• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.853-861
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• 2007

To understand the concept of dynamic motion in two degree nonlinear coupled system, free vibration not including damping and excitation is investigated with the concept of nonlinear normal mode. Stability analysis of a coupled system is conducted, and the theoretical analysis performed for the bifurcation phenomenon in the system. Bifurcation point is estimated using harmonic balance method. When the bifurcation occurs, the saddle point is always found on Poincare's map. Nonlinear phenomenon result in amplitude modulation near the saddle point and the internal resonance in the system making continuous interchange of energy. If the bifurcation in the normal mode is local, the motion remains stable for a long time even when the total energy is increased in the system. On the other hand, if the bifurcation is global, the motion in the normal mode disappears into the chaos range as the range becomes gradually large.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.262-267
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• 2002

A nonlinear dynamic modeling method for cantilever beams undergoing axially oscillating motion is presented in this paper. Hybrid deformation variables are employed for the modeling method with which frequency response characteristics of a axially oscillating cantilever beams are investigated. It is shown that the geometric nonlinear effects of stretching and curvature play important roles to accurately predict the frequency response characteristics. The effects of the amplitude and the damping constant on the frequency characteristics are also exhibited.

• Journal of KSNVE
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• v.4 no.2
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• pp.221-230
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• 1994

This paper deals with the dynamic stability and the nonlinear behavior of a check valve system. The nonlinear equations of motion of fluid-valve interation model are derived, which are composed of the unsteady Bernoulli's equation included the jet flow mechanism and equation of motion of a check valve formulated by one degree of freedom. Also, the derived equations of motion are nondimensionalized. According to the change of the nondimensional parameters, the stabilities of the system are analyzed, and the nonlinear interaction responses of the check valve and the passing flow rate are obtained. As the results, the stability charts are constructed for the variation of nondimensional parameters. It is shown that self-excited vibrations exist in a check valve system. And also the Hopf bifurcation and the periodic doubling are found. The presented theoretical model of a check valve system can be utilized to the design and operation of a piping system with the check valve.

• Structural Engineering and Mechanics
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• v.88 no.5
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• pp.405-417
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• 2023

This paper reveals theoretical research to the nonlinear dynamic response and initial geometric imperfections sensitivity of the spinning graphene platelets reinforced metal foams (GPLRMF) cylindrical shell under different boundary conditions in thermal environment. For the theoretical research, with the framework of von-Karman geometric nonlinearity, the GPLRMF cylindrical shell model which involves Coriolis acceleration and centrifugal acceleration caused by spinning motion is assumed to undergo large deformations. The coupled governing equations of motion are deduced using Euler-Lagrange principle and then solved by a combination of Galerkin's technique and modified Lindstedt Poincare (MLP) model. Furthermore, the impacts of a set of parameters including spinning velocity, initial geometric imperfections, temperature variation, weight fraction of GPLs, GPLs distribution pattern, porosity distribution pattern, porosity coefficient and external excitation amplitude on the nonlinear harmonic resonances of the spinning GPLRMF cylindrical shells are presented.

• Journal of Ship and Ocean Technology
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• v.3 no.2
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• pp.17-26
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• 1999

An experimental investigation on hydrodynamic forces acting on a porpoising craft at high advanced speeds up to Froude numbers Fn=6.0(Fn=U\ulcorner:Lo\ulcorner denote overall length of ship) in calm water is performed. Captive model tests and forced motion tests are carried out to measure the hydrodynamic forces. The results show that significant nonlinear effects for motion amplitudes appear in the restoring, the added mass and the damping coefficients. The experimental results are compared with the results of a prediction method of the hydrodynamic forces include the nonlinear effects, and show a good agreement with them. A simulation using the predicted hydrodynamic forces in a nonlinear motion equation is carried out to obtain the porpoising motion of a craft in calm water. The calculated results are in fairly good agreement with experimental ones.

• Structural Engineering and Mechanics
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• v.22 no.6
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• pp.647-664
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• 2006

The main purpose of this paper is to investigate the effect of transient stochastic analysis on nonlinear response of earth and rock-fill dams to spatially varying ground motion. The dam models are analyzed by a stochastic finite element method based on the equivalent linear method which considers the nonlinear variation of soil shear moduli and damping ratio as a function of shear strain. The spatial variability of ground motion is taken into account with the incoherence, wave-passage and site response effects. Stationary as well as transient stochastic response analyses are performed for the considered dam types. A time dependent frequency response function is used throughout the study for transient stochastic responses. It is observed that stationarity is a reasonable assumption for earth and rock-fill dams to typical durations of strong shaking.

• Journal of KSNVE
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• v.6 no.2
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• pp.233-244
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• 1996

In this paper chaotic mothions of a straight pipe conveying oscillatory flow and being subjected to external forces such as earthquake are theoretically investigated. The nonlinear partial differential equation of motion is derived by Newton's method. In this equation, the nonlinear curvature of the pipe and the thermal expansion effects are contained. The nonlinear ordinary differential equation transformed from that partial differential equation is a type of Hill's equations, which have the parametric and external exciation term. This original system is transfered to the averaged system by the averaging theory. Bifurcation curves of chaotic motion of the piping system are obtained in the general case of the frequency ratio, n by applying Melnikov's method. Numerical simulations are performed to demonstrate theorectical results and show strange attactors of the chaotic motion.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.326-331
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• 2004

The linear motion (LM) guide using ball bearing has many advantages compared with conventional sliding guides. Therefore, LM guide using ball bearing has been used widely to increase the accuracy of the position of a system. This research investigates dynamic characteristics of LM guide through mainly linear analysis. Linear analysis is accomplished by Lagrange equation and finite element method. And another trial that is nonlinear analysis about one mode of LM guide(bouncing mode) from Hertzian contact theory is accomplished in the latter half of this research. Through nonlinear analysis we could observe the softening characteristic due to the Hertzian contact nonlinearity.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.441-448
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• 2000

An investigation into the nonlinear free vibrations of a cantilever beam which can have not only planar motion but also nonplanar motion is made. Using Galerkin's method based on the first mode in each motion, we transform the boundary and initial value problem into an initial value problem of two-degree-of-freedom system. The system turns out to have two normal modes. By Synge's stability concept we examine the stability of each mode. In order to check validity of the stability we obtain the numerical Poincare map of the motions neighboring on each mode.

• Korean Journal of Computational Design and Engineering
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• v.15 no.1
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• pp.70-83
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• 2010

Recently, floating cranes are mainly used to erect heavy blocks or cargos for constructing ships in many shipyards. It is important to estimate the dynamic motion of the heavy cargo suspended by a floating crane and the tension of the wire ropes between the floating crane and the heavy cargo. In this paper, the coupled dynamic equations of motion are set up for considering the 6 degree-of-freedom floating crane and the 6-degrees-of-freedom heavy cargo based on multibody system dynamics. Depending on the cargo weight, the motion of the floating crane would be changed to nonlinear state. The nonlinear terms in the equation of motion are considered. In addition, the nonlinear hydrostatic force, the linear hydrodynamic force, wire rope force, mooring force and gravity force are considered as the external forces. As the result of this paper, we analyze the engineering effect for erecting the heavy cargo by using the floating crane.