• Ocean Systems Engineering
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• v.1 no.3
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• pp.249-261
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• 2011

The stochastic nonlinear dynamic behavior and probability density function of ship rolling are studied using the nonlinear dynamical systems approach and probability theory. The probability density function of the rolling response is evaluated through solving the Fokker Planck Equation using the path integral method based on a Gauss-Legendre interpolation scheme. The time-dependent probability of ship rolling restricted to within the safe domain is provided and capsizing is investigated from the probability point of view. The random differential equation of ships' rolling motion is established considering the nonlinear damping, nonlinear restoring moment, white noise and colored noise wave excitation.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.133-136
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• 1999

Many researches on the identification of a system have been carried out using a least square method, an adaptive filter, and so on. However, it is difficult to apply these methods in a nonlinear system. In the case of a nonlinear system, it is known that the signal compression method is able to estimate uncertain parameters of linear element in a nonlinear system because it is able to separate linear element and nonlinear element in a nonlinear system. However, the signal compression method cannot be applied to a motion simulator because actuators of the simulator is single-rod cylinders which includes expansion and compression dynamic properties. Therefore, this paper proposes a modified signal compression method which is able to estimate uncertain parameters of the motion simulator dynamics. The dynamic properties of this system are identified by separating expansion and compression properties when applying the signal compression method. And then, the identified parameters are applied to design a sliding mode controller for the simulator. The performance of the designed sliding mode controller is evaluated experimentally.

• International Journal of Naval Architecture and Ocean Engineering
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• v.3 no.1
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• pp.95-104
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• 2011

As sea state harsher in the ocean space, more large motion and wave loads occurs on ships hull by non-linear phenomena. To consider nonlinear effect on ships hull in the structural design verification, the direct calculation method with numerical approach is used rather than rule values for the reliable accuracy. In this paper, the non-linear wave loads analysis in time domain is performed by using a Rankine Panel Method together with numerical schemes. Linear calculations have been carried out based on DNV CSA-2 notation to generate the motion responses and wave loads of large ships. By short and long term analysis, the design wave amplitudes are selected for the nonlinear analysis. The maximum wave induced bending moment in hogging and sagging conditions are calculated in the nonlinear analysis. Also, the green water effect on the wave induced vertical bending moment was investigated. The results show the vertical bending moments are more influenced by green water in sagging condition than in hogging condition due to green water loading.

• Journal of Ocean Engineering and Technology
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• v.30 no.6
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• pp.458-467
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• 2016

In this paper, a strongly coupled method for investigating the interaction between a cable and tow-fish is presented. The nodal position finite element method was utilized to analyze the nonlinear cable dynamics, and 6DOF equations of motion were employed to describe the 3D rigid body motion of the tow-fish. Combining cable and tow-fish systems into a single formulation allowed the two nonlinear systems to be strongly coupled into a unified nonlinear system. This strongly coupled system was numerically integrated in the time domain using a predictor/multi-corrector Newmark algorithm. To demonstrate the validity, efficacy, and applicability of the current approach, two different scenarios (virtual and sea trial) were simulated, and the simulation results were validated using the physical plausibility and the sea trial test.

• International Journal of Naval Architecture and Ocean Engineering
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• v.3 no.1
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• pp.53-64
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• 2011

The present study considers multi-level approach for the analysis of parametric roll phenomena. Three kinds of computation method, GM variation, impulse response function (IRF), and Rankine panel method, are applied for the multi-level approach. IRF and Rankine panel method are based on the weakly nonlinear formulation which includes nonlinear Froude-Krylov and restoring forces. In the computation result of parametric roll occurrence test in regular waves, IRF and Rankine panel method show similar tendency. Although the GM variation approach predicts the occurrence of parametric roll at twice roll natural frequency, its frequency criteria shows a little difference. Nonlinear roll motion in bichromatic wave is also considered in this study. To prove the unstable roll motion in bichromatic waves, theoretical and numerical approaches are applied. The occurrence of parametric roll is theoretically examined by introducing the quasi-periodic Mathieu equation. Instability criteria are well predicted from stability analysis in theoretical approach. From the Fourier analysis, it has been verified that difference-frequency effects create the unstable roll motion. The occurrence of unstable roll motion in bichromatic wave is also observed in the experiment.

• Journal of the Earthquake Engineering Society of Korea
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• v.27 no.2
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• pp.83-90
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• 2023

The recent increase in earthquake activities has highlighted the importance of seismic performance evaluation for civil infrastructures. In particular, the container crane essential to maintaining the national logistics system with port operation requires an exact evaluation of its seismic response. Thus, this study aims to assess the seismic vulnerability of container cranes considering their seismic characteristics. The seismic response of the container crane should account for the structural members' yielding and buckling, as well as the crane wheel's uplifting derailment in operation. The crane's yielding and buckling limit states were defined using the stress of crane members based on the load and displacement curve obtained from nonlinear static analysis. The derailment limit state was based on the height of the rail, and nonlinear dynamic analysis was performed to obtain the seismic fragility curves considering defined limit states and seismic characteristics. The yield and derailment probabilities of the crane in the near-fault ground motion were approximately 1.5 to 4.7 and 2.8 to 6.8 times higher, respectively, than those in the far-fault ground motion.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.12
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• pp.1852-1865
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• 2017

The vibration of the structures with restrained motion has long been observed in various engineering fields. When the motion of vibrating structure is restrained due to the adjacent objects, the frequencies and the mode shapes of the structure change and its vibration characteristics becomes unpredictable, in general. Although the importance of the study on this type of vibration model increases in many engineering areas, most studies conducted so far are limited to the theoretical study on dynamic responses of the structure with stops, including some experimental works. Specially, the study on the nonlinear phenomena due to the impact between the structure and the stops have been mainly performed theoretically. In the paper, both numerical analyses and experiments are conducted to study the chaotic vibration characteristics of the nonlinear motion and the dynamic response of a cantilevered beam which has restrained motion at the free end by the stops. Results are presented for various magnetic forces and gaps between the beam and stops. The conclusions are as follows : Firstly, Numerical simulation results have a good agreement with experimental ones. Secondly, the effect of higher modes of beams are increased with increasing magnitude of exciting force, and displacement and velocity curves become more complicated shapes. Thirdly, nonlinear characteristics tend to appear greatly with increasing magnitude of exciting force, and fractal dimension is increased.

• Steel and Composite Structures
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• v.21 no.2
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• pp.395-409
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• 2016

Nonlinear vibration characteristics of composite laminated trapezoidal plates are studied. The geometric nonlinearity of the plate based on the von Karman's large deformation theory is considered, and the finite element method (FEM) is proposed for the present nonlinear modeling. Hamilton's principle is used to establish the equation of motion of every element, and through assembling entire elements of the trapezoidal plate, the equation of motion of the composite laminated trapezoidal plate is established. The nonlinear static property and nonlinear vibration frequency ratios of the composite laminated rectangular plate are analyzed to verify the validity and correctness of the present methodology by comparing with the results published in the open literatures. Moreover, the effects of the ply angle and the length-high ratio on the nonlinear vibration frequency ratios of the composite laminated trapezoidal plates are discussed, and the frequency-response curves are analyzed for the different ply angles and harmonic excitation forces.

• Advances in aircraft and spacecraft science
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• v.3 no.4
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• pp.379-397
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• 2016

In this manuscript, free vibrations of a unidirectional composite orthotropic Timoshenko beam based on finite strain have been studied. Using Green-Lagrange strain tensor and comprising all of the nonlinear terms of the tensor and also applying Hamilton's principle, equations of motion and boundary conditions of the beam are obtained. Using separation method in single-harmonic state, time and locative variables are separated from each other and finally, the equations of motion and boundary conditions are gained according to locative variable. To solve the equations, generalized differential quadrature method (GDQM) is applied and then, deflection and cross-section rotation of the beam in linear and nonlinear states are drawn and compared with each other. Also, frequencies of carbon/epoxy and glass/epoxy composite beams for different boundary conditions on the basis of the finite strain are calculated. The calculated frequencies of the nonlinear free vibration of the beam utilizing finite strain assumption for various geometries have been compared to von Karman one.

• Journal of Mechanical Science and Technology
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• v.17 no.12
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• pp.1922-1927
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• 2003

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6$\^$th/ order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhoff-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.