• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.21 no.8
• /
• pp.698-707
• /
• 2011

This paper is to analyze the stability of the thick plate on inhomogeneous Pasternak foundation, with linearly varying thickness and concentrated mass by finite element method. To verify this finite element method, the results of natural frequencies and buckling stresses by the proposed method are compared with the existing solutions. The dynamic instability regions are decided by the dynamic stability analysis of the thick plate on inhomogeneous Pasternak foundation, with linearly varying thickness and concentrated mass. The non-dimensional Winkler foundation parameter is applied as 100, 1000 and non-dimensional shear foundation parameter is applied as 5. The tapered ratios are applied as 0.25 and 1.0, the ratios of concentrated mass to plate mass as 0.25 and 1.0, and the ratio of in-plane force to critical load as 0.4. As the result of numerical analysis of the thick plate on inhomogeneous Pasternak foundation for $u{\times}v=300cm{\times}300cm$ and $a{\times}b=600cm{\times}600cm$, instability areas of the thick plate which has the larger rigidity of inner area are farther from ${\beta}$-axis and narrower than those which has the larger rigidity of outer area.

• Interaction and multiscale mechanics
• /
• v.3 no.1
• /
• pp.95-110
• /
• 2010

In recent years, study of the static response of pavements to moving vehicle and aircraft loads has received significant attention because of its relevance to the design of pavements and airport runways. The static response of beams resting on an elastic foundation and subjected to moving loads was studied by several researchers in the past. However, most of these studies were limited to steady-state analytical solutions for infinitely long beams resting on Winkler-type elastic foundations. Although the modelling of subgrade as a continuum is more accurate, such an approach can hardly be incorporated in analysis due to its complexity. In contrast, the two-parameter foundation model provides a better way for simulating the underlying soil medium and is conceptually more appealing than the one-parameter (Winkler) foundation model. The finite element method is one of the most suitable mathematical tools for analysing rigid pavements under moving loads. This paper presents an improved solution algorithm based on the finite element method for the static analysis of rigid pavements under moving vehicular or aircraft loads. The concrete pavement is discretized by finite and infinite beam elements, with the latter for modelling the infinity boundary conditions. The underlying soil medium is modelled by the Pasternak model allowing the shear interaction to exist between the spring elements. This can be accomplished by connecting the spring elements to a layer of incompressible vertical elements that can deform in transverse shear only. The deformations and forces maintaining equilibrium in the shear layer are considered by assuming the shear layer to be isotropic. A parametric study is conducted to investigate the effect of the position of moving loads on the response of pavement.

• Structural Engineering and Mechanics
• /
• v.2 no.1
• /
• pp.95-112
• /
• 1994

This paper describes the formulation and application of a dynamic model for a conventional rail track subjected to arbitary loading functions that simulate wheel/rail impact forces. The rail track is idealized as a periodic elastically coupled beam system resting on a Winkler foundation. Modal parameters of the track structure are first obtained from the natural vibration characteristics of the beam system, which is discretized into a periodic assembly of a specially-constructed track element and a single beam element characterized by their exact dynamic stiffness matrices. An equivalent frequency-dependent spring coefficient representing the resilient, flexural and inertial characteristics of the rail support components is introduced to reduce the degrees of freedom of the track element. The forced vibration equations of motion of the track subjected to a series of loading functions are then formulated by using beam bending theories and are reduced to second order ordinary differential equations through the use of mode summation with non-proportional modal damping. Numerical examples for the dynamic responses of a typical track are presented, and the solutions resulting from different rail/tie beam theories are compared.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2006.04a
• /
• pp.681-688
• /
• 2006

This paper has the object of investigating natural frequencies of tapered thick plate 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 use of rectangular finite element with 8-nodes. In order to analysis plate which is supported on pasternak foundation. the Winkler parameter is varied with 10, $10^2,\;10^3$ and the shear foundation parameter is 5, 10. This paper is analyzed varying thickness by taper ratio. The taper ratio is applied as 0.0, 0.25, 0.5, 0.75, 1.0 respectively.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2004.05a
• /
• pp.794-798
• /
• 2004

This paper is analysis of stiffened opening thick plate on foundation. This paper has the object of investigating natural frequencies of opening thick plates on Pasternak foundation by means of finite element method and providing Kinematic design data for mat of building structures. In this paper, vibration analysis of rectangular opening thick plate is done by use of Serendipity finite element with 8 nodes by considering shearing strain of plate. And vibration analysis of stiffener is done by used of Timoshenko beam-column element wit 3 nodes. It is shown that natural frequencies depend on not only Winkler foundation parameter but also shear foundation parameter, opening position, opening size, stiffener size.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.45 no.4
• /
• pp.115-125
• /
• 2003

Shell structures are widely used in a variety of engineering application, and mathematical solution of shell structures are available only for a few special cases. The solution of shell structure is more complicated when it has such condition as winkler foundation, other problems. In this study many simplified methods (analogy of beam on elastic foudation, finite element method and transfer matrix method) are applied to analyze a hemisphere-cylindrical shell structures on elastic foundation. And the transfer matrix method is extensively used for the structural analysis because of its merit in the theoretical backgroud and applicability. Therefore, this paper presents the analysis of hemisphere-cylindrical shell structure base on the transfer matrix method. The technique is attractive for implementation on a numerical solution by means of a computer program coded in FORTRAN language with a few elements. To demonstrate this fact, it gives good results which compare well with finite element method.

• Structural Engineering and Mechanics
• /
• v.9 no.6
• /
• pp.519-540
• /
• 2000

In this study, a new functional based on the Reissner theory, for thick plates on a Winkler foundation is obtained. This functional has geometric and dynamic boundary conditions. In deriving the new functional, the $G{\hat{a}}teaux$ differential is used. This functional which is in polar coordinates is also transformable into the classical potential energy equation. Bending and torsional moments, transverse shear forces, rotations and displacements are the basic unknowns of the functional. Two different sectorial elements are developed with $3{\times}8$ degrees of freedom (SEC24) and $4{\times}8$ degrees of freedom (SEC32). The accuracy of the SEC24 and SEC32 elements together are verified by applying the method to some problems taken from literature.

• Journal of the Korean Institute of Rural Architecture
• /
• v.16 no.4
• /
• pp.59-66
• /
• 2014

This paper deals with vibration of plates with concentrated mass on elastic foundation. The object of investigating natural frequencies of tapered thick plate on pasternak foundation by means of finite element method and providing kinetic design data for mat of building structures. Free vibration analysis that tapered thick plate in this paper. Finite element analysis of rectangular plate is done by use of rectangular finite element with 8-nodes. In order to analysis plate which is supported on pasternak foundation. The Winkler parameter is varied with 10, $10^2$, $10^3$ and the shear foundation parameter is 5, 10. This paper is analyzed varying thickness by taper ratio. The taper ratio is applied as 0.0, 0.25, 0.5, 0.75, 1.0. And the Concentrated Mass is applied as P1, Pc, P2 respectively.

• Journal of the Earthquake Engineering Society of Korea
• /
• v.16 no.3
• /
• pp.13-22
• /
• 2012

Even with its significant influence on the dynamic analysis and foundation design of structures, sometimes the soil-structure interaction has been ignored during the design process. One of the reasons is due to the fact that the modeling procedures are too complicated to meet the requirements in practice. In this study, using the Cali(IT)2 building in California with high and frequent seismic activities, the analysis differences for different boundary conditions are reviewed. The Beam on Nonlinear Winkler Foundation Model, one of the foundation modeling methods, is modified for easy use by the Linear Matrix Inequalities Model Reduction Technique. The product of the proposed process is applied to create the Finite Element Model. The results show fairly good agreement with the real data acquired from the Cal(IT)2 building.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2006.04a
• /
• pp.675-680
• /
• 2006

This paper deals with the flexural free vibrations of strip foundations. Based on dynamic equilibrium equations of a beam element resting on Winkler foundation, differential equations governing free vibration of strip foundation are derived, in which effects of rotatory inertia and shear deformation are included. For obtaining the natural frequencies, differential equations are solved by numerical methods. As the numerical results, relationships between natural frequencies and various strip parameters are obtained and presented in Tables and Figures.