• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 1997년도 춘계학술대회 논문집
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• pp.113-118
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• 1997

This paper presents the dimensional synthesis and kinematic analysis of the RSCS-SSP motion generating spatial mechanism using the displacement matrix method. This type of spatial mechani는 is used for the Mcpherson suspension in small automobiles. It is modeled for the wheel bump/rebound and steering motion. First, the suspension is modeled as a multiloop spatial rigid body guidance mechanism for the two major motions. Then the design equations for SSP, RS, and SC strut links are applied to synthesize an RSCS-SSP for up to three prescribed positions for the steering motiom from the suspension design specification. Thus a RSCS-SSP mechanism which is synthesized is also analyzed for the displacement during the steering motion.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2000년도 춘계학술대회논문집 - 한국공작기계학회
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• pp.708-713
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• 2000

This paper reviews the concepts of the snake motion which can be often observed on the bodies moving along guide rails. A simple modelling is proposed in order to analyze the snake motion of the cross head assembly and force and moment equilibrium equations are established. It is determined the critical conditions at which snake motion just brings about. Some possible methods to reduce or prevent snake motion are discussed in detail.

• Structural Engineering and Mechanics
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• 제54권6호
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• pp.1153-1174
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• 2015

Deployable structures have gained more and more applications in space and civil structures, while it takes a large amount of computational resources to analyze this kind of multibody systems using common analysis methods. This paper presents a new approach for dynamic analysis of multibody systems consisting of both rigid bars and arbitrarily shaped rigid bodies. The bars and rigid bodies are connected through their nodes by ideal pin joints, which are usually fundamental components of deployable structures. Utilizing the Moore-Penrose generalized inverse matrix, equations of motion and constraint equations of the bars and rigid bodies are formulated with nodal Cartesian coordinates as unknowns. Based on the constraint equations, the nodal displacements are expressed as linear combination of the independent modes of the rigid body displacements, i.e., the null space orthogonal basis of the constraint matrix. The proposed method has less unknowns and a simple formulation compared with common multibody dynamic methods. An analysis program for the proposed method is developed, and its validity and efficiency are investigated by analyses of several representative numerical examples, where good accuracy and efficiency are demonstrated through comparison with commercial software package ADAMS.

• 한국소음진동공학회논문집
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• 제19권2호
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• pp.208-216
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• 2009

In this paper, we present the equations of motion by which the natural vibration of a rotating annular disk can be analyzed accurately. These equations are derived from the theory of finite deformation and the principle of virtual work. The radial displacements of annular disk at the steady state where the disk is rotating at a constant angular velocity are determined by non-linear static equations formulated with 1-dimensional finite elements in radial direction. The linearlized equations of the in-plane vibrations at the disturbed state are also formulated with 1-dimensional finite elements in radial direction along the number of nodal diameters. They are expressed as in functions of the radial displacements at the steady state and the disturbed displacements about the steady state. In-plane static deformation modes of an annular disk are used as the displacement functions for the interpolation functions of the 1-dimensional finite elements. The natural vibrations of an annular disk with different boundary conditions are analyzed by using the presented model and the 3-dimensional finite element model to verify accuracy of the presented equations of motion. Its results are compared and discussed.

• 대한기계학회논문집A
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• 제26권4호
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• pp.764-774
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• 2002

Dynamic behaviors are analyzed for an automatic ball balancer (ABB) with triple races, which is a device to reduce the unbalanced mass of optical disk drives (ODD) such as CD-ROM or DVD drives. The nonlinear equations of motion are derived by using Lagrange's equations with the polar coordinate system. It is shown that the polar coordinate system provides the complete stability analysis while the rectangular coordinate system used in other previous studies has limitations on the stability analysis. For the stability analysis, the equilibrium positions and the linearized perturbation equations are obtained by the perturbation method. Based on the linearized equations, the stability of the system is analyzed around the equilibrium positions; furthermore, to confirm the stability, the time responses for the nonlinear equations of motion are computed by using a time integration method and experimental analyses are performed. Theoretical and experimental results show a superiority of the ABB with triple races.

• 대한기계학회논문집A
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• 제25권11호
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• pp.1730-1736
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• 2001

A finite element analysis for a rotating cantilever beam is presented in this study. Based on a dynamic modeling method using the stretch deformation instead of the conventional axial deformation, three linear partial differential equations are (derived from Hamilton's principle. Two of the linear differential equations show the coupling effect between stretch and chordwise deformations. The other equation is an uncoupled one for the flapwise deformation. From these partial differential equations and the associated boundary conditions, two weak forms are derived: one is for the chordwise motion and the other is fur the flptwise motion. The weak farms are spatially discretized with newly defined two-node beam elements. With the discretized equations or the matrix-vector equations, the behaviors of the natural frequencies are investigated for the variation of the rotating speed.

• 한국소음진동공학회논문집
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• 제26권3호
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• pp.281-289
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• 2016

In this paper, a new dynamic model for modal analysis of a rotating cantilever beam with a tip-mass is developed. The nonlinear strain such as von Karman type and the corresponding linearized stress are used to consider the geometric nonlinearity, and Euler-Bernoulli beam theory is applied in the present model. The nonlinear equations of motion and the associated boundary conditions which include the inertia of the tip-mass are derived through Hamilton's principle. In order to investigate modal characteristics of the present model, the linearized equations of motion in the neighborhood of the equilibrium position are obtained by using perturbation technique to the nonlinear equations. Since the effect of the tip-mass is considered to the boundary condition of the flexible beam, weak forms are used to discretize the linearized equations. Compared with equations related to stiffening effect due to centrifugal force of the present and the previous model, the present model predicts the dynamic characteristic more precisely than the another model. As a result, the difference of natural frequencies loci between two models become larger as the rotating speed increases. In addition, we observed that the mode veering phenomenon occurs at the certain rotating speed.

• 대한기계학회논문집A
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• 제21권12호
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• pp.2038-2046
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• 1997

In this paper the instability of the system which has a disk and a mass-spring-damper system interacting through a medium having stiffness and damping is analyzed. To solve the equations of motion of this systme, it is assumed that the solution consists of the eigenfunctions which are the products of the Bessel functions and sine or cosine functions. The former represents the radial characteristics of the disk and the latter represents the circumferential characteristics. Using this assumed solution and the orthogonality of the eigenfunctions, the equations of motion can be transformed into a set of equations of motion with variables dependent only on the time. After this set is changed to the state equation, the eigenvalue problem can be made. Once the eigenvalues are calculated according to the angular velocity of the disk, the dynamic characteristics ofthis system is obtained. Because the thickness of the disk and the element characteristics of the mass-spring-damper system have important effects on the stability of the system, it will be understood how these factors affect the system and then a method to ameliorate the stability of the system with a disk will be presented.

• Structural Engineering and Mechanics
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• 제62권1호
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• pp.65-77
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• 2017

The free vibration analysis of fluid conveying Timoshenko pipeline with different boundary conditions using Differential Transform Method (DTM) and Adomian Decomposition Method (ADM) has not been investigated by any of the studies in open literature so far. Natural frequencies, modes and critical fluid velocity of the pipelines on different supports are analyzed based on Timoshenko model by using DTM and ADM in this study. At first, the governing differential equations of motion of fluid conveying Timoshenko pipeline in free vibration are derived. Parameter for the nondimensionalized multiplication factor for the fluid velocity is incorporated into the equations of motion in order to investigate its effects on the natural frequencies. For solution, the terms are found directly from the analytical solution of the differential equation that describes the deformations of the cross-section according to Timoshenko beam theory. After the analytical solution, the efficient and easy mathematical techniques called DTM and ADM are used to solve the governing differential equations of the motion, respectively. The calculated natural frequencies of fluid conveying Timoshenko pipelines with various combinations of boundary conditions using DTM and ADM are tabulated in several tables and figures and are compared with the results of Analytical Method (ANM) where a very good agreement is observed. Finally, the critical fluid velocities are calculated for different boundary conditions and the first five mode shapes are presented in graphs.

• 한국정밀공학회지
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• 제16권12호
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• pp.126-132
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• 1999

The paper presents the modeling and optimal control for the reduction of transverse vibration of simply supported beam under a moving mass. The equations of motion are derived by using assumed mode method. The coriolis and centripetal accelerations are accommodated in the equations of motion to account for the dynamic effect of the traveling mass. In order to reduce the transverse vibration of the beam, an optimal controller with full state feedback is designed based on the linearized equations of motion. The optimal actuator locations are determined with the evaluation of an optimal cost functional defined by the worst initial condition with the trade-off of controlled mode performance. Numerical simulations are performed with respect to various velocities and different traveling masses. Even if the velocity of the traveling mass reaches to the critical speed which can cause the resonance of the beam, the controller with two piezoelectric actuators shows the excellent performance under severe time-varying disturbances of the system.