uniform symmetric squared holes arranged array with equal space. The partial differential equations of motion and boundary conditions of viscoelastic perforated nonlocal nanobeam with elastic foundation are derived by Hamilton principle. Closed form solutions of damped and natural frequencies are evaluated explicitly and verified with prestigious studies. Parametric studies are performed to signify the impact of elastic foundation parameters, viscoelastic coefficients, nanoscale, supporting boundary conditions, and perforation geometry on the dynamic behavior. The closed form solutions can be implemented in the analysis of viscoelastic NEMS/MEMS with perforations and embedded in elastic medium.

• Advances in aircraft and spacecraft science
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• v.10 no.5
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• pp.419-437
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• 2023

This paper presents the study of the effects of rigid-body motion simultaneously with the presence of the effects of temporal variation due to the existence of morphing speed on the aeroelastic stability of the two-stage telescopic wings, and hence this is the main novelty of this study. To this aim, Euler-Bernoulli beam theory is used to model the bending-torsional dynamics of the wing. The aerodynamic loads on the wing in an incompressible flow regime are determined by using Peters' unsteady aerodynamic model. The governing aeroelastic equations are discretized employing a finite element method based on the beam-rod model. The effects of rigid-body motion on the length-based stability of the wing are determined by checking the eigenvalues of system. The obtained results are compared with those available in the literature, and a good agreement is observed. Furthermore, the effects of different parameters of rigid-body such as the mass, radius of gyration, fuselage center of gravity distance from wing elastic axis on the aeroelastic stability are discussed. It is found that some parameters can cause unpredictable changes in the critical length and frequency. Also, paying attention to the fuselage parameters and how they affect stability is very important and will play a significant role in the design.

• Advances in aircraft and spacecraft science
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• v.11 no.1
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• pp.55-81
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• 2024

This paper presents the exact solutions and closed forms for of nonlinear stability and vibration behaviors of straight and curved beams with nonlinear viscoelastic boundary conditions, for the first time. The mathematical formulations of the beam are expressed based on Euler-Bernoulli beam theory with the von Karman nonlinearity to include the mid-plane stretching. The classical boundary conditions are replaced by nonlinear viscoelastic boundary conditions on both sides, that are presented by three elements (i.e., linear spring, nonlinear spring, and nonlinear damper). The nonlinear integro-differential equation of buckling problem subjected to nonlinear nonhomogeneous boundary conditions is derived and exactly solved to compute nonlinear static response and critical buckling load. The vibration problem is converted to nonlinear eigenvalue problem and solved analytically to calculate the natural frequencies and to predict the corresponding mode shapes. Parametric studies are carried out to depict the effects of nonlinear boundary conditions and amplitude of initial curvature on nonlinear static response and vibration behaviors of curved beam. Numerical results show that the nonlinear boundary conditions have significant effects on the critical buckling load, nonlinear buckling response and natural frequencies of the curved beam. The proposed model can be exploited in analysis of macrosystem (airfoil, flappers and wings) and microsystem (MEMS, nanosensor and nanoactuators).

• Steel and Composite Structures
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• v.52 no.5
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• pp.501-513
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• 2024

Two-directional functionally graded materials (2D-FGMs) show extraordinary physical properties which makes them ideal candidates for designing smart micro-switches. Pull-in instability is one of the most critical challenges in the design of electrostatically-actuated microswitches. The present research aims to bridge the gap in the static pull-in instability analysis of microswitches composed of 2D-FGM. Euler-Bernoulli beam theory with geometrical nonlinearity effect (i.e. von-Karman nonlinearity) in conjunction with the modified couple stress theory (MCST) are employed for mathematical formulation. The micro-switch is subjected to electrostatic actuation with fringing field effect and Casimir force. Hamilton's principle is utilized to derive the governing equations of the system and corresponding boundary conditions. Due to the extreme nonlinear coupling of the governing equations and boundary conditions as well as the existence of terms with variable coefficients, it was difficult to solve the obtained equations analytically. Therefore, differential quadrature method (DQM) is hired to discretize the obtained nonlinear coupled equations and non-classical boundary conditions. The result is a system of nonlinear coupled algebraic equations, which are solved via Newton-Raphson method. A parametric study is then implemented for clamped-clamped and cantilever switches to explore the static pull-in response of the system. The influences of the FG indexes in two directions, length scale parameter, and initial gap are discussed in detail.

• Earthquakes and Structures
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• v.27 no.4
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• pp.263-283
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• 2024

This research introduces a new composite system that utilizes multiple moving masses to identify cracks in structures resembling beams. The process starts by recording displacement time data from a set of these moving masses and converting this information into a relative time history through weighted aggregation. This relative time history then undergoes wavelet transform analysis to precisely locate cracks. Following wavelet examinations, specific points along the beam are determined as potential crack sites. These points, along with locations on the beam susceptible to cracked point due to support conditions, are marked as crack locations within the optimization algorithm's search domain. The model uses equations of motion based on the finite element method for the moving masses on the beam and employs the Runge-Kutta numerical solution within the state space. The proposed system consists of three successive moving masses positioned at even intervals along the beam. To assess its effectiveness, the method is tested on two examples: a simply supported beam and a continuous beam, each having three scenarios to simulate the presence of one or multiple cracks. Additionally, another example investigates the influence of mass speed, spacing between masses, and noise effect. The outcomes showcase the method's effectiveness and efficiency in localizing crack, even in the presence of noise effect in 1%, 5% and 20%.