• Computers and Concrete
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• v.32 no.6
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• pp.543-551
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• 2023

In this article, thermal post-buckling and primary resonance of the porous functionally graded material (FGM) beams in thermal environment considering the geometric imperfection are studied, the material properties of FGM beams are assumed to vary along the thickness of the beam, meanwhile, the porosity volume fraction, geometric imperfection, temperature, and the elastic foundation are considered, using the Euler-Lagrange equation, the nonlinear vibration equations are derived, after the dimensionless processing, the dimensionless equations of motion can be obtained. Then, the two-step perturbation method is applied to solve the vibration problems, the resonance and thermal post-buckling response relations are obtained. Finally, the functionally graded index, the porosity volume fraction, temperature, geometric imperfection, and the elastic foundation on the resonance behaviors of the FGM beams are presented. It can be found that these parameters can influence the thermal post-buckling and primary resonance problems.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.7
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• pp.502-507
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• 2016

In this paper, we propose a tracking control method for a quadrotor equipped with a 2-DOF manipulator, which is based on the multiple sliding surface control (MSSC) method. To derive the model of a quadrotor equipped with a 2-DOF manipulator, we obtain the models of a quadrotor and a 2-DOF manipulator based on the Lagrange-Euler formulation separately - and include the inertia and the reactive torque generated by a manipulator when these obtained models are combined. To make a quadrotor equipped with a manipulator track the desired path, we design a double-loop controller. The desired position is converted into the desired angular position in the outer controller and the system's angle tracks the desired angular position through the inner controller based on the MSSC method. We prove that the position-tracking error asymptotically converges to zero based on the Lyapunov stability theory. Finally, we demonstrate the effectiveness of the proposed control system through a computer simulation.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.318-322
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• 1996

This paper presents a technique to control a robot which has a flexible manipulator moving in a vertical plane. The flexible manipulator is modeled as an Euler-Bernoulli beam. Elastic deformation 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. A control algorithm is developed using a simple PID control technique. The proportional, integral and derivative control gains are determined based on the dominant pole placement method and tuned to show no overshoot and having a short settling time. The effectiveness of the developed control scheme is showed experimentally. In the position control experiment, three different end masses are used. The experimental results shows little overshoot, no steady state error, and less than 2.5 second settling time in case of having an end mass which is equivalent to 45% of the total system weight. Also the residual vibration of the end point is effectively controlled.

• The Journal of the Korea institute of electronic communication sciences
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• v.16 no.1
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• pp.151-156
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• 2021

The speed and direction of the earth's fluid motion is measured by a remote sensing method using electromagnetic waves. Using UHF radar and GPS Sonde, the vertical profile of fluid velocity was calculated by the Euler measurement method and the Lagrange measurement method, respectively. Since the wind direction, which is the direction of motion of the atmosphere, is indicated in the direction of the wind blowing, and a circular value of 0° - 360° is used, it is necessary to pay attention to statistical analysis. Errors caused by calculation conditions are provided, and the corrected accuracy of comparison results is improved by 400%.

• 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.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2004.05a
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• pp.204-209
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• 2004

This paper describes dynamic manipulability analysis of robotic arms moving in viscous fluid. The Manipulability is a functionality of manipulator system in a given configuration and under the limits of joint ability with respect to the tasks required to bt performed. To investigate the manipulability of underwater robotic arms, a modeling and analysis method are presented. The dynamic equation of motion of underwater manipulator is derived from the Lagrange - Euler equation considering with the hydraulic forces caused by added mass, buoyancy and hydraulic drag. The hydraulic drag term in the equation: is established as analytical form using Denavit - Hartenberg (D-H) link coordination of manipulator. Two analytical approaches based on Manipulability Ellipsoid are presented to visualize the manipulability of robotic arm moving in viscous fluid. The one is scaled ellipsoid which transforms the boundary of joint torque to acceleration boundary of end-effector by normalizing the torque in joint space while the other is shifted ellipsoid which depicts total acceleration boundary of end-effector by shifting the ellipsoid in work space. An analysis example of 2-link manipulator with proposed analysis scheme is presented to validate the method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.12
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• pp.2012-2018
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• 2004

The vibration of a semi-circular pipe conveying fluid is studied when the pipe is clamped at both ends. To consider the geometric nonlinearity, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived from the Galerkin method. The natural frequencies varying with the flow velocity are computed from the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized-$\alpha$ method. From these results, we should consider the geometric nonlinearity to analyze dynamics of a semi-circular pipe conveying fluid more precisely.

• Structural Engineering and Mechanics
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• v.46 no.3
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• pp.417-431
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• 2013

This paper presents responses of the free end of a cantilever micro beam under the effect of an impact force based on the modified couple stress theory. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Bernoulli-Euler beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the difference of the modified couple stress theory and the classical beam theory is investigated for the wave propagation. A few of the obtained results are compared with the previously published results. The influences of the material length scale parameter on the wave propagation are investigated in detail. It is clearly seen from the results that the classical beam theory based on the modified couple stress theory must be used instead of the classical theory for small values of beam height.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.677-682
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• 2003

The non-linear dynamic characteristics of a semi-circular pipe conveying fluid are investigated when the pipe is clamped at both ends. To consider the geometric non-linearity for the radial and circumferential displacements, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived form the Galerkin method. The natural frequencies varying with the flow velocity are computed fen the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized- method. From these results, we should to describe the non-linear behavior to analyze dynamics of a semi-circular pipe conveying fluid more precisely.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.8
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• pp.688-695
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• 2005

This paper describes dynamic manipulability analysis of robotic arms moving in viscous fluid. The manipulability is a functionality of manipulator system in a given configuration under the limits of joint ability with respect to the task required to be performed. To investigate the manipulability of underwater robotic arms, a modeling and analysis method is presented. The dynamic equation of motion of underwater manipulator is derived based on the Lagrange-Euler equation considering with the hydrodynamic forces caused by added mass, buoyancy and hydraulic drag. The hydrodynamic drag term in the equation is established as analytical form using Denavit-Hartenberg (D-H) link coordination of manipulator. Two analytical approaches based oil manipulability ellipsoid are presented to visualize the manipulability of robotic arm moving in viscous fluid. The one is scaled ellipsoid which transforms the boundary of joint torque to acceleration boundary of end-effector by normalizing the torques in joint space, while the other is shifted ellipsoid which depicts total acceleration boundary of end-effector by shifting the ellipsoid as much as gravity and velocity dependent forces in work space. An analysis example of 2-link manipulator with proposed analysis scheme is presented to validate the method.