• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.5
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• pp.992-1002
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• 1988

The dynamic response of rotor-bearing systems subjected to six-component nonststionary earthquake ground accelerations is analyzed. The governing equations of motion for the rotor are derived using Lagrangian approach. The six-component earthquake inputs result in both inhomogeneous and parametric excitations, so that the conventional spectral analysis of random vibration is not applicable. The method of Monte Carlo simulation is utilized to simulate the six-component nonstationary earthquake ground motions and to determine the response statistics of rotor-bearing systems. The significant influences due to rotational motions of seismic base on the overall structural response is demonstrated by a numerical example.

• Coupled systems mechanics
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• v.7 no.6
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• pp.707-729
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• 2018

The semi-active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, the differential equations of motion of the coupling torsion-bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, the minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.

• Journal of the Society of Naval Architects of Korea
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• v.52 no.3
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• pp.187-197
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• 2015

This study aims the development of a semi-analytic method for the parametric roll of large containerships advancing in longitudinal waves. A 1.5 Degree-of-Freedom(DOF) model is proposed to account the change of transverse stability induced by wave elevations and vertical motions (heave and pitch). By approximating the nonlinearity of restoring moment at large heel angles, the magnitude of roll amplitude is predicted as well as susceptibility check for parametric roll occurrence. In order to increase the accuracy of the prediction, the relationship between righting arm(GZ) and metacentric height(GM) is examined in the presence of incident waves, and then a new formula is proposed. Based on the linear approximation of the mean and first harmonic component of GM, the equation of parametric roll in irregular wave excitations is introduced, and the computational results of the proposed model are validated by comparing those of weakly nonlinear simulation based on an impulse-response-function method combined with strip theory. The present semi-analytic doesn’ t require heavy computational effort, so that it is very efficient particularly when numerous sea conditions for the analysis of parametric roll should be considered.

• Wind and Structures
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• v.28 no.4
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• pp.225-238
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• 2019

In this paper a novel and efficient computational framework to estimate the stress range versus number of cycles curves experienced by a cable due to external excitations (e.g., seismic excitations, traffic and wind-induced vibrations, among others) is proposed. This study is limited to the wind-cable interaction governed by the Vortex Shedding mechanism which mainly rules cables vibrations at low amplitudes that may lead to their failure due to bending fatigue damage. The algorithm relies on a stochastic approach to account for the uncertainties in the cable properties, initial conditions, damping, and wind excitation which are the variables that govern the wind-induced vibration phenomena in cables. These uncertainties are propagated adopting Monte Carlo simulations and the concept of importance sampling, which is used to reduce significantly the computational costs when new scenarios with different probabilistic models for the uncertainties are evaluated. A high fidelity cable model is also proposed, capturing the effect of its internal wires distribution and helix angles on the cables stress. Simulation results on a 15 mm diameter high-strength steel strand reveal that not accounting for the initial conditions uncertainties or using a coarse wind speed discretization lead to an underestimation of the stress range experienced by the cable. In addition, parametric studies illustrate the computational efficiency of the algorithm at estimating new scenarios with new probabilistic models, running 3000 times faster than the base case.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.113-114
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• 2006

Vibration of a non-linear system under random excitations was evaluated by probabilistic methods. The non-linear characteristic terms of a system structure were quasi-linearized and excitation terms were remained as they were. An analytical method where the square mean of error was minimized was used. An alternative method was an energy method where the damping energy and restoring energy of the linearized system were equalized to those of the original non-linear system. The numerical results were compared with those obtained by Monte Carlo simulation. The comparison showed the results obtained by Monte Carlo simulation located between those by the analytical method and those by the energy method.

• Structural Engineering and Mechanics
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• v.61 no.4
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• pp.497-510
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• 2017

A framed structure may be composed of two sub-structures, which are linked by a hinged joint. One sub-structure is the primary system and the other is the secondary system. The primary system, which is subjected to the periodic external load, can give rise to an auto-parametric resonance of the second system. Considering the geometric-stiffness effect produced by the axially internal force, the element equation of motion is derived by the extended Hamilton's principle. The element equations are then assembled into the global non-homogeneous Mathieu-Hill equations. The Newmark's method is introduced to solve the time-history responses of the non-homogeneous Mathieu-Hill equations. The energy-growth exponent/coefficient (EGE/EGC) and a finite-time Lyapunov exponent (FLE) are proposed for determining the auto-parametric instability boundaries of the structural system. The auto-parametric instabilities are numerically analyzed for the two frames. The influence of relative stiffness between the primary and secondary systems on the auto-parametric instability boundaries is investigated. A phenomenon of the "auto-parametric internal resonance" (the auto-parametric resonance of the second system induced by a normal resonance of the primary system) is predicted through the two numerical examples. The risk of auto-parametric internal resonance is emphasized. An auto-parametric resonance experiment of a ${\Gamma}$-shaped frame is conducted for verifying the theoretical predictions and present calculation method.

• Smart Structures and Systems
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• v.15 no.2
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• pp.425-445
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• 2015

Parametric identification of structures is one of the important aspects of structural health monitoring. Most of the techniques available in the literature have been proved to be effective for structures with small degree of freedoms. However, the problem becomes challenging when the structure system is large, such as bridge structures. Therefore, it is highly desirable to develop parametric identification methods that are applicable to complex structures. In this paper, the LSE based techniques will be combined with the substructure approach for identifying the parameters of a cable-stayed bridge with large degree of freedoms. Numerical analysis has been carried out for substructures extracted from the 2-dimentional (2D) finite element model of a cable-stayed bridge. Only vertical white noise excitations are applied to the structure, and two different cases are considered where the structural damping is not included or included. Simulation results demonstrate that the proposed approach is capable of identifying the structural parameters with high accuracy without measurement noises.

• Structural Engineering and Mechanics
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• v.30 no.1
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• pp.37-66
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• 2008

This paper focuses on the nonlinear vibrations of stay cables and evaluates the dynamic characteristics of stay cables by using the nonlinear enhanced MECS approach and the approximate approach. The nonlinear enhanced MECS approach is that both the girder-tower vibrations and the cable vibrations including parametric cable vibrations are simultaneously considered in the numerical analysis of cable-stayed bridges. Cable finite element method is used to simulate the responses including the parametric vibrations of stay cables. The approximate approach is based on the assumption that cable vibrations have a small effect on girder-tower vibrations, and analyzes the local cable vibrations after obtaining the girder-tower responses. Under the periodic excitations or the moderate ground motion, the differences of the responses of stay cables between these two approaches are evaluated in detail. The effect of cable vibrations on the girder and towers are also discussed. As a result, the dynamic characteristics of the parametric vibrations in stay cables can be evaluated by using the approximate approach or the nonlinear enhanced MECS approach. Since the different axial force fluctuant of stay cables in both ends of one girder causes the difference response values between two approach, it had better use the nonlinear enhanced MECS approach to perform the dynamic analyses of cable-stayed bridges.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.2
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• pp.160-168
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• 2008

This paper presents the study on the stability of nonlinear oscillations of a thin cantilever beam subject to harmonic base excitation in vertical direction. Two partial differential governing equations under combined parametric and external excitations were derived and converted into two-degree-of-freedom ordinary differential Mathieu equations by using the Galerkin method. We used the method of multiple scales in order to analyze one-to-one combination resonance. From these, we could obtain the eigenvalue problem and analyze the stability of the system. From the thin cantilever experiment using foamax, we could observe the nonlinear modes of bending, twisting, sway, and snap-through buckling. In addition to qualitative information, the experiment using aluminum gave also the quantitative information for the stability of combination resonance of a thin cantilever beam under parametric excitation.

• International Journal of Naval Architecture and Ocean Engineering
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• v.2 no.3
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• pp.119-126
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• 2010

The response of ship roll oscillation under random ice impulsive loads modeled by Poisson arrival process is very important in studying the safety of ships navigation in cold regions. Under both external and parametric random excitations the evolution of the probability density function of roll motion is evaluated using the path integral (PI) approach. The PI method relies on the Chapman-Kolmogorov equation, which governs the response transition probability density functions at two close intervals of time. Once the response probability density function at an early close time is specified, its value at later close time can be evaluated. The PI method is first demonstrated via simple dynamical models and then applied for ship roll dynamics under random impulsive white noise excitation.