• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.521-525
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• 2004

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. vibration analysis that tapered thick plate subjected to In-plane stress is presented in this paper Finite element analysis of rectangular plate is done by use of rectangular finite element with 8-nodes. In order to analysis tapered plate which is supported on pasternak foundation. The ratio of In-plane stress to critical load is varied with $0.2\sigma_{cr},\;0.4\sigma_{cr},\;0.6\sigma_{cr}$, and the Winkler parameter is 0, 10, 100, 1000 the shear foundation parameter 0, 10. The taper ratio is applied as 0.0, 0.2, 0.4, 0.6, 0.8 respectively. This paper is analyzed varying thickness by taper ratio with In-plane stress.

• Structural Engineering and Mechanics
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• v.72 no.1
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• pp.61-70
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• 2019

The functionally graded materials (FGM) used in plates contain probably a porosity volume fraction which needs taking into account this aspect of imperfection in the mechanical bahavior of such structures. The present work aims to study the effect of the distribution forms of porosity on the bending of simply supported FG plate reposed on the Winkler-Pasternak foundation. A refined theory of shear deformation is developed to study the effect of the distribution shape of porosity on static behavior of FG plates. It was found that the distribution form of porosity significantly influence the mechanical behavior of FG plates, in terms of deflection, normal and shear stress. It can be concluded that the proposed theory is simple and precise for the resolution of the behavior of flexural FGM plates resting on elastic foundations while taking into account the shape of distribution of the porosity.

• Structural Engineering and Mechanics
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• v.37 no.1
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• pp.61-77
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• 2011

Static and dynamic responses of a completely free elastic beam resting on a two-parameter tensionless Pasternak foundation are investigated by assuming that the beam is symmetrically subjected to a uniformly distributed load and concentrated load at its middle. Governing equations of the problem are obtained and solved by paying attention on the boundary conditions of the problem including the concentrated edge foundation reaction in the case of complete contact and lift-off condition of the beam ina two-parameter foundation. The nonlinear governing equation of the problem is evaluated numerically by adopting an iterative procedure. Numerical results are presented in figures to demonstrate the non-linear behavior of the beam-foundation system for various values of the parameters of the problem comparatively by considering the static and dynamic loading cases.

• Geomechanics and Engineering
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• v.11 no.1
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• pp.95-116
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• 2016

A novel higher order shear-deformable beam model, which provides linear variation of transversal normal strain and quadratic variation of shearing strain, is proposed to describe the beam resting on foundation. Then, the traditional two-parameter Pasternak foundation model is modified to capture the effects of the axial deformation of beam. The Masing's friction law is incorporated to deal with nonlinear interaction between the foundation and the beam bottom, and the nonlinear properties of the beam material are also considered. To solve the mathematical problem, a displacement-based finite element is formulated, and the reliability of the proposed model is verified. Finally, numerical examples are presented to study the effects of the interfacial friction between the beam and foundation, and the mechanical behavior due to the tensionless characteristics of the foundation is also examined. Numerical results indicate that the effects of tensionless characteristics of foundation and the interfacial friction have significant influences on the mechanical behavior of the beam-foundation system.

• Steel and Composite Structures
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• v.32 no.6
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• pp.795-806
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• 2019

In this paper, free vibration of sandwich beam with flexible core resting on orthotropic Pasternak is investigated. The top and bottom layers are reinforced by carbon nanotubes (CNTs). This sandwich structural is modeled by Euler and Frostig theories. The effect of agglomeration using Mori-Tanaka model is considered. The Eringen's theory is applied for size effect. The structural damping is investigated by Kelvin-voigt model. The motion equations are calculated by Hamilton's principle and energy method. Using analytical method, the frequency of the structure is obtained. The effect of agglomeration and CNTs volume percent for different parameter such as damping of structure, thickens and spring constant of elastic medium are presented on the frequency of the composite structure. Results show that with increasing CNTs agglomeration, frequency is decreased.

• Advances in nano research
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• v.7 no.4
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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.

• Steel and Composite Structures
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• v.32 no.2
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• pp.281-292
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• 2019

Nonlocal elasticity and Reddy plant theory are used to study the vibration response of functionally graded (FG) nanoplates resting on two parameters elastic medium called Pasternak foundation. Nonlocal higher order theory accounts for the effects of both scale and the effect of transverse shear deformation, which becomes significant where stocky and short nanoplates are concerned. It is assumed that the properties of FG nanoplate follow a power law through the thickness. In addition, Poisson's ratio is assumed to be constant in this model. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction of nanoplate with surrounding elastic medium. Using Hamilton's principle, size-dependent governing differential equations of motion and corresponding boundary conditions are derived. A differential quadrature approach is being utilized to discretize the model and obtain numerical solutions for various boundary conditions. The model is validated by comparing the results with other published results.

• Advances in nano research
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• v.7 no.5
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• pp.337-349
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• 2019

The size-dependent vibration analysis of a cross-/angle-ply laminated composite plate when embedded on the Pasternak elastic foundation and exposed to an in-plane magnetic field are investigated by adopting an analytical eigenvalue approach. The formulation, which is based on refined-hyperbolic-shear-deformation-plate theory in conjunction with the Eringen Nonlocal Differential Model (ENDM), is tested against considering problems for which numerical/analytical solutions available in the literature. The findings of this study demonstrated the role of magnetic field, size effect, elastic foundation coefficients, geometry, moduli ratio, lay-up numbers and fiber orientations on the nonlocal frequency of cross-/angle-ply laminated composite plates.

• Advances in nano research
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• v.7 no.2
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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.

• Coupled systems mechanics
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• v.9 no.6
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• pp.575-597
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• 2020

Equilibrium equations of a porous FG plate resting on Winkler-Pasternak foundations with various boundary conditions are derived using a new refined shear deformation theory. Different types of porosity distribution rate are considered. Governing equations are obtained including the plate-foundation interaction. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The novel rule of mixture is proposed to describe and approximate material properties of the FG plates with different distribution case of porosity. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature. Effects of variation of porosity distribution rate, boundary conditions, foundation parameter, power law index, plate aspect ratio, side-to-thickness ratio on the deflections and stresses are all discussed.