• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.2
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• pp.298-309
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• 1990

In this paper, a new method is suggested to analyze impulsive stresses at loading poing of concentrated impact load under certain impact conditions determined by impact velocity, stiffness of plate and mass of impact body, etc. The impulsive stresses are analyzed by using the three dimensional dynamic theory of elasticity so as to analytically clarify the generation phenomenon of cone crack at the impact fracture of fragile materials (to be discussed if the second paper). The Lagrange's plate theory and Hertz's law of contact theory are used for the analysis of impact load, and the approximate equation of impact load is suggested to analyze the impulsive stresses at the impact point to decide the ranage of impact load factor. When impact load factors are over and under 0.263, approximate equations are suggested to be F(t)=Aexp(-Bt)sinCt and F(t)=Aexp(-bt) {1-exp(Ct)} respectively. Also, the inverse Laplace transformation is done by using the F.F.T.(fast fourier transform) algorithm. And in order to clarity the validity of stress analysis method, experiments on strain fluctuation at impact point are performed on a supported square glass plate. Finally, these analytical results are shown to be in close agreement with experimental results.

• Wind and Structures
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• v.22 no.3
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• pp.349-368
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• 2016

A preconditioning technique is presented for a simultaneous solution to wind-membrane interaction. In the simultaneous equations, a linear elastic model was employed to deal with the fluid-structure data transfer at the interface. A Lagrange multiplier was introduced to impose the specified boundary conditions at the interface and strongly coupled simultaneous equations are derived after space and time discretization. An initial linear elastic model preconditioner and modified one were derived by treating the linearized elastic model equation as a saddle point problem, respectively. Accordingly, initial and modified fluid-structure interaction (FSI) preconditioner for the simultaneous equations were derived based on the initial and modified linear elastic model preconditioners, respectively. Wind-membrane interaction analysis by the proposed preconditioners, for two and three dimensional membranous structures respectively, was performed. Comparison was made between the performance of initial and modified preconditioners by comparing parameters such as iteration numbers, relative residuals and convergence in FSI computation. The results show that the proposed preconditioning technique greatly improves calculation accuracy and efficiency. The priority of the modified FSI preconditioner is verified. The proposed preconditioning technique provides an efficient solution procedure and paves the way for practical application of simultaneous solution for wind-structure interaction computation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11a
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• pp.155-160
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• 2001

Actual engineering structure is frequently very complex, and parts of structure are designed independently by different engineers. Also each structure contains so many degree of freedom. For these reason, methods have been developed which permits the structure to be divided into components or substructures, with analysis being done on a small substructure in order to obtain a full structural system. In such case, because of different mesh size among finite element model (FEM) or different matching points among FEM models and experimentally obtained models, their interfacing points may be non-matching. Solving this non-matching problem is useful to other application such as structural dynamic modification or model updating. In this work, virtual node concept is introduced. Lagrange multipliers are used to enforce the interface compatibility constraint, and interface displacement is approximated by polynomial presentation. The governing equation of whole structure is derived using hybrid variational principle. The eigenvalue of whole structure are calculated using the determinant search method. The number of degree of freedom in the eigenvalue problem can be drastically reduced to just the number of interface degree of freedom. Some numerical simulation is performed to show usefulness of synthesis method.

• Structural Engineering and Mechanics
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• v.51 no.3
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• pp.377-402
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• 2014

In this study, optimal distribution of springs which supports a cantilever beam is investigated to minimize two objective functions defined. The optimal size and location of the springs are ascertained to minimize the tip deflection of the cantilever beam. Afterwards, the optimization problem of springs is set up to minimize the tip absolute acceleration of the beam. The Fourier Transform is applied on the equation of motion and the response of the structure is defined in terms of transfer functions. By using any structural mode, the proposed method is applied to find optimal stiffness and location of springs which supports a cantilever beam. The stiffness coefficients of springs are chosen as the design variables. There is an active constraint on the sum of the stiffness coefficients and there are passive constraints on the upper and lower bounds of the stiffness coefficients. Optimality criteria are derived by using the Lagrange Multipliers. Gradient information required for solution of the optimization problem is analytically derived. Optimal designs obtained are compared with the uniform design in terms of frequency responses and time response. Numerical results show that the proposed method is considerably effective to determine optimal stiffness coefficients and locations of the springs.

• Smart Structures and Systems
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• v.26 no.5
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• pp.641-656
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• 2020

The finite element solutions of thermal buckling load values of the graded sandwich curved shell structure are reported in this research using a higher-order kinematic model including the shear deformation effect. The numerical buckling temperature has been computed using an in-house specialized code (MATLAB environment) prepared in the framework of the current mathematical formulation. In addition, the mathematical model includes the excess structural distortion under the influence of elevated environment via Green-Lagrange nonlinear strain. The corresponding eigenvalue equation has been solved to predict the critical buckling temperature of the graded sandwich structure. The numerical stability and the accuracy of the current solution have been confirmed by comparing with the available published results. Thereafter, the model is extended to bring out the influences of structural parameters i.e. the curvature ratio, core-face thickness ratio, support conditions, power-law indices and sandwich types on the thermal buckling behavior of graded sandwich curved shell panels.

• Journal of the Korean Institute of Intelligent Systems
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• v.21 no.2
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• pp.192-197
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• 2011

In this paper, the output feedback control of inverted pendulum systems is experimented for the practicality verification of the linear state observer. For the experiment, a pendulum system, CEM-IP-01 of Cemware Inc. is used and Lagrange equation and Jacobian linearization are adopted for the dynamic analysis of the pendulum system. In addition, the output responses of the state feedback control and the output feedback control of the pendulum system are compared before the experiment by Matlab. Finally, we directly verify the practical use of the linear state observer by recognizing and solving some real problem to control the inverted pendulum system in practice.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.666-671
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• 2002

For a large structure, substructure based SDM(structural dynamics modification) method is very effective to raise its dynamic characteristics. Dividing into smaller substructures has a major advantage in the aspect of computation especially for getting sensitivities, which are in the core of SDM process. But quite often, non-matching nodes problem occurs in the process of synthesizing substructures. The reason is that, in general, each substructure is modelled separately, then later combined together to form a entire structure model under interface constraint conditions. Without solving the non-matching nodes problem, the substructure based SDM can not be processed. In this work, virtual node concept is introduced. Lagrange multipliers are used to enforce the interface compatibility constraint. The governing equation of whole structure is derived using hybrid variational principle. The eigenvalues of whole structure are calculated using determinant search method. The number of degrees of freedom of the eigenvalue problem can be drastically reduced to just the number of interface degree of freedom. Thus, the eigenvalue sensitivities can be easily calculated, and further SDM can be efficiently performed. Some numerical problems are tested to show the effectiveness of handling non-matching nodes.

• Journal of the Korean Society of Industry Convergence
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• v.19 no.2
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• pp.81-87
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• 2016

This paper presents a new approach to control of stable motion of single wheel driving robot system of a pitch that is controlled by an in-wheel motor and a roll that is controlled by a reaction wheel. This robot doesn'thave any actuator for a yaw axis control, which makes the derivation of the dynamics relatively simple. The Lagrange equations was applied to derive the dynamic equations of the one wheel driving robot to implement the dynamic speed control of the mobile robot. To achieve the real time speed control of the unicycle robot, the sliding mode control and optical regulator are utilized to prove the reliability while maintaining the desired speed tracking performance. In the roll controller, the sigmoid-function based robust controller has been adopted to reduce the vibration by the situation function. The optimal controller has been implemented for the pitch control to drive the unicycle robot to follow the desired velocity trajectory in real time using the state variables of pitch angle, angular velocity, angle and angular velocity of the driving wheel. The control performance of the control systems from a single dynamic model has been illustrated by the real experiments.

• Journal of Aerospace System Engineering
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• v.7 no.2
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• pp.1-7
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• 2013

Recently, there are a number of studies over dynamic analysis for minimizing vibration of flexible structures such as solar panel for agility of high-agility satellite. The traditional studies perform dynamic analysis of a solar panel assumed as rigid structure since the stiffness of solar panel is higher than the stiffness of solar panel's hinge spring. However, there are vibrations that have modes of bending and torsion when high-agility satellite rotate speedily. This vibrations result in delaying safety time of satellite or degrading image quality. This paper presents dynamic analysis's technique of satellites including the spring hinge of solar panel and flexible structural solar panel's effects described as the linear equation of motion using Lagrange's theorem, and verifies the validity of an established dynamic analysis's technique of satellites by comparing the finite element method. In addition high-agility satellite's dynamic characteristics of a torque profile are analyzed from the established dynamic analysis's technique of satellites.