• 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 Power System Engineering
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• v.20 no.2
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• pp.5-16
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• 2016

Generally, methods using transfer techniques, like the transfer matrix method and the transfer stiffness coefficient method, find natural frequencies using the sign change of frequency determinants in searching frequency region. However, these methods may omit some natural frequencies when the initial frequency interval is large. The Sylvester-transfer stiffness coefficient method ("S-TSCM") can always obtain all natural frequencies in the searching frequency region even though the initial frequency interval is large. Because the S-TSCM obtain natural frequencies using the number of natural frequencies existing under a searching frequency. In this paper, the algorithm for the free vibration analysis of axisymmetric conical shells was formulated with S-TSCM. The effectiveness of S-TSCM was verified by comparing numerical results of S-TSCM with those of other methods when analyzing free vibration in two computational models: a truncated conical shell and a complete (not truncated) conical shell.

• Journal of Power System Engineering
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• v.19 no.6
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• pp.60-67
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• 2015

While designing and operating machines, it is very important to understand the dynamic characteristic of the machines. Authors developed the Sylvester-transfer stiffness coefficient method in order to analyze effectively the free vibration of machines or structures. The Sylvester-transfer stiffness coefficient method was derived from the combination of the Sylvester's inertia theorem and the transfer stiffness coefficient method. In this paper, the authors formulate the computational algorithm for flexural free vibration analysis of axisymmetric annular plate using the Sylvester-transfer stiffness coefficient method. To confirm the usefulness of the Sylvester-transfer stiffness coefficient method, the natural frequencies and modes for two computational models computed using the Sylvester-transfer stiffness coefficient method are compared with those computed using the exact solution and the finite element method.

• Structural Engineering and Mechanics
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• v.23 no.2
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• pp.115-127
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• 2006

The axisymmetric free vibrations of transversely isotropic magnetoelectroelastic laminated circular plates are studied. Based on the three-dimensional governing equations of magnetoelectroelastic medium, the state space equations of laminated circular plates are obtained. By using the finite Hankel transform and rendering the free terms left by the transform in terms of the boundary quantities, the solutions of the state space equations are given for two kinds of boundary conditions. The frequency equations of the free vibration are derived using the propagator matrix method and the boundary conditions at top and bottom surfaces. By virtue of the inverse Hankel transform, the mode shapes are also determined. Since the solutions strictly satisfy the governing equations in the region and the boundary conditions at the edges, they are the three-dimensionally exact. Finally, the natural frequencies of such plates are tabulated and compared with those of the piezoelectric and elastic plates in the numerical example.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.3
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• pp.44-49
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• 2002

A study of free vibration of axisymmetric circular plates based on Mindlin theory using a pseudospectral method is presented. The analysis is based on Chebyshev polynomials that are widely used in the fluid mechanics research community. Clamped, simply supported and flee boundary conditions are considered, and numerical results are presented for various thickness-to-radius ratios.

• Computers and Concrete
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• v.23 no.5
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• pp.303-309
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• 2019

This study investigates axisymmetric fractional vibration of an isotropic hyperelastic semi-linear thin disc with a view to examine effects of finite deformation associated with the material of the disc and effects of fractional vibration associated with the motion of the disc. The generalized three-dimensional equation of motion is reduced to an equivalent time fraction one-dimensional vibration equation. Using the method of variable separable, the resulting equation is further decomposed into second-order ordinary differential equation in spatial variable and fractional differential equation in temporal variable. The obtained solution of the fractional vibration problem under consideration is described by product of one-parameter Mittag-Leffler and Bessel functions in temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem in literature. Finally, and amongst other things, the Cauchy's stress distribution in thin disc under finite deformation exhibits nonlinearity with respect to the displacement fields whereas in infinitesimal deformation hypothesis, these stresses exhibit linear relation with the displacement field.

• Proceedings of the KSR Conference
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• 2010.06a
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• pp.13-17
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• 2010

This presentation examines the characteristics of torsional vibration in axisymmetric out-of-plane vibrations of an annular Mindin plate. The out-of-plane vibration of circular or annular plates have been investigated since a long years ago by many researchers. When the classical Kirchhoff plate theory neglecting the effect of transverse shear deformation is applied to a thick plate, its out-of-plane natural frequencies are much different from reality. And so, since Minlin presented a plate theory considering the effect of rotary inertia and transverse shear deformation, many researches for the out-of-plane natural vibration of circular or annular Mindin plates have been performed. But almost all researchers missed the torsional vibration due to transverse shear deformation in axisymmetric out-of-plane vibrations of the circular or annular Mindin plate. Therefore, in this presentation, we verify the existence of torsional vibration of an annular plate and present the natural frequencies of an annular plate with free outer boundary surface.

• Journal of Mechanical Science and Technology
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• v.18 no.10
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• pp.1747-1754
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• 2004

In this study, a new harmonic axisymmetric thick shell element for static and dynamic analyses is proposed. The newly proposed element considering shear strain is based on a modified Hellinger-Reissner variational principle, and introduces additional nodeless degrees for displacement field interpolation in order to enhance numerical performance. The stress parameters selected via the field-consistency concept. are very important in formulating a trouble-free hybrid-mixed elements. For computational efficiency, the stress parameters are eliminated by the stationary condition and then the nodeless degrees are condensed out by the dynamic reduction. Several numerical examples confirm that the present element shows improved efficiency and yields very accurate results for static and vibration analyses.

• Journal of Mechanical Science and Technology
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• v.17 no.10
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• pp.1458-1465
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• 2003

An eigenvalue analysis of the circular Mindlin plates with free boundary conditions is presented. The analysis is based on the Chebyshev-Fourier pseudospectral method. Even though the eigenvalues of lower vibration modes tend to convergence more slowly than those of higher vibration modes, the eigenvalues converge for sufficiently fine pseudospectral grid resolutions. The eigenvalues of the axisymmetric modes are computed separately. Numerical results are provided for different grid resolutions and for different thickness-to-radius ratios.

• Journal of Korean Society of Steel Construction
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• v.18 no.1
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• pp.1-10
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• 2006

paper presents the results of the use of the differential transformation technique in analyzing the free vibration of circular plates.calculations were carried out and were compared with previously published results. The results that were obtained when this method was used coincide with the results of The present analysis shows the usefulness and validity of differential transformation in solving a solid-circular and annular-plate problem in terms of free-vibration responses.