• Journal of Advanced Marine Engineering and Technology
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• v.16 no.5
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• pp.67-76
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• 1992

This paper describes the vibration characteristic of second-order nonlinear systems subjected to parametric excitation. Emphasis is put on the examination of the hydrodynamic nonlinear damping effect on limiting the response amplitudes of parametric vibration. Since the parametric vibration is described by the Mathieu equation, the Mathieu stability chart is examined in this paper. In addition, the steady-state solutions of the nonlinear Mathieu equation in the first instability region are obtained by using a perturbation technique and are compared with those by a numerical integration method. It is shown that the response amplitudes of parametric vibration are limited even in unstable conditions by hydrodynamic nonlinear damping force. The largest reponse amplitude of parametric vibration occurs in the first instability region of Mathieu stability chart. The parametric excitation induces the response of a dynamic system to be subharmonic, superharmonic or chaotic according to their dynamic conditions.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.7 s.100
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• pp.851-858
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• 2005

The response characteristics of one to one resonance on the quadrangle cantilever beam in which basic harmonic excitations are applied by nonlinear coupled differential-integral equations are studied. This equations have 3-dimensional non-linearity of nonlinear inertia and nonlinear curvature. Galerkin and multi scale methods are used for theoretical approach to one-to-one internal resonance. Nonlinear response characteristics of 1st, 2nd, 3rd modes are measured from the experiment for basic harmonic excitation. From the experimental result, geometrical terms of non-linearity display light spring effect and these terms play an important role in the response characteristics of low frequency modes. Nonlinear nitration in the out of plane are also studied.

• Tribology and Lubricants
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• v.15 no.1
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• pp.68-76
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• 1999

This paper presents the nonlinear characteristics of the oil lubricated hydrodynamic journal bearing. The traditional approach is to characterize the behavior and performance of fluid film hydrodynamic journal bearings by means of linearized bearing analysis. The objective of this paper is to examine the nonlinear characteristics of the journal bearing when an external sinusoidal shock is given to the system. The oil film force is obtained by solving the finite width Reynolds equation at each time step by the solution of the column method. Frequency response function and journal orbit obtained from both linear and nonlinear bearing simulations are compared with each other.

• Earthquakes and Structures
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• v.1 no.2
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• pp.215-230
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• 2010

The main objectives of this work were to investigate the effects of the nonlinear behavior of the isolation pads on the seismic response of bridges with rubber bearings, and to identify when base isolation improved their seismic performance. To achieve these objectives a parametric study was conducted designing a set of bridges for three different soil types and varying the number of spans, span lengths, and pier heights. The seismic responses (accelerations, displacements and pier seismic forces) were evaluated for three different structural models subjected to three earthquakes with different dynamic characteristics. The first represented bridges without base isolation; the second corresponded to the same bridges including now rubber bearings as an isolation system, with linear elastic behavior that shifted the natural period of the bridge by a factor of 2 to 4. In the third model the seismic response of bridges supported on lead-Rubber bearings was studied accounting for the nonlinear behavior of the lead. The results show clearly the importance of the nonlinear behavior on the seismic performance of the bridges.

• Smart Structures and Systems
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• v.30 no.3
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• pp.239-243
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• 2022

We investigate the influence of nonlinear viscoelastic damping on the response of a cantilever sensor covered by piezoelectric layers in a symmetric or asymmetric configuration. We formulate an initial-boundary-value problem which consistently incorporates both geometric and material nonlinearities including the effect of viscoelastic damping which cannot be ignored for micro- and nano-mechanical sensor operation in a vacuum environment. We employ an asymptotic multiple-scales methodology to yield the system nonlinear frequency response near its primary resonance and employ a model-based estimation procedure to deduce the system damping backone curve from controlled experiments in vacuum. We discuss the effect of nonlinear damping on sensor applications for scanning probe microscopy.

• Journal of the Earthquake Engineering Society of Korea
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• v.1 no.4
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• pp.1-9
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• 1997

This paper examined various aspects of a linear and a nonlinear response spectrum method in seismic response analysis of multi-story building structures. The response spectrum method that has been widely used in the analysis of linear structures was proposed different mode superposition method by several ivestigators, and the differences between combinations with an elastic modal analysis reviwed closely. It seems, however, that this method is not used to nonlinear seismic analysis. It is the purpose of this paper to propose an alternative method by means of which a nonlinear MDOF structure with long period may be analysed by an extention of response spectrum method. For nonlinear seismic analysis of high-rise building structures using technique proposed in this study, it is intended to serve primarily as a tool in preliminary designs instead of time history analysis.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.10a
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• pp.275-281
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• 1996

In order to examine the validity of an asymptotic solution obtained from the method of multiple scales, we investigate a third-order subharmonic resonance response of a bar constrained by a nonlinear spring to a harmonic excitation. The motion of the bar is governed by a linear partial differential equation with a nonlinear boundary condition. The nonlinear boundary value problem is solved by using the finite difference method. The numerical solution is compared with the asymptotic solution.

• Structural Engineering and Mechanics
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• v.83 no.3
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• pp.401-413
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• 2022

The collapse of civil infrastructure due to natural disasters results in financial losses and many casualties. In particular, the recent increase in earthquake activities has highlighted on the importance of assessing the seismic performance and predicting the seismic risk of a structure. However, the nonlinear behavior of a structure and the uncertainty in ground motion complicate the accurate seismic response prediction of a structure. Artificial intelligence can overcome these limitations to reasonably predict the nonlinear behavior of structures. In this study, a deep learning-based algorithm was developed to estimate the time-history seismic response of bridge structures. The proposed deep neural network was trained using structural and ground motion parameters. The performance of the seismic response prediction algorithm showed the similar phase and magnitude to those of the time-history analysis in a single-degree-of-freedom system that exhibits nonlinear behavior as a main structural element. Then, the proposed algorithm was expanded to predict the seismic response and fragility prediction of a bridge system. The proposed deep neural network reasonably predicted the nonlinear seismic behavior of piers and bearings for approximately 93% and 87% of the test dataset, respectively. The results of the study also demonstrated that the proposed algorithm can be utilized to assess the seismic fragility of bridge components and system.

• Structural Engineering and Mechanics
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• v.83 no.6
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• pp.709-727
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• 2022

Fastening systems have a significant role in the response of railway slab track systems. Although experimental tests indicate nonlinear behavior of fastening systems, they have been simulated as a linear spring-dashpot element in the available literature. In this paper, the influence of the nonlinear behavior of fastening systems on the slab track response was investigated. In this regard, a nonlinear model of vehicle/slab track interaction, including two commonly used fastening systems (i.e., RFFS and RWFS), was developed. The time history of excitation frequency of the fastening system was derived using the short time Fourier transform. The model was validated, using the results of a comprehensive field test carried out in this study. The frequency response of the track was studied to evaluate the effect of excitation frequency on the railway track response. The results obtained from the model were compared with those of the conventional linear model of vehicle/slab track interaction. The effects of vehicle speed, axle load, pad stiffness, fastening preload on the difference between the outputs obtained from the linear and nonlinear models were investigated through a parametric study. It was shown that the difference between the results obtained from linear and nonlinear models is up to 38 and 18 percent for RWFS and RFFS, respectively. Based on the outcomes obtained, a nonlinear to linear correction factor as a function of vehicle speed, vehicle axle load, pad stiffness and preload was derived. It was shown that consideration of the correction factor compensates the errors caused by the assumption of linear behavior for the fastening systems in the currently used vehicle track interaction models.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.6 s.177
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• pp.1593-1600
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• 2000

A method based on frequency domain approaches is presented for the nonlinear parameters identification of structure having nonlinear joints. The finite element model of linear substructure is us ed to calculating its frequency response functions needed in parameter identification process. This method is easily applicable to a complex real structure having nonlinear elements since it uses the frequency response function of finite element model. Since this method is performed in frequency domain, the number of equations required to identify the unknown parameters can be easily increased as many as it needed, just by not only varying excitation amplitude but also selecting excitation frequencies. The validity of this method is tested numerically and experimentally with a cantilever beam having the nonlinear element. It was verified through examples that the method is useful to identify the nonlinear parameters of a structure having arbitary nonlinear boundaries.