• Structural Engineering and Mechanics
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• 제17권1호
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• pp.1-14
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• 2004

Numerical solution to linear bending analysis of circular plates is obtained by the method of harmonic differential quadrature (HDQ). In the method of differential quadrature (DQ), partial space derivatives of a function appearing in a differential equation are approximated by means of a polynomial expressed as the weighted linear sum of the function values at a preselected grid of discrete points. The method of HDQ that was used in the paper proposes a very simple algebraic formula to determine the weighting coefficients required by differential quadrature approximation without restricting the choice of mesh grids. Applying this concept to the governing differential equation of circular plate gives a set of linear simultaneous equations. Bending moments, stresses values in radial and tangential directions and vertical deflections are found for two different types of load. In the present study, the axisymmetric bending behavior is considered. Both the clamped and the simply supported edges are considered as boundary conditions. The obtained results are compared with existing solutions available from analytical and other numerical results such as finite elements and finite differences methods. A comparison between the HDQ results and the finite difference solutions for one example plate problem is also made. The method presented gives accurate results and is computationally efficient.

• Structural Engineering and Mechanics
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• 제72권2호
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• pp.229-244
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• 2019

Weak form integral equations are developed to investigate the flapwise bending vibration of the rotating beams. Rayleigh and Eringen nonlocal elasticity theories are used to investigate the rotatory inertia and Size-dependency effects on the flapwise bending vibration of the rotating cantilever beams, respectively. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. The novelty of the presented approach is the approximation of the mode shape function by a power series which converts the equations into solvable one. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the influence of the geometry properties, rotatory inertia, rotational speed, taper ratio and size-dependency are investigated on the natural frequencies of the rotating beam. Application of the weak form integral equations has made the solution simpler and shorter in the mathematical process. Presented relations can be used to obtain a close-form solution for quick calculation of the first five natural frequencies of the beams with flapwise vibration and non-local effects. The analysis results are compared with those obtained from other available published references.

• Structural Engineering and Mechanics
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• 제55권3호
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• pp.655-674
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• 2015

In this paper, a new and simplified method is presented in which the natural frequencies of the uniform and non-uniform beams are calculated through simple mathematical relationships. The various vibration problems such as: Rayleigh beam under variable axial force, axial vibration of a bar with and without end discrete spring, torsional vibration of a bar with an attached mass moment of inertia, flexural vibration of the beam with laterally distributed elastic springs and also flexural vibration of the beam with effects of viscose damping are investigated. The governing differential equations are first obtained and then; according to a harmonic vibration, are converted into single variable equations in terms of location. Through repetitive integrations, the governing equations are converted into weak form integral equations. The mode shape functions of the vibration are approximated using a power series. Substitution of the power series into the integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of a non-trivial solution for system of equations. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained with those obtained from other published references and results of available finite element software.

• Steel and Composite Structures
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• 제52권5호
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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.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2000년도 추계학술대회 논문집
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• pp.670-673
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• 2000

This paper attempt analysis and computer simulation of dynamics of a set of dual multi-joint fingers with soft-deformable tips which are grasping. Firstly, a set of differential equation describing dynamics of the fingers and object together with geometric constraint of tight area-contacts is formulated by Euler-Lagrange's formalism. Secondly, problems of controlling both the internal force and the rotation angle of the grasped object under the constraints of area-contacts of tight area-contacts are discussed. The effect of geometric constraints of area-contacts on motion of the overall system is analyzed and a method of computer simulation for overall system of differential-algebraic equations is presented. Finally, simulation results are shown and the effects of geometric constraints of area-contact is discussed.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.132.6-132
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• 2001

This paper aims to derive a mathematical model of the dynamics of handling tasks in field robot which stable grasping and manipulates a rigid object with some dexterity. Firstly, a set of differential equation describing dynamics of the manipulators and object together with geometric constraint of tight area-contacts is formulated by Lagrange equation. Secondly, problems of controlling both the internal force and the rotation angle of the grasped object under the constraints of area-contacts of tight area-contacts are discussed. The effect of geometric constraints of area-contacts on motion of the overall system is analyzed and a method of computer simulation for overall system of differential-algebraic equations is presented. Thirdly, simulation results are shown and the effects of geometric constraints of area-contact is discussed.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2002년도 ICCAS
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• pp.108.4-108
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• 2002

This paper aims to derive a mathematical model of the dynamics of handling tasks in robot fingers which stably grasps and manipulates a rigid object with some dexterity. Firstly, a set of differential equation describing dynamics of the manipulators and object together with geometric constraint of tight area-contacts is formulated by Lagrange's equation. Secondly, problems of controlling both the internal force and the rotation angle of the grasped object under the constraints of tight area-contacts are discussed. The effect of geometric constraints of area-contacts on motion of the overall system is analyzed and a method of computer simulation for differential-algebraic equations of overall...

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1997년도 추계학술대회 논문집
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• pp.492-495
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• 1997

This paper aims to derive a mathematical model of the dynamics of handling task in field robot which stable grasping and manipulates a rigid object with some dexterity. Firstly, a set of differential equation describing dynamics of the manipulators and object together with geometric constraints of tight area-contacts on motion of the overall system is analyzed and a method of computer simulation for overall system of differential-algebraic equations is presented. Thirdly, simulation results are shown and the effects of geometric constraints of contact-area are discussed. Finally, it is shown that even in the simplest case of dual single D.O.F. manipulators there exists a sensory feedback from sensing data of he rotational angle of the object to command inputs to joint actuators and this feedback connection from sensing to action eventually realizes secure grasping of the object, provided that he object is of rectangular shape and motion is confined to a horizontal

• 대한기계학회논문집
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• 제12권2호
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• pp.193-199
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• 1988

본 연구의 목적은 SCPA방법을 이용한 비선형 2자유도 비감쇠계의 해석을 통하여 응답곡선을 구하고, 그 응답곡선의 분기현상을 규명함에 있다. 결과의 비교를 위하여 4차의 Runge-Kutta방법을 이용한 수치실험을 수행하였다.

• 대한기계학회논문집A
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• 제21권8호
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• pp.1311-1321
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• 1997

In multibody dynamics, differential and algebraic equations which can satisfy both equation of motion and kinematic constraint equation should be solved. To solve these equations, coordinate partitioning method and constraint stabilization method are commonly used. In the coordinate partitioning method, the coordinates are divided into independent and dependent and coordinates. The most typical coordinate partitioning method are LU decomposition, QR decomposition, and SVD (singular value decomposition). The objective of this research is to find an efficient coordinate partitioning method in the dynamic analysis of flexible multibody systems. Comparing two coordinate partitioning methods, i.e. LU and QR decomposition in the flexible multibody systems, a new hybrid coordinate partitioning method is suggested for the flexible multibody analysis.