• Journal of KSNVE
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• v.5 no.3
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• pp.345-352
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• 1995

A very simple and computationally efficient numerical method is developed for the free vibration of arbitrary shape plates. A set of two- dimensional simple series functions is used as an admissible displacement functions in the Rayleigh-Ritz method to obtain the natural frequencies for the arbitrary shape plates. From the prescribed starting function satisfying only the geometric boundary conditions, the higher terms in the series function are constructed with adding order of polynomial. Natural frequencies are obtained for the arbitrary shape plates, with combinational boundary conditions. The obtained numerical results are presented, some cases are verified with other numerical methods in the literature.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.10 s.181
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• pp.2513-2519
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• 2000

Free vibration characteristics of an initially stressed CD/DVD disk, which is designed for increasing critical speeds of current optical disks, are analyzed using the Rayleigh-Ritz technique based on variational formulations. Natural frequencies of the new disk depend on membrane stresses caused by disk rotation as well as residual stresses imposed during the cooling process of the injection molding. Critical speeds are calculated for the various initial patterns of radial and circumferential stresses. Initially imposed tensile stresses increase the natural frequencies of all the vibration modes except zero nodal diameter mode, whose natural frequency is independent of circumferential stress. A new disk with initial tensile stress of 0.5MPa is shown to have its critical speed about 30 % higher than the current optical disk.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.788-793
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• 2004

The main purpose of this paper is to Investigate the free vibrations of circular curved members resting on nonhomogeneous elastic foundations. The governing differential equations derived in a previous paper are used. The governing equations are solved numerically to obtain frequencies. Hinged-hinged end constraint is considered in numerical examples. The lowest three natural frequencies are calculated over a wide range of non-dimensional system parameters: the foundation rested ratio, the foundation parameter, the horizontal rise to span length ratio, the slenderness ratio, and the width ratio of the contact area between the member and the foundation.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.6A
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• pp.827-833
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• 2008

This paper deals with the free vibrations of elastica shaped arches. The elastica shaped arches are formed by the post-buckled column whose arc length is always constant. The equations governing free, planar vibration of general arch in open literature are modified for applying the free vibrations of elastica shaped arch and solved numerically to obtain frequencies and mode shapes for hinged-hinged, clamped-hinged and clamped-clamped end constraints. The effects of rotatory inertia, rise ratio and slenderness ratio on natural frequencies are presented. The frequencies of elastica shaped arches are greater than those of parabolic shaped ones. Also, typical mode shapes are presented in figures.

• Ocean Systems Engineering
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• v.10 no.1
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• pp.67-86
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• 2020

The main goal of this study is to investigate the free vibration analysis of a large sag catenary with application to the jumper in hybrid riser system. The equation of motion is derived by using the variational method based on the virtual work principle. The finite element method is applied to evaluate the numerical solutions. The large sag catenary is utilized as an initial configuration for vibration analysis. The nonlinearity due to the large sag curvature of static configuration is taken into account in the element stiffness matrix. The natural frequencies of large sag catenary and their corresponding mode shapes are determined by solving the eigenvalue problem. The numerical examples of a large sag catenary jumpers are presented. The influences of bending rigidity and large sag shape on the free vibration behaviors of the catenary jumper are provided. The results indicate that the increase in sag reduces the jumper natural frequencies. The corresponding mode shapes of the jumper with large sag catenary shape are comprised of normal and tangential displacements. The large sag curvature including in the element stiffness matrix increases the natural frequency especially for a case of very large sag shape. Mostly, the mode shapes of jumper are dominated by the normal displacement, however, the tangential displacement significantly occurs around the lowest point of sag. The increase in degree of inclination of the catenary tends to increase the natural frequencies.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.04a
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• pp.180-185
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• 2013

A new formulation of the MNDIF method is introduced to extract highly accurate natural frequencies of concave plates with arbitrary shape. Originally, the MNDIF method cannot yield accurate natural frequencies for concave plates. To overcome this weak point, a new approach of dividing a concave plate into two convex domains is proposed and the validity and accuracy is shown in a verification example.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.334-339
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• 1998

The free vibration analysis of the simply supported steel and composite cylindrical shells are investigated. The natural frequencies and mode shapes of the shell are experimentally obtained by impact testing using an impact hammer and an accelerometer. The effects of the material and geometry on the vibrational characteristics of the shell are examined. The experimental results are compared with the analytical and a finite element results. They showed good agreement with each other.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1990.04a
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• pp.12-17
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• 1990

Stepped bean with immovable ends for large amplitude of vibration including effects of longitudinal displacement, shear deformation and rotary inertia is investigated for free and forced vibration using finite element method. Modified harmonic force matrix is introduced for analysis of vibration with finite amplitude of the stepped beam under uniform hamonic loading and beam with nonuniform harmonic loading. Numerical examples of stepped beam with various support conditions are analysed for deflections and natural frequencies. Results show that the proposed method is valid and efficient.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.117-120
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• 2007

This study deals with the free vibrations and buckling loads of column with clamped-spring ends and constant volume. The column has the regular polygon cross-section whose depth is varied with the linear functional fashion. The differential equation governing the free vibration of such column is derived in which the effect of axial load is included. The differential equation is solved numerically for calculating frequencies. By using the relationship between loads and frequencies, the buckling loads are also obtained.

• Steel and Composite Structures
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• v.25 no.4
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• pp.427-442
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• 2017

This paper presents unprecedented damped oscillation behaviours of a precast steel-concrete composite slab panel for track support. The steel-concrete composite slab track is an innovative slab track, a form of ballastless track which is becoming increasingly attractive to asset owners as they seek to reduce lifecycle costs and deal with increasing rail traffic speeds. The slender nature of the slab panel due to its reduced depth of construction makes it susceptible to vibration problems. The aim of the study is driven by the need to address the limited research available to date on the dynamic behaviour of steel-concrete composite slab panels for track support. Free vibration analysis of the track slab has been carried out using ABAQUS. Both undamped and damped eigenfrequencies and eigenmodes have been extracted using the Lancsoz method. The fundamental natural frequencies of the slab panel have been identified together with corresponding mode shapes. To investigate the sensitivity of the natural frequencies and mode shapes, parametric studies have been established, considering concrete strength and mass and steel's modulus of elasticity. This study is the world first to observe crossover phenomena that result in the inversion of the natural orders without interaction. It also reveals that replacement of the steel with aluminium or carbon fibre sheeting can only marginally reduce the natural frequencies of the slab panel.