• Structural Engineering and Mechanics
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• v.77 no.5
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• pp.587-599
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• 2021

Based on Euler-Bernoulli beam theory and continuous element method, the free vibration of bi-dimensional functionally graded beams is investigated. It is assumed that the material properties vary exponentially along the beam thickness and length. The characteristic frequency equations of beams with different boundary conditions are obtained by transfer matrix method. The validity of the proposed method is assessed through comparison with available results. Parametric studies are carried out to analyze the influences of the gradient indexes and the beam slenderness ratio on the natural frequencies of bi-dimensional functionally graded beams.

• 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.

• 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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.7
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• pp.787-794
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• 2016

In this study, the exact rigidity and the free vibration of trapezoidal corrugated plate are analyzed by being based on the Kirchhoff's plate theory and the Ritz method. The previous rigidity of corrugated plate analyzed by considering just a geometric characteristic, a basic assumption and an equivalent idea can cause large errors in practical behaviors. Accordingly, the exact rigidity supplemented by correction factors of the theoretical rigidity is needed. Therefore an analysis on the exact rigidity and the free vibration using the rigidity for the plate is performed in this paper.

• Journal of Korean Society of Steel Construction
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• v.28 no.5
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• pp.365-371
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• 2016

In the case of the superstructure which is consist of two I girders and slab, the section can behave as II section, so that the neutral axis with respect to out of plane direction flexure can be regarded as major axis. Therefore in-plane flexural mode might govern the free vibration mode. Meanwhile, horizontally curved girders always experience not only bending moments but also torsional moments although the primary load is usually supposed to be gravitational load. The interaction due to bending and torsional moments make the behavior complicated and torsional mode may govern the free vibration mode. In other words, structure can have different dynamic characteristic due to its initial curvature. In this research, using 3-dimensional sell elements, free-vibration analyses are carried out due to initial curvature. The analysis models are assumed to be composite and non-composite and finally natural frequency and eigen mode are discussed.

• Journal of the Society of Naval Architects of Korea
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• v.42 no.4 s.142
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• pp.396-401
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• 2005

In this study, the assumed mode method using characteristic polynomials of Timoshenko beam is applied to the free vibration analysis for the stiffened plate of ship tank side in contact with water. The hydro-elastic effect of the fluid-structure interaction is considered by fluid velocity potential, derived from boundary conditions for fluid and structure, and utilized in the calculation of added mass matrix using assumed modes. To verify the validity and effectiveness of the presented method, free vibration analysis for the stiffened plates in contact with finite and infinite fluids have been carried out and its results were compared with those obtained by a general purpose FEA software.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.928-933
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• 2004

The vibration characteristic is a primary design factor. The cylindrical shells are used as a primary components of complex structure. also, The cylindrical shells have oblique angle. In this study, The vibrational characteristics of steel and plain wave GFRP cylindrical shell with an oblique end are given by experimental and finite element method. To be find characteristic of the oblique end, the mass of the cylindrical shell is maintained. Natural frequency and mode shapes of isotropic and plain weave composite shells are obtained by modal test. The results are compared with those of the finite element method. The simply supported boundary conditions with bolts along the circumferential direction of the GFRP shell are well achieved. Also, The clamped boundary conditions is applied to the steel specimen. Those are shown to agree well with the analytical results and finite element analysis results.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.12 s.105
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• pp.1416-1421
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• 2005

This paper presents an analytical approach for the vibration characteristics of a piezoelectric disc for torsional vibration transducers. The characteristic equation of the piezoelectric annular disc has been derived from Gibbs' free energy equations and mechanical and electrical equilibrium. With an anisotropic material properties of the disc, the characteristic equation has yielded resonance frequencies. Numerically-calculated results have been compared with the results obtained by the finite element analysis and experiments and have confirmed the validity of the theoretical analysis.

• Structural Engineering and Mechanics
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• v.7 no.1
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• pp.53-67
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• 1999

The natural frequencies and modes of free vibration of specially orthotropic elliptic and circular plates are analysed using the Rayleigh-Ritz method. The assumed functions used are two-dimensional boundary characteristic orthogonal polynomials which are generated using the Gram-Schmidt orthogonalization procedure. The first five natural frequencies are reported here for various values of aspect ratio of the ellipse. Results are given for various boundary conditions at the edges i.e., the boundary may be any of clamped, simply-supported or fret. Numerical results are presented here for several orthotropic material properties. For rectilinear orthotropic circular plates, a few results are available in the existing literature, which are compared with the present results and are found to be in good agreement.

• Structural Engineering and Mechanics
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• v.24 no.5
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• pp.543-560
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• 2006

In this paper, first, the equations of motion for a rectangular isotropic plate have been derived. This derivation is based on the Von Karmann theory and the effects of shear deformation have been considered. Introducing an Airy stress function, the equations of motion have been transformed to a nonlinear coupled equation. Using Galerkin method, this equation has been separated into position and time functions. By means of the dimensional analysis, it is shown that the orders of magnitude for nonlinear terms are small with respect to linear terms. The Multiple Scales Method has been applied to the equation of motion in the forced vibration and free vibration cases and closed-form relations for the nonlinear natural frequencies, displacement and frequency response of the plate have been derived. The obtained results in comparison with numerical methods are in good agreements. Using the obtained relation, the effects of initial displacement, thickness and dimensions of the plate on the nonlinear natural frequencies and displacements have been investigated. These results are valid for a special range of the ratio of thickness to dimensions of the plate, which is a characteristic of the Multiple Scales Method. In the forced vibration case, the frequency response equation for the primary resonance condition is calculated and the effects of various parameters on the frequency response of system have been studied.