• 한국농촌건축학회논문집
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• 제16권4호
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• pp.59-66
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• 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.

• Structural Engineering and Mechanics
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• 제18권2호
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• pp.263-276
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• 2004

The purpose of this paper is to determine the subsoil depth affected from the load on the plate resting on elastic foundation using stress distribution within the subsoil that will be occurred depending on the loading and dimension of the plate. An iterative method is developed in order to determine the effective depth of the subsoil under the plate. Numerical examples from the technical literature are solved by means of the method suggested herein and displacements, bending moments and shear forces are presented in graphical and tabular forms to evaluate the effects of the limit depth considered in the study. Results showed the efficiency and simplicity of the present approach for the plate resting on an elastic foundation.

• Structural Engineering and Mechanics
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• 제82권6호
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• pp.701-711
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• 2022

The nonlocal elasticity as well as Mindlin's first-order shear deformation plate theory are proposed to investigate thermal vibrational of a nanoplate placing on a three-factor foundation. The Winkler-Pasternak elastic foundation is connected with the viscous damping to obtain the present three-parameter viscoelastic model. Differential equations of motion are derived and resolved for simply-supported nanoplates to get their natural frequencies. The influences of the nonlocal index, viscous damping index, and temperature changes are investigated. A comparison example is dictated to validate the precision of present results. Effects of other factors such as aspect ratio, mode numbers, and foundation parameters are discussed carefully for the vibration problem. Additional thermal vibration results of nanoplates resting on the viscoelastic foundation are presented for comparisons with future investigations.

• Structural Engineering and Mechanics
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• 제8권6호
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• pp.607-622
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• 1999

Being a significant mode of deformation, shear effect in addition to the other modes of stretching and bending have been considered to develop two finite element models for the analysis of beams on elastic foundation. The first beam model is developed utilizing the differential-equation approach; in which the complex variables obtained from the solution of the differential equations are used as interpolation functions for the displacement field in this beam element. A single element is sufficient to exactly represent a continuous part of a beam on Winkler foundation for cases involving end-loadings, thus providing a benchmark solution to validate the other model developed. The second beam model is developed utilizing the hybrid-mixed formulation, i.e., Hellinger-Reissner variational principle; in which both displacement and stress fields for the beam as well as the foundation are approxmated separately in order to eliminate the well-known phenomenon of shear locking, as well as the newly-identified problem of "foundation-locking" that can arise in cases involving foundations with extreme rigidities. This latter model is versatile and indented for utilization in general applications; i.e., for thin-thick beams, general loadings, and a wide variation of the underlying foundation rigidity with respect to beam stiffness. A set of numerical examples are given to demonstrate and assess the performance of the developed beam models in practical applications involving shear deformation effect.

• Coupled systems mechanics
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• 제5권3호
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• pp.255-267
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• 2016

To investigate the surface effects on vibration of embedded circular curved nanosize beams, nonlocal elasticity model is used in combination with surface properties including surface elasticity, surface tension and surface density for modeling the nano scale effect. The governing equations are determined via the energy method. Analytically Navier method is utilized to solve the governing equations for simply supported at both ends. Solving these equations enables us to estimate the natural frequency for circular curved nanobeam including Winkler and Pasternak elastic foundations. The results determined are verified by comparing the results by available ones in literature. The effects of various parameters such as nonlocal parameter, surface properties, Winkler and Pasternak elastic foundations and opening angle of circular curved nanobeam on the natural frequency are successfully studied. The results reveal that the natural frequency of circular curved nanobeam is significantly influenced by these effects.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권1호
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• pp.1-15
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• 2013

In this paper the three dimensional wave propagation in a homogeneous isotropic thermo elastic cylindrical panel embedded in an elastic medium (Winkler model) is investigated in the context of the L-S (Lord-Shulman) theory of generalized thermo elasticity. The analysis is carried out by introducing three displacement functions so that the equations of motion are uncoupled and simplified. A Bessel function solution with complex arguments is then directly used for the case of complex Eigen values. This type of study is important for design of structures in atomic reactors, steam turbines, wave loading on submarine, the impact loading due to superfast train and jets and other devices operating at elevated temperature. In order to illustrate theoretical development, numerical solutions are obtained and presented graphically for a zinc material with the support of MATLAB.

• Advances in nano research
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• 제7권4호
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• pp.265-275
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• 2019

In this work, the effect of size on the axial buckling behavior of single-layered graphene sheets embedded in elastic media is studied. We incorporate Eringen's nonlocal elasticity equations into three plate theories of first order shear deformation theory, higher order shear deformation theory, and classical plate theory. The surrounding elastic media are simulated using Pasternak and Winkler foundation models and their differences are evaluated. The results obtained from different nonlocal plate theories include the values of Winkler and Pasternak modulus parameters, mode numbers, nonlocal parameter, and side lengths of square SLGSs. We show here that axial buckling behavior strongly depends on modulus and nonlocal parameters, which have different values for different mode numbers and side lengths. In addition, we show that in different nonlocal plate theories, nonlocality is more influential in first order shear deformation theory, especially in certain range of nonlocal parameters.

• Advances in nano research
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• 제7권2호
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• pp.77-88
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• 2019

This paper infer the transient vibration of piezoelectric sandwich nanobeams, In present work, the flexoelectric effect on the mechanical properties of vibration piezoelectric sandwich nanobeam with different boundary conditions is investigated. According to the Nonlocal elasticity theory in nanostructures, the flexoelectricity is believed to be authentic for such size-dependent properties. The governing equations are derived by Hamilton's principle and boundary condition solved by Galerkin-based solution. This research develops a nonlocal flexoelectric sandwich nanobeam supported by Winkler-Pasternak foundation. The results of this work indicate that natural frequencies of a sandwich nanobeam increase by increasing the Winkler and Pasternak elastic constant. Also, increasing the nonlocal parameter at a constant length decreases the natural frequencies. By increasing the length to thickness ratio (L/h) of nanobeam, the nonlocal frequencies reduce.

• Steel and Composite Structures
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• 제44권1호
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• pp.17-31
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• 2022

This investigation studies the characteristics of wave dispersion in sigmoid functionally graded (SFG) curved beams lying on an elastic substrate for the first time. Homogenization process was performed with the help of sigmoid function and two power laws. Moreover, various materials such as Zirconia, Alumina, Monel and Nickel steel were explored as curved beams materials. In addition, curved beams were rested on an elastic substrate which was modelled based on Winkler-Pasternak foundation. The SFG curved beams' governing equations were derived according to Euler-Bernoulli curved beam theory which is known as classic beam theory and Hamilton's principle. The resulted governing equations were solved via an analytical method. In order to validate the utilized method, the obtained outcomes were compared with other researches. Finally, the influences of various parameters, including wave number, opening angle, gradient index, Winkler coefficient and Pasternak coefficient were evaluated and indicated in the form of diagrams.

• 한국지반공학회논문집
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• 제22권6호
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• pp.63-69
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• 2006

본 연구에서는 얕은 기초의 지지력을 평가할 수 있는 개별요소법에 근거한 해석기법이 제안되었다. 제안된 해석기법은 토체 간의 거동에 관한 적합조건을 탄소성 Winkler 스프링으로 모사함으로써 파괴면에서의 응력상태와 극한지지력을 함께 구할 수 있다. 기법의 적용성을 검토하기 위하여 단일층 및 이층지반에 설치된 얕은 기초의 지지력 해석을 수행하였다.