• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.429-434
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• 2002

The differential equations governing in-plane free vibrations of stepped circular arcs, including the effects of axial deformation, rotatory inertia and shear deformation, are derived and solved numerically to obtain frequencies and mode shapes. Numerical results are calculated for the clamped-clamped symmetric and unsymmetric circular arcs with thickness varying in a discontinuous fashion. The lowest four natural frequencies and mode shapes are presented over a range of non-dimensional system parameters: the subtended angle, the slenderness ratio, the section ratio and the ratio of discontinuous section.

• Steel and Composite Structures
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• v.6 no.3
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• pp.221-236
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• 2006

The objective of this work is to describe the main steps involved in the derivation of a GBT (Generalised Beam Theory) formulation to analyse the vibration behaviour of loaded cold-formed steel members and also to illustrate the application and capabilities of this formulation. In particular, the paper presents and discusses the results of a detailed investigation about the local and global free vibration behaviour of lipped channel simply supported columns. After reporting some relevant earlier GBT-based results dealing with the buckling and vibration behaviours of columns and load-free members, the paper addresses mostly issues concerning the variation of the column fundamental frequency and vibration mode nature/shape with its length and axial compression level. For validation purposes, some GBT-based results are also compared with values obtained by means of 4-node shell finite element analyses performed in the code ABAQUS.

• Journal of KSNVE
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• v.4 no.2
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• pp.137-146
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• 1994

An analytical method for linear free vibration of fully liquid-filled circular cylindrical shell with various boundary conditions is developed by the Fourier series expansion based on the Stokes' transformation. A set of modal displacement functions and their derivatives of a circular cylindrical shell is substituted into the Sanders' shell equations in order to explicitily represent the Fourier coefficients as functions of the end point displacements, forces, and moments. For the vibration relevant to the liquid motion, the velocity potential of liquid is assumed as a sum of linear combination of suitable harmonic functions in the axial directions. The unknown parameter of the velocity potential is selected to satisfy the boundary condition along the wetted shell surface. An explicit expression of the natural frequency equation can be obtained for any kind of classical boundary conditions. The natural frequencies of the liquid-filled cylindrical shells with the clamped-free, the clamped-clamped, and the simply supported-simply supported boundary conditions examined in the previous works, are obtained by the analytical method. The results are compared with the previous works, and excellent agreement is found for the natural frequencies of the shells.

• Computers and Concrete
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• v.3 no.5
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• pp.285-299
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• 2006

The free vibration of stiffened and damaged coupled shear walls is investigated using the mixed finite element method. The anisotropic damage model is adopted to describe the damage extent of the reinforced concrete shear wall element. The internal energy of a locally damaged shear wall element is derived. Polynomial shape functions established by Kwan are used to present the component of displacements vector on each point within the wall element. The principle of virtual work is employed to deduce the stiffness matrix of a damaged shear wall element. The stiffened system is reinforced by an additional stiffening beam at some level of the structure. This induces additional axial forces, and thus reduces the bending moments in the walls and the lateral deflection, and increases the natural frequencies. The effects of the damage extent and the stiffening beam on the free vibration characteristics of the structure are studied. The optimal location of the stiffening beam for increasing as far as possible the first natural frequency of vibration is presented.

• Structural Engineering and Mechanics
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• v.45 no.2
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• pp.259-275
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• 2013

Free vibration of symmetric angle-ply layered conical shell frusta of variable thickness is analyzed under shear deformation theory with different boundary conditions by applying collocation with spline approximation. Linear and exponential variation in thickness of layers are assumed in axial direction. Displacements and rotational functions are approximated by Bickley-type splines of order three and obtained a generalized eigenvalue problem. This problem is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration of three and five-layered conical shells, made up of two different type of materials are considered. Parametric studies are made for analysing the frequencies of the shell with respect to the coefficients of thickness variations, length-to-radius ratio, length-to-thickness ratio and ply angles with different combination of the materials. The results are compared with the available data and new results are presented in terms of tables and graphs.

• Computers and Concrete
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• v.31 no.1
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• pp.1-7
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• 2023

In this paper, Timoshenko-beam model is developed for the vibration of double carbon nanotubes. The resulting frequencies are gained for axial wave mode and length-to-diameter ratios. The natural frequency becomes more prominent for lower length-to-diameter ratios and diminished for higher ratios. The converse behavior is observed for axial wave mode with clamped-clamped and clamped-free boundary conditions. The frequencies of clamped-free are lower than that of clamped-clamped boundary condition. The eigen solution is obtained to extract the frequencies of double walled carbon nanotubes using Galerkin's method through axial deformation function. Computer softer MATLAB is used for formation of frequency values. The frequency data is compared with available literature and found to be in agreement.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.7
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• pp.2223-2233
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• 1996

The analytical solutions for the free vibration of cross-ply laminated composite cyllindrical shell with axial stiffeners(stringers) are presented usint the energy method. The stiffeners are taken to be smeared over the surface of shell with the smeared stffener theory. The effect of the parameters such as the stacking sequences, the shell thichness, the shell radius-to stringer depth ratio, the stringer depth-to width ratio, the shell length-to radius ratio are studied. By comparison with the previously published experimental results and the analytical results for the stiffened isotropic cylindrical shell and the unstiffened orthotropic composite laminated cylindrical shell, it is shown that natural frequencies can be determined with adequate accuracy.

• Journal of KSNVE
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• v.2 no.3
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• pp.203-211
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• 1992

The main purpose of this paper is to present both the natural frequencies and the first critical loads of tapered columns. The ordinary differential equation governing the free vibration for tapered columns under compressive axial force is derived. Three kinds of cross sectional shape are considered in the governing equation. The Runge-Kutta method and determinant search method are used to perform the integration of the differential equation and to determine the natural frequencies, respectively. Additionally, the bisection method is used to determine the critical loads. In numerical examples, the effects of compressive axial force on the natural frequencies of tapered columns are investigated varying the end conditions. The first critical loads of tapered columns are determined on the basis of dynamic concepts. The first critical loads of tapered columns are determined on the basis of dynamic concept. The effects of cross sectional shapes are shown and some typical mode shapes are also presented.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.501-508
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• 2001

Free vibration analysis of multi-delaminated composite beam-columns subjected to axial compression load is performed in the present study. In order to investigate the effects of multi-delaminations on the natural frequency and elastic buckling load of multi-delaminated beam-columns, the general kinematic continuity conditions are derived from the assumption of constant slope and curvature at the multi-delamination tip. Characteristic equation of multi-delaminated beam-column is obtained by dividing the global multi-delaminated beam-columns into segments and by imposing recurrence relation from the continuity conditions on each sub-beam-column. The natural frequency and elastic buckling load of multi-delaminated beam-columns according to the incremental load of axial compression, which is limited to the maximum elastic buckling load of sound laminated beam-column, are obtained. It is found that the sizes, locations and numbers of multi-delaminations have significant effect on natural frequency and elastic buckling load, especially the latter ones.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.3
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• pp.261-267
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• 2014

The free vibration characteristics of cylindrical shells on inclined partial elastic foundations are investigated by an analytical method. The cylindrical shell is partially surrounded by the elastic foundations, these are represented by the Winkler or Pasternak model. The area of elastic foundation is not uniform and varies along the axial direction of the shell. The motion of shell is represented by first-order shear deformation theory(FSDT) to account for rotary inertia and transverse shear strains. The governing equation is obtained using the Rayleigh-Ritz method and a variation approach. To validate the present method, the numerical example is presented and compared with the present FEA results. The numerical results reveal that the elastic foundation has significant effect on vibration characteristics.