• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.1
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• pp.63-69
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• 2003

The ordinary differential equations governing free vibrations of elastic horizontally curved beams are derived, in which the effects of rotatory inertia and shear deformation as well as the effects of both vertical and torsional inertias are included. Frequencies and mode shapes are computed numerically for parabolic curved beams with the hinged-hinged, hinged-clamped and clamped-clamped ends. Comparisons of natural frequencies between this study and ADINA are made to validate the theories and numerical methods developed herein. The lowest three natural frequency parameters are reported. with and without the effects of rotatory inertia and shear deformation. as functions of the three non-dimensional system parameters: the horizontal rise to span length ratio. the slenderness ratio and the stiffness parameter.

• Journal of KSNVE
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• v.3 no.4
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• pp.331-339
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• 1993

The main purpose of this paper is to present an analytical method for free vibration of arches with thickness varying in a discontinuous fashion. The ordinary differential equations governing the free vibration of these arches are derived as nondimensional forms including the effect of rotatory inertia. The governing equation are solved numerically for the circular and sinusoidal arches with hinged-hinged-hinged end clamped-clamped end constraints. As the numerical results, the effect of rotatory inertia on the natural frequencies is reported. The lowest four natural frequencies are presented as the functions of four nondimensional system parameters; the rise to span length ratio, the slenderness ratio, the section ratio and the ratio of discontinuous section.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.301-308
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• 1998

This paper deals with the influence of elastic foundations on natural frequencies of curved beams. Taking into account the effects of rotatoy inertia and shear deformation, the differential equations governing free, out-of-plane vibrations of circular curved beams resting on Winkler-type foundations are derived and solved numerically. Hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered in numerical examples. The lowest three natural frequencies are claculated over a range of non-dimensional system parameters: the horizontal rise to span length ratio, the slenderness ratio, the foundation parameter, and the width ratio of contact area between the beam and foundation. The effects of rotatory inertia and shear deformation are also analyzed.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.391-397
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• 2001

This paper explores the free vibrations of double hinged curved beams with transition segment. In this study, the clothoid curve is chosen as the transition segment of beams. The differential equations governing free vibration of such beams are derived in which the effects of rotatory inertia and shear deformation are included. The Runge-Kutta method and Determinant Search method are used to perform the integration of differential equations and to compute natural frequencies, respectively. In numerical examples, the double hinged end constraint is considered. The lowest four natural frequencies are presented as functions of three non-dimensional system parameters: the slenderness ratio, shear parameter and stiffness parameter.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.768-771
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• 2005

The purpose of this paper is to investigate the free vibration of stepped noncircular arches. Taking into account the effects of axial deformation, rotatory inertia and shear deformation, the governing differential equations are solved numerically for the elliptic and sinusoidal geometries with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. The lowest four natural frequencies are presented as functions of four non-dimensional system parameters: the arch rise to span length ratio, the slenderness ratio, the section ratio, and the discontinuous sector ratio.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.435-440
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• 2002

The free vibration of partially embedded piles is investigated. The pile model is based on the Bernoulli-Euler beam theory and the soil is idealized as a Winkler model for mathematical simplicity. The governing differential equation for the free vibrations of such members is solved numerically The piles with one typical end constraint (clamped/hinged/free) and the other hinged end with rotational spring are applied in numerical examples. The lowest three natural frequencies are calculated over a range of non-dimensional system parameters: the rotational spring parameter, the relative stiffness and the embedded ratio.

• Magazine of the Korean Society of Agricultural Engineers
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• v.38 no.3
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• pp.50-57
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• 1996

A numerical method is presented to obtain the natural frequencies and mode shapes of the arbitrary tapered beams with static deflection due to arbitrary distributed dead loads. The differential equation governing free vibration of such beams is derived and solved numerically. The double integration method using the trapezoidal rule is used to solve the static behaviour of beams loaded arbitrary distributed dead load. Also, the Improved Euler method and the determinant search method are used to integrate the differential equation subjected to the boundary conditions and to determine the natural frequencies of the beams, respectively. In the numerical examples, the various geometries of the beams are considered : (1) linearly tapered beams as the arbitrary variable cross-section, (2) the triangular, sinusoidal and uniform loads as the arbitrary distributed dead loads and (3) the hinged-hinged, clamped-clamped and hinged-clamped ends as the end constraints. All numerical results are shown as the non-dimensional forms of the system parameters. The lowest three natural frequencies versus load parameter, slenderness ratio and section ratio are reported in figures. And for the comparison purpose, the typical mode shapes with and without the effects of static deflection are presented in the figure. According to the numerical results obtained in this analysis, the following conclusions may be drawn : (1) the natural frequencies increase when the effects of static deflections are included, (2) the effects are larger at the lower modes than the higher ones and (3) it should be betteF to include the effect of static deflection for calculating the frequencies when the beams are supported by both hinged ends or one hinged end.

• The Journal of Korean Physical Therapy
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• v.27 no.1
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• pp.43-49
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• 2015

Purpose: The aim of the current study was to examine the effects of hinged ankle-foot orthosis (HAFO) on walking function in children with spastic diplegic cerebral palsy (CP). Methods: Thirty-two children (mean age: $6.79{\pm}0.35years$, age range: 5-7 years) who were diagnosed with spastic diplegic cerebral palsy participated in the study. Each subject typically walked through 10 meters of a gait platform with markers on the subject's proper body segments and underwent 3-D motion analysis system with and without hinged ankle-foot orthosis. The HAFOs were all custom-made for individual CP children and had plantarflexion stop at $0^{\circ}C$ with no dorsiflexion stop. The interventions were conducted over three trials in each group, and measurements were performed on each subject by one examiner in three trials. 3-D motion analysis system was used to measure gait parameters such as walking velocity, cadence, step-length, step-width, stride-length, and double support period in two conditions. Results: The walking velocity, cadence, step-length, and stride-length were significantly greater for the HAFO condition as compared to the no HAFO condition (p<0.05). However, no significant difference in step-width and double support period was observed between two conditions. Conclusion: These findings suggest that using the HAFO during walking would suggest positive evidence for improving the spatiotemporal parameters of gait in children with spastic diplegic cerebral palsy.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2008.11a
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• pp.577-578
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• 2008

• Journal of KSNVE
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• v.6 no.5
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• pp.587-594
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• 1996

The differential equation governing both the free vibrations and buckling loads of tapered beam-columns of regular polygon cross-section with constant volume were derived and solved numerically. The parabolic and sinusoidl tapers were chosen as the variable depth of cross-section for the tapered beam-column. In numerical examples, the clamped-clamped, hinged-clamped and hinged-hinged end constraints were considered. The variations of frequency parameters and first buckling load parameters with the non-dimensional system parameters are reported in figures, and typical vibrating mode shapes are presented. Also, the configurations of strongest columns were determined.