• Structural Engineering and Mechanics
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• 제11권2호
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• pp.185-197
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• 2001

This paper presents the effect of axial stretching on large amplitude free vibration of an extensible suspended cable supported at the same level. The model formulation developed in this study is based on the virtual work-energy functional of cables which involves strain energy due to axial stretching and work done by external forces. The difference in the Euler equations between equilibrium and motion states is considered. The resulting equations govern the horizontal and vertical motion of the cables, and are coupled and highly nonlinear. The solution for the nonlinear static equilibrium configuration is determined by the shooting method while the solution for the large amplitude free vibration is obtained by using the second-order central finite difference scheme with time integration. Numerical examples are given to demonstrate the vibration behaviour of extensible suspended cables.

• 대한기계학회논문집
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• 제19권3호
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• pp.697-704
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• 1995

The dynamic characteristics of a system can be critically influenced by system uncertainty, so the dynamic system must be analyzed stochastically in consideration of system uncertainty. This study presents the stochastic model of a nonlinear dynamic system with uncertain parameters under nonstationary stochastic inputs. And this stochastic system is analyzed by a new stochastic process closure method and moment equation method. The first moment equation is numerically evaluated by Runge-Kutta method and the second moment equation is numerically evaluated by stochastic process closure method, 4th cumulant neglect closure method and Runge-Kutta method. But the first and the second moment equations are coupled each other, so this equations are approximately evaluated by a iterative method. Finally the accuracy of the present method is verified by Monte Carlo simulation.

• Journal of Mechanical Science and Technology
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• 제19권spc1호
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• pp.461-472
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• 2005

A formulation for flexible multibody systems (MBS) is investigated, where rigid MBS substructures are coupled with flexible bodies described by a nonlinear finite element (FE) approach. Several aspects that turned out to be crucial for the presented approach are discussed. The system describing equations are given in differential algebraic form (DAE), where many sophisticated solvers exist. In this paper the performance of several solvers is investigated regarding their suitability for the application to the usually highly stiff DAE. The substructures are connected with each other by nonlinear algebraic constraint equations. Further, partial derivatives of the constraints are required, which often leads to extensive algebraic trans-formations. Handcoding of analytically determined derivatives is compared to an approach utilizing algorithmic differentiation.

• Coupled systems mechanics
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• 제9권6호
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• pp.539-562
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• 2020

In this paper the linear elastic coupling between a 2 degree of freedom shear-type frame system and a rigid block is analytically and experimentally investigated. As demonstrated by some of the authors in previous papers, it is possible to choose a coupling system able to guarantee advantages, whatever the mechanical characteristics of the frame. The main purpose of the investigation is to validate the analytical model. The nonlinear equations of motion of the coupled system are obtained by a Lagrangian approach and successively numerically integrated under harmonic and seismic excitation. The results, in terms of gain graphs, maps and spectra, represent the ratio between the maximum displacements or drifts of the coupled and uncoupled systems as a function of the system's parameters. Numerical investigations show the effectiveness of the nonlinear coupling for a large set of parameters. Thus experimental tests are carried out to verify the analytical results. An electro-dynamic long-stroke shaker sinusoidally and seismically forces a shear-type 2 d.o.f frame coupled with a rigid aluminium block. The experimental investigations confirm the effectiveness of the coupling as predicted by the analytical model.

• 한국지반공학회논문집
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• 제27권3호
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• pp.75-83
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• 2011

일반적인 불포화지반의 거동뿐만 아니라, 열과 관련된 분야, 지반환경 분야 등 다양한 분야에서 불포화 다공질 재료의 열적-수리적-역학적으로 결합된 문제들이 대두되면서 이러한 문제들을 해석하기 위한 수치도구 개발의 필요성이 대두되고 있다. 본 논문에서는 거시적 접근법(macroscopic approach)에 근거하여 불포화지반에 대한 열-수리-역학거동의 수식화를 하였다. 흙, 물, 공기에 대한 질량보존의 법칙, 에너지 보존법칙, 그리고 하중평형 조건식으로부터 결합된(coupled) 4개의 지배방정식을 유도하였다. Galerkin 간략화와 시간적분으로부터 주 변수인 변위(u), 가스압($P_g$), 유체압($P_1$), 온도(T)를 Newton의 반복과정을 이용하여 구하는 유한요소 프로그램(FEM)을 작성하였다. 개발된 프로그램을 이용하여 다공질재료에서 2상 흐름 문제 중 일차원 배수실험(u-$P_g-P_1$), 온도 압밀(u-$P_1$-T), 그리고 지표면 온도변화에 의한 말뚝의 주변지반에 대한 영향(u-$P_1$-T)에 대하여 수치해석을 수행하고 논의하였다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2002년도 추계학술대회논문집
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• pp.914-920
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• 2002

Nonlinear flow-induced vibration characteristics of a generic missile wing (or control surface) are investigated in this study. The wing model has freeplay structural nonlinearity at its pitch axis. Nonlinear aerodynamic flows with unsteady shock waves are considered in the transonic flow region. To practically consider the effects of freeplay structural nonlinearity, the fictitious mass method (FMM) is applied to structural vibration analysis based on a finite element method (FEM). A computational fluid dynamics (CFD) technique is used for computing the nonlinear unsteady aerodynamics of all-movable wings. The aerodynamic analysis is based on the efficient transonic small-disturbance aerodynamic equations of motion using the potential-flow theory. To solve the nonlinear aeroelastic governing equations including the freeplay effect, a modal-based computational structural dynamic (CSD) analysis technique based on fictitious mass method (FMM) is used in time-domain. In addition, CSD and unsteady CFD techniques are simultaneously coupled to give accurate computational results. Various aeroelastic computations have been performed for a generic missile wing model. Linear and nonlinear aeroelastic computations have been conducted and the characteristics of flow-induced vibration are introduced.

• Structural Engineering and Mechanics
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• 제24권5호
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• pp.543-560
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• 2006

In this paper, first, the equations of motion for a rectangular isotropic plate have been derived. This derivation is based on the Von Karmann theory and the effects of shear deformation have been considered. Introducing an Airy stress function, the equations of motion have been transformed to a nonlinear coupled equation. Using Galerkin method, this equation has been separated into position and time functions. By means of the dimensional analysis, it is shown that the orders of magnitude for nonlinear terms are small with respect to linear terms. The Multiple Scales Method has been applied to the equation of motion in the forced vibration and free vibration cases and closed-form relations for the nonlinear natural frequencies, displacement and frequency response of the plate have been derived. The obtained results in comparison with numerical methods are in good agreements. Using the obtained relation, the effects of initial displacement, thickness and dimensions of the plate on the nonlinear natural frequencies and displacements have been investigated. These results are valid for a special range of the ratio of thickness to dimensions of the plate, which is a characteristic of the Multiple Scales Method. In the forced vibration case, the frequency response equation for the primary resonance condition is calculated and the effects of various parameters on the frequency response of system have been studied.

• Advances in nano research
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• 제10권5호
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• pp.481-491
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• 2021

Graphene Nanosheets play an important role in nanosensors due to their proper surface to volume ratio. Therefore, the main purpose of this paper is to consider the nonlinear vibration behavior of graphene nanosheets (GSs) under the influence of electromagnetic fields and electrical current create forces. Considering more realistic assumptions, new equations have been proposed to study the nonlinear vibration behavior of the GSs carrying electrical current and placed in magnetic field. For this purpose, considering the influences of the magnetic tractions created by electrical and eddy currents, new relationships for electromagnetic interaction forces with these nanosheets have been proposed. Nonlinear coupled equations are discretized by Galerkin method, and then solved via Runge-Kutta method. The effect of different parameters such as size effect, electrical current magnitude and magnetic field intensity on the vibration characteristics of GSs is investigated. The results show that the magnetic field increases the linear natural frequency, and decreases the nonlinear natural frequency of the GSs. Excessive increase of the magnetic field causes instability in the GSs.

• 대한기계학회논문집A
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• 제21권11호
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• pp.1809-1818
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• 1997

Mathematical models of industrial robots or manipulators are highly nonlinear equations with nonlinear coupling between the variables of motion. As the working speed has been fast, the effects of nonlinear terms have become serious. So the control algorithm based on approximately linearized equation looses the efficiency. In order to design the control law for the nonlinear models, Hunt-Su's nonlinear transformation method and Marino's feedback equivalence condition are used with linear quadratic regulator(LQR) theory in this study. Nonlinear terms of the system are eliminated and coupled terms are decoupled by this feedback law. This method is applied to a 3-D.O.F. vertical articulated manipulator by both experiments and simulations and compared with PID control which is widely used in the industry.

• Structural Engineering and Mechanics
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• 제29권5호
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• pp.581-597
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• 2008

In this paper, the double displacement coupled statics and dynamics of the electromechanical integrated electrostatic harmonic drive are developed. The linearization of the nonlinear dynamic equations is completed. Based on natural frequency and mode function, the double displacement coupled forced response of the drive system to voltage excitation are obtained. Changes of the forced response along with the system parameters are investigated. The voltage excitation can cause the radial and tangent coupled forced responses of the flexible ring. The flexible ring radius, ring thickness and clearance between the ring and stator have obvious influences on the double displacement coupled forced responses.