• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.6
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• pp.674-680
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• 2008

A new meshless method for obtaining natural frequencies of arbitrarily shaped plates with the free boundary condition is introduced in the paper. In order to improve the characteristics of convergence and accuracy of the method, a special local polar coordinates system is devised and located for each of nodes distributed along the boundary of the plate of interest. In addition, a new way of decreasing the size of the system matrix that gives natural frequencies of the plate is employed to reduce the amount of numerical calculations, which is needed for computing the determinant of the system matrix. Finally the excellence of the characteristics of convergence and accuracy of the method is shown in several case studies, which indicate that natural frequencies by the proposed method are very accurate and converged swiftly to exact values as the number of boundary nodes increases.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1997.04a
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• pp.205-210
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• 1997

The analysis of the free vibrations of a circular cylindrical shell with a logitudinal, interior rectangular plate is performed. The natural frequencies and the mode shapes of the combined shells are experimentally obtained by impact testing using an impact hammer and an accelerometer. The effects of the position of the plate on the frequencies and mode shapes of the combined system are examined. The experimental results are compared with a finite element analysis and show good agreement.

• Structural Engineering and Mechanics
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• v.77 no.4
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• pp.535-547
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• 2021

This paper concerns with free torsional vibration analysis of size dependent circular nanobars with von kármán type nonlinearity. Although review of the literature suggests several studies employing nonlocal elasticity theory to investigate linear torsional behavior, linear/nonlinear transverse vibration and buckling of the nanoscale structures, so far, no study on the nonlinear torsional behavior of the nanobars, considering the size effect, has been reported. This study employs nonlocal elasticity theory along with a variational approach to derive nonlinear equation of motion of the nanobar. Then, the nonlinear equation is solved using the elliptic functions to extract the natural frequencies of the structure under fixed-fixed and fixed-free end conditions. Finally, the natural frequencies of the nanobar under different nanobar lengths, diameters, nonlocal parameters, and amplitudes of vibration are reported to illustrate the effect of these parameters on the vibration characteristics of the nanobars. In addition, the phase plane diagrams of the nanobar for various cases are reported.

• Journal of KSNVE
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• v.6 no.1
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• pp.45-56
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• 1996

Frequency equation for clamped-free circular cylindrical thin shell is derived by the application of Rayleigh-Ritz method using the Sanders shell equation. The cubic frequency equation is solved for each axial and circumferential mode number. Integration of the beam characteristic funcitions was performed via Mathematica which results in more accurate integration of the beam functions that affect the accuracy of the frequency. The natural frequencies from this calculation are compared with existing results. It shows that this calculation predicts natural frequencies closer to the test results than existing results.

• Structural Engineering and Mechanics
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• v.61 no.3
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• pp.335-345
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• 2017

Free vibration analysis for continuous bridge under any number of vehicles is conducted in this paper. Calculation strategy for natural frequency and mode shape is proposed based on Euler-Bernoulli beam theory and numerical assembly method. Firstly, a half-car planar model is adopted; equations of motion and displacement functions for bridge and vehicle are established, respectively. Secondly, the undermined coefficient matrices for wheels, vehicles, intermediate support, left-end support and right-end support are derived. Then, the numerical assembly technique for conventional finite element method is adopted to construct the overall matrix of coefficients for whole system. Finally, natural frequencies and corresponding mode shapes are determined based on iterative method and overall matrix solution. Numerical simulation is presented to verify the effectiveness of the proposed method. The results reveal that the solutions of present method are exact ones. Natural frequencies and associate modal shapes of continuous bridge under different conditions of vehicles are investigated. The influences of vehicle parameters on natural frequencies are also demonstrated.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.6
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• pp.607-613
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• 2009

A new formulation of NDIF method to the algebraic eigenvalue problem is introduced to efficiently extract natural frequencies of arbitrarily shaped plates with the simply supported boundary condition. NDIF method, which was developed by the authors for the free vibration analysis of arbitrarily shaped membranes and plates, has the feature that it yields highly accurate natural frequencies compared with other analytical methods or numerical methods(FEM and BEM). However, NDIF method has the weak point that it needs the inefficient procedure of searching natural frequencies by plotting the values of the determinant of a system matrix in the frequency range of interest. A new formulation of NDIF method developed in the paper doesn't require the above inefficient procedure and natural frequencies can be efficiently obtained by solving the typical algebraic eigenvalue problem. Finally, the validity of the proposed method is shown in several case studies, which indicate that natural frequencies by the proposed method are very accurate compared to other exact, analytical, or numerical methods.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.1169-1172
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• 2007

This paper deals with the free vibrations of cantilever arches with constant volume. Its cross-sectional shape is the regular polygon whose depth is varied with the linear functional fashion. The non-dimensional differential equations governing the free vibration of such arch are derived and solved numerically for calculating the natural frequencies. As the numerical results, the effects of arch parameters such as side number of cross section, section ratio and aspect ratio on the natural frequencies are reported in figures.

• Journal of Power System Engineering
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• v.17 no.2
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• pp.46-55
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• 2013

In this paper, the computational algorithm for free vibration analysis of an axisymmetric cylindrical shell is formulated by the Sylvester-transfer stiffness coefficient method (S-TSCM) which combines the Sylvester's inertia theorem and the transfer stiffness coefficient method. After the computational programs for obtaining the natural frequencies and natural modes of the axisymmetric cylindrical shell are made by the S-TSCM and the finite element method (FEM), the computational results which are natural frequencies, natural modes, and computational times by both methods are compared. From the computational results, we can confirm that S-TSCM has the reliability in the free vibration analysis of the axisymmetric cylindrical shell and is superior to FEM in the viewpoint of computational times.

• Journal of KSNVE
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• v.8 no.4
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• pp.623-631
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• 1998

The free vibration analyses of the isotropic and composite(CFRP, GFRP) rectangular plates with point supports at the free edge and middle position are performed. The natural frequencies and nodal patterns of plates with point supports are experimentally determined by impact testing using an impact hammer. To compare and verify these experimental results, the finite element analysis is also carried out. The effect of the point support position, the number of point supports, and the anisotropic parameters on the natural frequencies and nodal patterns of cantilevered rectangular plates are investigated.

• Journal of Korean Association for Spatial Structures
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• v.4 no.4 s.14
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• pp.99-111
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• 2004

An exact solution procedure is formulated for the free vibration and buckling analysis of rectangular plates having two opposite edges simply supported when these edges are subjected to linearly varying normal stresses. The other two edges may be clamped, simply supported or free, or they may be elastically supported. The transverse displacement (w) is assumed as sinusoidal in the direction of loading (x), and a power series is assumed in the lateral (y) direction (i.e., the method of Frobenius). Applying the boundary conditions yields the eigenvalue problem of finding the roots of a fourth order characteristic determinant. Care must be exercised to obtain adequate convergence for accurate vibration frequencies and buckling loads, as is demonstrated by two convergence tables. Some interesting and useful results for vibration frequencies and buckling loads, and their mode shapes, are presented for a variety of edge conditions and in-plane loadings, especially pure in-plane moments.