• Steel and Composite Structures
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• v.50 no.4
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• pp.429-441
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• 2024

This paper studies the free vibration behavior of trapezoidal shaped coupled double-layered graphene sheets (DLGS) system using first-order shear deformation theory (FSDT) and incorporating nonlocal elasticity theory. Two nanoplates are assumed to be bonded by an interlayer van der walls force and surrounded by an external kelvin-voight viscoelastic medium. The governing equations together with related boundary condition are discretized using a mapping-differential quadrature method (DQM) in the spatial domain. Then the natural frequency of the system is obtained by solving the eigen value matrix equation. The validity of the current study is evaluated by comparing its numerical results with those available in the literature and then a parametric study is thoroughly performed, concentrating on the series effects of angles and aspect ratio of GS, viscoelastic medium, and nonlocal parameter. The model is used to study the vibration of DLGS for two typical deformation modes, the in-phase and out-of-phase vibrations, which are investigated. Numerical results indicate that due to Increasing the damping parameter of the viscoelastic medium has reduced the frequency of both modes and this medium has been able to overdamped the oscillations and by increasing stiffness parameters both in-phase and out-of-phase vibration frequencies increased.

• Journal of Ocean Engineering and Technology
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• v.24 no.6
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• pp.61-70
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• 2010

This study presents free vibration analyses of perforates steel plates with various cutouts. Four different parameters (shape, size, curvature radius ratio, and rotation of cutouts) were considered to investigate the effects of those parameters on the free vibration characteristics, such as natural frequencies of the perforated steel plates. Three different shapes of cutouts are circle, square, and triangle, and the considered sizes are 5, 10, 15, 20, and 25 mm. For the triangular and square cutouts, the characteristic radii of the inscribed circles of those cutouts were defined. In addition, the curvature radius ratio was defined as the ratio of curvature radius of bluntness and the characteristic radius. Then, total seven different curvature radius ratios (0, 0.1, 0.3, 0.5, 0.7, 0.9, and 1) were considered. To investigate the rotation effect of the cutouts, it was considered four rotations ($0^{\circ}$, $15^{\circ}$, $30^{\circ}$, and $45^{\circ}$) for the square cutouts and three rotations (0, 15, and 30) for the triangular cutouts. All the free vibration analyses were conducted using a general purpose finite element program. From the analyses we found that the most influential parameter for the free vibration response of the perforated plates is the size of cutout. The other factors such as the shape, curvature radius ratio, and rotation are minors; they mainly change the natural frequency as long as the size effect is accompanied.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.1
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• pp.189-195
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• 2002

This paper deals with the free vibration of horizontally curved beams with transition currie. Based on the dynamic equilibrium equations of a curved beam element subjected to the stress resultants and inertia forces, the governing differential equations are derived for the out-of-plane vibration of curved beam with variable curvature. These equations are applied to the beam having transition curve in which the clothiod curve is chosen in this study. The differential equations are solved by the numerical methods lot calculating the natural frequencies and mode shapes. For verifying theories developed herein, the frequency parameters obtained from this studs and ADINA are compared with each other. As the numerical results, the various parametric studies effecting on natural frequencies are investigated and those results are presented in tables and figures.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.12
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• pp.32-40
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• 2018

In order to avoid excessive vibration, it is required to carry out a vibration analysis of heat-exchanger/nuclear-reactor at the design stage. Information of eigen-frequency in the vibration problem is required to evaluate safety of heat-exchange/nuclear reactor. This paper describes a numerical method, Galerkin's method, to solve the eigenvalue problem occurred in a cantilever beam. The beam is restrained with added mass and spring at the free end or a node point of a mode shape. The numerical results of eigen-frequency were compared with simple analytical and experimental results given by simple approach and simple test, respectively. It is found that Galerkin's method is applicable to estimate the eigen-frequency of the cantilever beam. The frequencies become lower with increasing the added mass and the frequencies increase with the spring force. It is shown the heavy added mass has a role of support on the flexible tube. The eigen-frequency of the first mode, for the system with the added mass mounted at the free end, can be calculated by the approximate analytical method existing with more or less accuracy.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.596-601
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• 2000

The paper presents free vibration and stability analyses of a non-uniform Timoshenko beam resting on a two-parameter elastic soil. The soil parameters can vary along the spat and is assumed to be two-parameter model including the effects of both transverse shear deformation and elastic foundation Governing equations related to the vibration and the stability of the beam are derived from Hamilton's principle, and the resulting eigen-value problems can be solved to give natural frequencies and critical force by finite element method. Numerical results for both vibration and stability of beams under an axial force are presented and compared with other available solutions. Finally, vibration frequencies, mode shapes and critical forces are investigated for various thickness ratios, shear foundation parameter, Winkler foundation parameter and boundary conditions of tapered Timoshenko beams.

• Computational Structural Engineering
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• v.10 no.4
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• pp.291-302
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• 1997

This paper presents an analytical method for evaluating the free vibration of a circular cylindrical tank filled with bounded compressible fluid. The analytical method was developed by means of the finite Fourier series expansion method. The compressible fluid motion was determined by means of the linear velocity potential theory. To clarify the validity of the analytical method, the natural frequencies of a circular cylindrical tank with the clamped-clamped boundary condition, and filled with water, were obtained by the analytical method and the finite element method using a comercial ANSYS 5.2 software. Excellent agreement on the natural frequencies of the liquid-filled tank structure was found. The compressiblity and the fluid density effects on the normalized coupled natural frequencies were investigated. The density of fluid affects on all coupled natural frequencies of the tank, whereas the compressibility of fluid affects mainly on the natural frequencies of lower circumferential modes.

• Proceedings of the Korean Geotechical Society Conference
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• 2006.03a
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• pp.1340-1347
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• 2006

Dynamic response of buried pipelines both in the axial and the transverse directions on concrete pipe and steel pipe, FRP pipe were investigated through a free vibration analysis. End boundary conditions considered herein consist of free ends, fixed ends, and fixed-free ends in the axial and the transverse direction. Guided ends, simply supported ends, and supported-guided ends were added to the transverse direction. The buried pipeline was regarded as a beam on an elastic foundation and the ground displacement of sinusoidal wave was applied to it. Natural frequencies and mode shapes were determined according to end boundary conditions. In addition, the effects of parameters on the natural frequency were evaluated. The natural frequency is affected most significantly by the soil stiffness and the length of the buried pipelines. The natural frequency increases as the soil stiffness increases while it decreases as the length of the buried pipeline increases. Such behavior appears to be dominant in the axial direction rather than in the transverse direction of the buried pipelines.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.6
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• pp.929-936
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• 1986

Free vibration characteristics of laminated orthotropic circular cylindrical shells with clamped free boundary condition are investigated. The solution is obtained through a direct solution procedure with axial mode displacements represented as simple Fourier series expressions. On the basis of the thin shell theories of Sanders, Love, Loo, Morley and Donnell, the 4*$ frequency determinant is derived and is expressed in a unified form. Various numerical examples determining the natural frequencies of circular cylindrical shells with isotropic material and also with layers of orthotropic elastic material arbitraily laminated either symmetrically or anti-symmetrically about the shell middle surface. The results obtained compared very well with some available experimental and numerical results.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.308-314
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• 2000

This study explores the free, out-of-plane vibrations of horizontally circular curved beams. The differential equations governing the free vibration of such beams, including the effects of warping and rotatory inertia, are derived and solved numerically. The Runge-Kutta method and the Determinant Search method combined with Regula-Falsi method are used to integrate the differential equations and to obtain the natural frequencies, respectively. The lowest three natural frequencies are calculated over a wide range of non-dimensional system parameters: the horizontal rise to span length ratio, the slenderness ratio, the stiffness parameter, and the warping parameter. It is expected that the results obtained herein can be used practically for the design of curved member systems.

• Structural Engineering and Mechanics
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• v.3 no.5
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• pp.511-525
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• 1995

The differential equations governing in-plane free vibrations of the elastic, catenary arch with rotatory inertia are derived in Cartesian coordinates. Frequencies and mode shapes are computed numerically for such arches with unsymmetric axes, for both clamped-clamped and hinged-hinged end constraints. The lowest four natural frequency parameters are reported, with and without rotatory inertia, as a function of three nondimensional system parameters; the span to cord length ratio e, the slenderness ratio s, and the rise to cord length ratio f. Experimental measures of frequencies and mode shapes for several laboratory-scale catenary models serve to validate the theoretical results.