• Structural Engineering and Mechanics
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• v.35 no.5
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• pp.555-570
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• 2010

Shallow fixed arches have a nonlinear primary equilibrium path with limit points and an unstable postbuckling equilibrium path, and they may also have bifurcation points at which equilibrium bifurcates from the nonlinear primary path to an unstable secondary equilibrium path. When a shallow fixed arch is subjected to a central step load, the load imparts kinetic energy to the arch and causes the arch to oscillate. When the load is sufficiently large, the oscillation of the arch may reach its unstable equilibrium path and the arch experiences an escaping-motion type of dynamic buckling. Nonlinear dynamic buckling of a two degree-of-freedom arch model is used to establish energy criteria for dynamic buckling of the conservative systems that have unstable primary and/or secondary equilibrium paths and then the energy criteria are applied to the dynamic buckling analysis of shallow fixed arches. The energy approach allows the dynamic buckling load to be determined without needing to solve the equations of motion.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.457-464
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• 1998

The equilibrium path of shallow sinusoidal arches supported by hinges at both ends is investigated. The displacement increment method is used to get the solution of the nonlinear differential equations for these structures and to plot the equilibrium paths by the results. Using the equilibrium paths, the relations between the position of buckling point and buckling type for the case of sinusoidal distributed loads are inferred. From the result that the buckling type changes according to the normalized rise of arch, it is also shown that the arch rise is the governing factor to stability regions

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.233-242
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• 1998

Many papers which deal with the dynamic instability for shell-like structures under the step load have been published, but there are few papers which treat the essential phenomenon of the dynamic buckling using the phase plane for investigating occurrence of chaos. Dynamic buckling process in the phase plane is a very important thing for understanding why unstable phenomena are sensitively originated in nonlinear dynamics by various initial conditions. In this study, the direct and the indirect snap-buckling of shallow arches considering geometrical nonlinearity are investigated numerically and compared with the static critical load.

• International Journal of Railway
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• v.8 no.2
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• pp.46-49
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• 2015

In this paper, improved out-of-plane design of parabolic arches was proposed based on the current design code. The arches resist general loading by a combination of axial compression and bending actions, and the interaction formula between two extreme cases of axial and bending actions is generally used for the design. Firstly, the out-of-plane buckling strength of arches in a pure axial compression and a pure bending were studied. Then, out-of-plane design of parabolic aches under general transverse loading was investigated. From the results, it can be found that the proposed design equations provided good prediction of out-of-plane strength for parabolic arches which satisfy the thresholds for deep arches, while proposed design equations overestimated the buckling load of shallow arches.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.3
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• pp.407-415
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• 1999

There are two kinds of instability phenomena for shell-type structures which are snap-through and bifurcation buckling. These are very sensitive according to the shape characteristics including rise-span ratio and especially shape initial imperfection. In this study, the equilibrium path of shallow sinusoidal arches supported by hinges at both ends is investigated to grasp the instability behavior of shell-type structures with initial imperfection. The Galerkin method is used to get the nonlinear discretized equation of governing differential equation considering geometric nonlinearity of arches and the perturbation method is also used to transform the nonlinear equation to incremental form.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.2
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• pp.367-377
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• 2002

This paper deals with the free vibrations of shallow arches resting on elastic foundations. Foundations we assumed to follow the hypothesis proposed by Pasternak. The governing differential equation is derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. Two arch shapes with hinged-hinged and clamped-clamped end constraints we considered in analysis. The frequency equations (lowest symmetrical and antisymmetrical frequency equations) we obtained by Galerkin's method. The effects of arch rise, Winkler foundation parameter and shear foundation parameter on the lowest two natural frequencies are investigated. The effect of initial arch shapes on frequencies is also studied.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.405-432
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• 2022

Cracks in beams and shallow arches are modeled by massless rotational springs. First, we introduce a specially designed linear operator that "absorbs" the boundary conditions at the cracks. Then the equations of motion are derived from the first principles using the Extended Hamilton's Principle, accounting for non-conservative forces. The variational formulation of the equations is stated in terms of the subdifferentials of the bending and axial potential energies. The equations are given in their abstract (weak), as well as in classical forms.

• 한국공간정보시스템학회:학술대회논문집
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• 2004.05a
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• pp.161-168
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• 2004

The dynamic instability of snapping phenomena has been studied by many researchers. Few papers deal with dynamic buckling under loads with periodic characteristics, and the behavior under periodic excitations is expected to be different from behavior under STEP excitations. We investigate the fundamental mechanisms of the dynamic instability when the sinusoidally shaped arch structures are subjected to sinusoidally distributed excitations with pin-ends. The mechanisms of dynamic indirect snapping of shallow arches are especially investigated under not only STEP function excitations but also under sinusoidal harmonic excitations, applied in the up-and-down direction. The dynamic nonlinear responses are obtained by the numerical integration of the geometrically nonlinear equation of motion, and examined by Fourier spectral analysis in order to get the frequency-dependent characteristics of the dynamic instability for various load levels.

• Journal of The Korean Astronomical Society
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• v.40 no.4
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• pp.157-160
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• 2007

I present a model to explain the mass segregation and shallow mass functions observed in the central parts of starburst stellar clusters. The model assumes that the initial pre-stellar cores mass function resulting from the turbulent fragmentation of the proto-cluster cloud is significantly altered by the cores coalescence before they collapse to form stars. With appropriate, yet realistic parameters, this model based on the competition between cores coalescence and collapse reproduces the mass spectra of the well studied Arches cluster. Namely, the slopes at the intermediate and high mass ends, as well as the peculiar bump observed at $6M_{\bigodot}$. This coalescence-collapse process occurs on a short timescale of the order of the free fall time of the proto-cluster cloud (i.e., a few $10^4$ years), suggesting that mass segregation in Arches and similar clusters is primordial. The best fitting model implies the total mass of the Arches cluster is $1.45{\times}10^5M_{\bigodot}$, which is slightly higher than the often quoted, but completeness affected, observational value of a few $10^4M_{\bigodot}$. The model implies a star formation efficiency of ${\sim}30$ percent which implies that the Arches cluster is likely to a gravitationally bound system.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.945-966
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• 2017

The paper develops a rigorous mathematical framework for the behavior of arch and membrane like structures. Our main goal is to incorporate moving point loads. Both the weak and the strong damping cases are considered. First, we prove the existence and the uniqueness of the solutions. Then it is shown that the solution in the weak damping case is the limit of the strong damping solutions, as the strong damping vanishes. The theory is applied to a car moving on a bridge.