• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2006.10a
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• pp.134-143
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• 2006

Out of all types of motions the critical motions leading to capsize is roll. The dynamic amplification in case of roll motion may be large for ships as roll natural frequency generally falls within the frequency range of wave energy spectrum typical used for estimation of motion spectrum. Roll motion is highly non-linear in nature. Den are various representations of non-linear damping and restoring available in literature. In this paper an uncoupled non-linear roll equations with three representation of damping and cubic restoring term is solved using a perturbation technique. Damping moment representations are linear plus quadratic velocity damping, angle dependant damping and linear plus cubic velocity dependant damping. Numerical value of linear damping coefficient is almost same for all types but non-linear damping is different. Linear and non-linear damping coefficients are obtained form free roll decay tests. External rolling moment is assumed as deterministic with sinusoidal form. Maximum roll amplitude of non-linear roll equation with various representations of damping is calculated using analytical procedure and compared with experimental results, which are obtained form forced tests in regular waves by varying frequency with three wave heights. Experiments indicate influence of non-linearity at resonance frequency. Both experiment and analytical results indicates increase in maximum roll amplitude with wave slope at resonance. Analytical results are compared with experiment results which indicate maximum roll amplitude analytically obtained with angle dependent and cubic velocity damping are equal and difference from experiments with these damping are less compared to non-linear equation with quadratic velocity damping.

• Earthquakes and Structures
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• v.17 no.2
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• pp.191-204
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• 2019

Near-field earthquake records including long-period high-amplitude velocity pulses can cause large isolation system displacements leading to buckling or rupture of isolators. In such cases, providing supplemental damping in the isolation system has been proposed as a solution. However, it is known that linear viscous dampers can reduce base displacements in case of near-field earthquakes but at the potential expense of increased superstructure response in case of far-field earthquakes. But can non-linear dampers with different levels of non-linearity offer a superior seismic performance? In order to answer this question, the effectiveness of non-linear viscous dampers in reducing isolator displacements and its effects on the superstructure response are investigated. A comparison with linear viscous dampers via time history analysis is done using a base-isolated benchmark building model under historical near-field and far-field earthquake records for a wide range of different levels of non-linearity and supplemental damping. The results show that the non-linearity level and the amount of supplemental damping play important roles in reducing base displacements effectively. Although use of non-linear supplemental dampers may cause superstructure response amplification in case of far-field earthquakes, this negative effect may be avoided or even reduced by using appropriate combinations of non-linearity level and supplemental damping.

• Journal of the Korean Society for Railway
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• v.9 no.1 s.32
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• pp.63-68
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• 2006

This paper proposes a fast Fourier transform(FFT)-based spectral analysis method(SAM) for the dynamic responses of the linear discrete dynamic models with non-proportional damping. The SAM was developed by using discrete Fourier transform(DFT)-theory. To verify the proposed SAM, a three-DOF system with non-proportional viscous damping is considered as an illustrative example. The present SAM is evaluated by comparing the dynamic responses obtained by SAM with those obtained by Runge-Kutta method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.109-114
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• 2002

The purpose of this study is to propose the general method for evaluating the equivalent damping ratios of a structure with supplemental response control dampers. We define Lyapunov function of which derivative can be expressed in autoregressive form and evaluate the equivalent damping ratios by using Lyapunov function and its derivative. This Lyapunov function may be called as generalized structural energy. In this study, it is assumed that the response of a structure is stationary random process and control dampers do not affect the modal shapes of a structure, and the structure has proportional damping. Proposed method can be used to get the equivalent damping ratios of a structure with non-linear control dampers such as friction dampers as well as linear control dampers. To show the effectiveness of the proposed method. we evaluate the equivalent damping ratios of a structure with viscous dampers. AMDs. and friction dampers. The equivalent damping ratios from proposed method are compared to those from eigenvalue analysis for linear control dampers. and those from time history analysis for non-linear control dampers. respectively.

• Steel and Composite Structures
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• v.32 no.4
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• pp.509-519
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• 2019

In this paper, an analytical approach for the free vibration analysis of spiral stiffened functionally graded (SSFG) cylindrical shells is investigated. The SSFG shell is resting on linear and non-linear elastic foundation with damping force. The elastic foundation for the linear model is according to Winkler and Pasternak parameters and for the non-linear model, one cubic term is added. The material constitutive of the stiffeners is continuously changed through the thickness. Using the Galerkin method based on the von $K\acute{a}rm\acute{a}n$ equations and the smeared stiffeners technique, the non-linear vibration problem has been solved. The effects of different geometrical and material parameters on the free vibration response of SSFG cylindrical shells are adopted. The results show that the angles of stiffeners and elastic foundation parameters strongly effect on the natural frequencies of the SSFG cylindrical shell.

• Journal of Mechanical Science and Technology
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• v.20 no.11
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• pp.1813-1822
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• 2006

The dynamic analysis of a plate with non-linearity due to large deformation was investigated in this study. There have been many theoretical and numerical analyses of the non-linear dynamic behavior of plates examining theoretically or numerically. The problem is how correctly an analytical model can represent the dynamic characteristics of the actual system. To address the issue, the continuous-time system identification technique was used to generate non-linear models, for stiffness and damping terms, and to explain the observed behaviors with single mode assumption after comparing experimental results with the numerical results of a linear plate model.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.3
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• pp.473-478
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• 1987

In this paper the optimum values of natural frequency ratio and damping ratio for damped systems were studied by numerical analysis. The relation between the amplitude ratio and frequency ratio obtained for the non-linear dynamic vibration absorber was found and it was compared with that of linear system. The results shows that the optimum frequency ratio decreases and the optimum damping ratio increases when the mass ratio of the damped system increases. The resonance frequency ratio and amplitude ratio decrease as mass ratio increases for the non-linear spring system.

• Structural Engineering and Mechanics
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• v.75 no.1
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• pp.33-47
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• 2020

In this paper the dynamic behavior of an isolated building subjected to idealized near-fault pulses is investigated. The building is represented with a simple 2-DOF model. Both linear and non-linear behavior of the isolation system is considered. Using dimensional analysis, in conjunction with closed form mathematical idealized pulses, appropriate dimensionless parameters are defined and self-similar curves are plotted on dimensionless graphs, based on which various conclusions are reached. In the linear case, the role of viscous damping is examined in detail and the existence of an optimum value of damping along with its significant variation with the number of half-cycles is shown. In the nonlinear case, where the behavior of the building depends on the amplitude of the excitation, the benefits of dimensional analysis are evident since the influence of the dimensionless 𝚷-terms is easily examined. Special consideration is given to the normalized strength of the non-linear isolation system that appears to play a complex role which greatly affects the response of the 2-DOF. In the last part of the paper, a comparison of the responses to idealized pulses between a linear fixed-base SDOF and the respective isolated 2-DOF with both linear and non-linear damping is conducted and it is shown that, under certain values of the superstructure and isolation system characteristics, the use of an isolation system can amplify both the normalized acceleration and displacement of the superstructure.

• Structural Engineering and Mechanics
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• v.22 no.3
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• pp.279-292
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• 2006

A new approach using the differential quadrature method (DQM) is derived for analysis of non-uniform beams resting on nonlinear media in this study. The influence of velocity dependent viscous damping and strain rate dependent viscous damping is investigated. The results solved using the DQM have excellent agreement with the results solved using the FEM. Numerical results indicated that the DQM is valid and efficient for non-uniform beams resting on non-linear media.

• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.655-664
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• 2023

Reinforced concrete (RC) shear wall structures are one of the most widely used structural systems to resist seismic loading all around the world. Although there have been several efforts to provide conceptually simple procedures to reasonably assess the seismic demands of structures over recent decades, it seems that lesser effort has been put on a number of structural forms such as RC shear wall structures. Therefore, this study aims to represent a simple linear response spectrum-based method which can acceptably predict the nonlinear displacements of a non-ductile RC shear wall structure subjected to an individual ground motion record. An effective period and an equivalent damping ratio are introduced as the dynamic characteristics of an equivalent linear SDOF system relevant to the main structure. By applying the fundamental mode participation factor of the original MDOF structure to the linear spectral response of the equivalent SDOF system, an acceptable estimation of the nonlinear displacement response is obtained. Subsequently, the accuracy of the proposed method is evaluated by comparison with another approximate method which is based on linear response spectrum. Results show that the proposed method has better estimations for maximum nonlinear responses and is more utilizable and applicable than the other one.