• Journal of Korean Society of Steel Construction
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• v.9 no.4 s.33
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• pp.673-682
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• 1997

The main purpose of this paper is to investigate the effects of rotatory inertia and shear deformation on the natural frequencies of arches with variable curvature. The differential equations are derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. The governing equations are solved numerically for parabolic, circular and elliptic geometries with hinged-hinged, hinged-clamped and clamped-clamped end constraints. For each cases, the four lowest frequency parameters are presented as functions of the two dimensionless system parameters; the arch rise to span length ratio, and the slenderness ratio.

• Structural Engineering and Mechanics
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• v.24 no.6
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• pp.665-682
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• 2006

A vibration-based nondestructive damage evaluation technique for a curved thin beam is introduced. The proposed method is capable of detecting, locating, and sizing structural damage simultaneously by using a few of the lower natural frequencies and their corresponding mode shapes before and after a small damage event. The proposed approach utilizes modal flexibilities reconstructed from measured modal parameters. A rigorous system of equations governing damage and curvature of modal flexibility is derived in the context of elasticity. To solve the resulting system of governing equations, an efficient pseudo-inverse technique is introduced. The direct inspection of the resulting solutions provides the location and severity of damage in a curved thin beam. This study confirms that there is a strong linear relationship between the curvature of modal flexibility and flexural damage in the selected class of structures. Several numerical case studies are provided to justify the performance of the proposed approach. The proposed method introduces a way to avoid the singularity and mode selection problems from earlier attempts.

• Structural Engineering and Mechanics
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• v.78 no.3
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• pp.255-267
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• 2021

The analysis of simply supported single-cell skew-curved reinforced concrete (RC) box-girder bridges is carried out using a finite element based CsiBridge software. The behaviour of skew-curved box-girder bridges can not be anticipated simply by superimposing the individual effects of skewness and curvature, so it becomes important to examine the behaviour of such bridges considering the combined effects of skewness and curvature. A comprehensive parametric study is performed wherein the combined influence of the skew and curve angles is considered to determine the maximum bending moment, maximum shear force, maximum torsional moment and maximum vertical deflection of the bridge girders. The skew angle is varied from 0° to 60° at an interval of 10°, and the curve angle is varied from 0° to 60° at an interval of 12°. The scantly available literature on such bridges focuses mainly on the analysis of skew-curved bridges under dead and point loads. But, the effects of actual loadings may be different, thus, it is considered in the present study. It is found that the performance of these bridges having more curvature can be improved by introducing the skewness. Finally, several equations are deduced in the non-dimensional form for estimating the forces and deflection in the girders of simply supported skew-curved RC box-girder bridges, based upon the results of the straight one. The developed equations may be helpful to the designers in proportioning, analysing, and designing such bridges, as the correlation coefficient is about 0.99.

• Korean Journal of Hydrosciences
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• v.3
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• pp.45-59
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• 1992

The flow characteristics varying with rate of the radius of curvature to width (Rc/B) in open channel bends are investigated with a simplified numerical model. Secondary flow velocity and transverise bed slope are formulated from the equations of momentum and force balance analysis, respectively. The conservation equations of mass and streamwise momentum are simplified by depth integration and its solution could be obtained from the explicit finite difference method. Three sets of computer simulation are executed. The rates of Rc/B adopted in simulations are 2.7, 5.4 and 8.1. The terms analyzed in this paper secondary flow velocity, streamwise velocity, the path of maximum steamwise velocity, deviation angle, and mass-shift velocity.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.115-122
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• 1998

In this paper, when N is a compact Riemannian manifold, we discuss the method of using warped products to construct timelike or null future(or past) complete Lorentzian metrics on $M{\;}={\;}[a,{\;}{\infty}){\times}_f{\;}N$ with specific scalar curvatures.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.767-775
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• 2010

Let ${\varphi}\;:\;(M^n,\;F)\;{\rightarrow}\;(\overline{M}^{n+p},\;\overline{F})$ be an isometric immersion from a Finsler manifold to a Finsler manifold. In this paper, we shall obtain the Gauss and Codazzi equations with respect to the Chern connection on submanifolds M, by which we prove that if M is a weakly totally geodesic submanifold of $\overline{M}$, then flag curvature of M equals flag curvature of $\overline{M}$.

• The Pure and Applied Mathematics
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• v.6 no.2
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• pp.95-101
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• 1999

In this paper, when N is a compact Riemannian manifold, we discuss the method of using warped products to construct timelike or null future complete Lorentzian metrics on $M{\;}={\;}[\alpha,\infty){\times}_f{\;}N$ with specific scalar curvatures.

• Advances in aircraft and spacecraft science
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• v.8 no.4
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• pp.345-372
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• 2021

The analysis of nonlinear vibrations, buckling, post-buckling, flutter boundary determination and post-flutter behavior of a homogeneous curved plate assuming cylindrical bending is conducted in this article. Other assumptions include simply-supported boundary conditions, supersonic aerodynamic flow at the top of the plate, constant pressure conditions below the plate, non-viscous flow model (using first- and third-order piston theory), nonlinear structural model with large deformations, and application of mechanical and thermal loads on the curved plate. The analysis is performed with constant environmental indicators (flow density, heat, Reynolds number and Mach number). The material properties (i.e., coefficient of thermal expansion and modulus of elasticity) are temperature-dependent. The equations are derived using the principle of virtual displacement. Furthermore, based on the definitions of virtual work, the potential and kinetic energy of the final relations in the integral form, and the governing nonlinear differential equations are obtained after fractional integration. This problem is solved using two approaches. The frequency analysis and flutter are studied in the first approach by transferring the handle of ordinary differential equations to the state space, calculating the system Jacobin matrix and analyzing the eigenvalue to determine the instability conditions. The second approach discusses the nonlinear frequency analysis and nonlinear flutter using the semi-analytical solution of governing differential equations based on the weighted residual method. The partial differential equations are converted to ordinary differential equations, after which they are solved based on the Runge-Kutta fourth- and fifth-order methods. The comparison between the results of frequency and flutter analysis of curved plate is linearly and nonlinearly performed for the first time. The results show that the plate curvature has a profound impact on the instability boundary of the plate under supersonic aerodynamic loading. The flutter boundary decreases with growing thermal load and increases with growing curvature.

• The Journal of the Korea Contents Association
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• v.10 no.10
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• pp.451-455
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• 2010

Hydraulics usually deals with flows with free surface. When the surface curvature is small, the assumption of hydrostatic pressure distribution is enough. However, in the case, when the curvature is big, the non-hydrostatic pressure distribution should be taken into account and the Navier-Stokes equations should be employed instead of the depth-averaged shallow water equations. For the simulation of two immiscible fluids with different characteristics (e.g. water and air, water and oil), the level set method is selected for this purpose. The developed model is applied to classical dam break problem and the computational results are compared with the experimental data. The effectiveness of the developed model is confirmed.

• Transactions of the Korean Society of Automotive Engineers
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• v.21 no.2
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• pp.122-130
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• 2013

Rail geometries such as cant, grade and curvature can be easily represented by means of a track coordinate system. In this analysis, in order to derive a dynamic and constraint equation of a wheelset, the track coordinate system is used as an intermediate stage. Dynamic and constraint equations of railway vehicle bodies except the wheelset are written in the Cartesian coordinate system as a conventional method. Therefore, whole dynamic equations of a railway vehicle are derived by combining wheelset dynamic equations and dynamic equations of railway vehicle bodies. Constraint equations and constraint Jacobians are newly derived for the track coordinate system. A process for numerical analysis is suggested for the derived dynamic and constraint equations of a railway vehicle. The proposed dynamic analysis of a railway vehicle is validated by comparison against results obtained from VI-RAIL analysis.