• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.12
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• pp.947-955
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• 2003

This research analyzes the dynamic stability of stiffened plates on elastic foundations using the finite element method. For analyzing the stiffened plates, both the Mindlin plate theory and Timoshenko beam-column theory were applied. In application of the finite element method, 8-nodes serendipity element system and 3-nodes finite element system were used for plate and beam elements, respectively Elastic foundations were modeled as the Pasternak foundations in which the continuity effect of foundation is considered. In order to verify the theory of this study, solutions obtained by this analysis were compared with the classical solutions in open literature and experimental solutions. The dynamic stability legions of stiffened plates on Pasternak foundations were determined according to changes of in-plane stresses, foundation parameters and dimensions of stiffener.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.957-962
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• 2004

This paper deals with the free vibration analysis of beam-columns resting on Pasternak foundation by the Differential Quadrature Method. Based on the differential equation subjected to the boundary conditions, adopted from the open literature, which governs the free vibrations of such member, this equation is applied to the Differential Quadrature Method. For computing natural frequencies, the numerical procedures are developed by QR Algorithm, in which the Chebyshev-Gauss-Lobatto method is used for choosing the grid points. The numerical methods developed herein for computing natural frequencies are programmed in FORTRAN code, and all solutions obtained in this study are quite agreed with those in the open literature.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.4
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• pp.281-289
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• 2003

Recently, as high-rise buildings increase steeply, sub-structures of them are often supported on in-homogeneous foundation. And there are many machines in sub-structures of buildings, and slabs of sub-structures are affected by vibration which they make. This paper deals with vibration of plates with concentrated masses on in-homogeneous foundation. Machines on plates are considered as concentrated masses. In-homogeneous foundation is considered as assigning $k_{w1}$ and $k_{w2}$ to Winkler foundation parameters of central region and side region of plate respectively, and foundation is idealized to use Pasternak foundation model which considered both of Winkler foundation parameter and shear foundation parameter. In this paper, applying Winkler foundation parameters which $k_{w1}$and $k_{w2}$ are 10, $10^2$, $10^3$ and shear foundation parameter which are 10, 20 respectively, first natural frequencies of thick plates with concentrated masses on in-homogeneous foundations are calculated.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.4
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• pp.351-363
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• 2004

Equation of motion of non conservative system considering mass matrix, elastic stiffness matrix, load correction stiffness matrix by circulatory force's direction change and Winkler and Pasternak foundation stiffness matrix is derived. Also stability analysis due to the divergence and flutter loads is performed. And the influence of internal and external damping coefficient on flutter load is investigated applying the quadratic eigen problem solution. Additionally the influence of non-conservative force's direction parameter, internal and external damping and Winkler and Pasternak foundation on the critical load of Beck's and Leipholz's and Hauger's columns are investigated.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.14 no.3
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• pp.371-379
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• 2001

This paper deals with the free vibrations of horizontally curved members resting on elastic foundations with continuity effect. Taking into account the effects of rotatory inertia and shear deformation, differential equations governing the free vibrations of such beams are derived, in which the Pasternak foundation model is considered as the elastic foundation with continuity effect. The differential equations are solved numerically to calculate natural frequencies and mode shapes. The experiments were performed in which the natural frequencies of such curved beams in laboratorial scale were measured and these results agree quite well with the present numerical studies. In numerical examples, the circular, parabolic, sinusoidal and elliptic curved members with the hinged-hinged, hinged-clamped and clamped end constraints are considered. The parametric studies are conducted and the lowest four frequency parameters are reported in tables and figures as the non-dimensional forms. Also the typical mode shapes are presented.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.395.2-395
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• 2002

Recently, as size of building structure becomes larger, mat area of building structure is supported on Inhomogeneous foundation. The equipment machineries in building are mostly on basement story. The slab of the lowest basement story with equipment machineries is considerded as concentrated masses on plate supported on foundation. In this paper. vibration analysis of rectangular thin plate is done by use of rectangular finite element with 4 nodes. (omitted)

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.10
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• pp.1033-1041
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• 2008

The purpose of this paper is to investigate natural frequencies of tapered thick plate with concentrated masses subjected to in-plane force on pasternak foundation by means of finite element method and providing kinetic design data for mat of building structures. Finite element analysis of rectangular plate is done by using rectangular finite element with 8-nodes. For analysis, plates is supported on pasternak foundation. The Winkler parameter is varied with 10, 102, the shear foundation parameter is 5. The taper ratio is applied as 0.0, 0.25, 0.5 and the ratio of the concentrated mass to plate mass as 0.25, 0.5 respectively. As results, we can see that when stiffener's sizes or foundation parameter are larger, the natural frequency increases, and when the concentrated mass or taper ratio or in-plane stress is larger, the natural frequency decreases.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.6
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• pp.529-538
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• 2016

The simplified plate theory is presented for static and free vibration analysis of power-law(P) and sigmoid(S) Functionally Graded Materials(FGM) plates. This theory considers the parabolic distribution of the transverse shear stress, and satisfies the condition that requires the transverse shear stress to be zero on the upper and lower surfaces of the plate, without the shear correction factor. The simplified plate theory uses only four unknown variables and shares strong similarities with classical plate theory(CPT) in many aspects such as stress-resultant expressions, equation of motion and boundary conditions. The material properties of the plate are assumed to vary according to the power-law and sigmoid distributions of the volume fractions of the constituents. The Hamilton's principle is used to derive the equations of motion and Winkler-Pasternak elastic foundation model is employed. The results of static and dynamic responses for a simply supported FGM plate are calculated and a comparative analysis is carried out. The results of the comparative analysis with the solutions of references show relevant and accurate results for static and free vibration problems of FGM plates. Analytical solutions for the static and free vibration problems are presented so as to reveal the effects of the power law index, elastic foundation parameter, and side-to-thickness ratio.

• Magazine of the Korean Society of Agricultural Engineers
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• v.43 no.5
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• pp.106-115
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• 2001

This paper deals with the free vibrations of horizontally curved beams partially supported on elastic foundations. Taking account of the effects of rotatory inertia and shear deformation, differential equations governing the free vibrations of such beams are derived, in which the Pasternak foundation model is considered as the elastic foundation. Differential equations are numerically solved to calculate natural frequencies and mode shapes. The experiments were performed in which the free vibration frequencies of such curved beams in laboratorial scale were measured and these results agreed quite well with the present studies. In numerical examples, the circular, parabolic, sinusoidal and elliptic curved members are considered. The parametric studies are performed and the lowest four frequency parameters are reported in tables and figures as the non-dimensional forms. Also the typical mode shapes are presented.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.982-987
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• 2002

Recently, as size of building structure becomes larger, mat area of building structure is supported on Inhomogeneous foundation. The equipment machineries in building are mostly on basement story. The slab of the lowest basement story with equipment machineries is considered as plate supported on foundation with concentrated masses. In this paper, vibration analysis of rectangular thin plate is done by use of rectangular finite element with 4 nodes. The solution of this paper are compared with existing solution and natural frequencies of thin plates, with concented mass, on inhomogeneous Pasternak foundation are calculated