• Smart Structures and Systems
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• v.17 no.5
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• pp.753-771
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• 2016

This paper addresses the free and transient responses of a SDOF linear complex stiffness system by making use of the Hilbert transform and the convolution integral. Because the second-order differential equation of motion having the complex stiffness give rise to the conjugate complex eigen values, its time-domain analysis using the standard time integration scheme suffers from the numerical instability and divergence. In order to overcome this problem, the transient response of the linear complex stiffness system is obtained by the convolution integral of a green function which corresponds to the unit-impulse free vibration response of the complex system. The damped free vibration of the complex system is theoretically derived by making use of the state-space formulation and the Hilbert transform. The convolution integral is implemented by piecewise-linearly interpolating the external force and by superimposing the transient responses of discretized piecewise impulse forces. The numerical experiments are carried out to verify the proposed time-domain analysis method, and the correlation between the real and imaginary parts in the free and transient responses is also investigated.

• Proceedings of the KSME Conference
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• 2005.11a
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• pp.185.1-185.1
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• 2005

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.467-478
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• 1997

A nonlinear Galerkin method for the Burgers equation is considered. Due to the lack of the divergence free condition, the nonlinear term is treated differently compared to that of the Navier-Stokes equations. Strong convergence results are proved for the nonlinear Galerkin method.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1059-1079
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• 2021

We show that given any chain transitive set of a C¹ generic diffeomorphism f, if a diffeomorphism f has the eventual shadowing property on the locally maximal chain transitive set, then it is hyperbolic. Moreover, given any chain transitive set of a C¹ generic vector field X, if a vector field X has the eventual shadowing property on the locally maximal chain transitive set, then the chain transitive set does not contain a singular point and it is hyperbolic. We apply our results to conservative systems (volume-preserving diffeomorphisms and divergence-free vector fields).

• Journal of the Korean Mathematical Society
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• v.60 no.5
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• pp.987-998
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• 2023

It is shown that every continuum-wise expansive C¹ generic vector field X on a compact connected smooth manifold M satisfies Axiom A and has no cycles, and every continuum-wise expansive homoclinic class of a C¹ generic vector field X on a compact connected smooth manifold M is hyperbolic. Moreover, every continuum-wise expansive C¹ generic divergence-free vector field X on a compact connected smooth manifold M is Anosov.

• Journal of Korean Society of Steel Construction
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• v.17 no.6 s.79
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• pp.699-705
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• 2005

This paper investigates critical loads of tapered cantilever columns with a tip mass, subjected to a follower force. The linearly tapered solid rectangular cross-sections are adopted as the column taper. The differential equation governing free vibrations of such columns, also called Beck's columns, is derived using the Bernoulli-Euler beam theory. Both divergence and flutter critical loads are calculated from the load-frequency curves that are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters, namely, the taper type, the subtangential parameter, and the mass ratio.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.1 s.71
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• pp.85-92
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• 2006

This paper investigates critical loads of the tapered Beck's columns with clamped and spring supports, subjected to a subtangential follower force. The linearly tapered columns with the solid rectangular cross-section is adopted as the column taper. The differential equation governing free vibrations of such Beck's columns is derived using the Bemoulli-Euler beam theory. Both divergence and flutter critical loads are calculated from the load-frequency curves which are obtained by solving the differential equation. The critical loads are presented as functions of various non-dimensional system parameters: the taper type, the subtangential parameter and the spring stiffness.

• Journal of Korea Water Resources Association
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• v.46 no.2
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• pp.139-153
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• 2013

For analyzing shallow-water flows over the uneven bottom, the HLLL scheme and the divergence form for bed slope source term (DFB) technique, respectively were applied to the flux gradient and the bottom gradient source terms in a finite-volume model for the shallow water equations. And also the model incorporated the volume/free-surface relationship (VFR) to consider the partially submerged cells (PSC). It was identified that a simpler version of the weighted surface-depth gradient method in the MUSCL was equivalent to the original one in the accuracy for 1D steady flows. It was verified that the flux gradient term and the bottom gradient source term were well-balanced exactly by the VFR for the 1D PSC. The VFR for the triangular PSC settled the problem which the governing equations were not well-balanced by the DFB technique for the 2D PSC. There were good agreements in simulations and experiments for 2D dam-break flows over a triangular sill and a round bump. In addition, the partial dam-break flow was successfully simulated for flooding of roughnesses in an irregular bottom as well as a sloping one. Therefore, this model is expected to be applied to the real river with uneven topography.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.11 s.104
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• pp.1287-1294
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• 2005

The purpose of this paper is to investigate free vibrations and critical loads of the Beck's columns with a tip spring, which carry a tip mass. The ordinary differential equation governing free vibrations of Beck's column subjected to a follower force is derived based on the Bernoulli-Euler beam theory Both the divergence and flutter critical loads are calculated from the load-frequency corves that are obtained by solving the differential equation numerically. The critical loads are presented in the figures as functions of various non-dimensional system parameters such as the subtangential parameter, mass ratio and spring parameter.

• Smart Structures and Systems
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• v.19 no.4
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• pp.383-391
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• 2017

In this paper, we investigate the impacts of network topology on the performance of a distributed estimation algorithm, namely combine-then-adaptive (CTA) diffusion LMS, based on the data with or without the assumptions of temporal and spatial independence with noisy links. The study covers different network models, including the regular, small-world, random and scale-free whose the performance is analyzed according to the mean stability, mean-square errors, communication cost (link density) and robustness. Simulation results show that the noisy links do not cause divergence in the networks. Also, among the networks, the scale free network (heterogeneous) has the best performance in the steady state of the mean square deviation (MSD) while the regular is the worst case. The robustness of the networks against the issues like node failure and noisier node conditions is discussed as well as providing some guidelines on the design of a network in real condition such that the qualities of estimations are optimized.