• Steel and Composite Structures
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• v.14 no.1
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• pp.85-104
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• 2013

The present work deals with the thermomechanical bending response of functionally graded plates resting on Winkler-Pasternak elastic foundations. Theoretical formulations are based on a recently developed refined trigonometric shear deformation theory (RTSDT). The theory accounts for trigonometric distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the present refined trigonometric shear deformation theory contains only four unknowns as against five in case of other shear deformation theories. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The elastic foundation is modelled as two-parameter Pasternak foundation. The results of the shear deformation theories are compared together. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and elastic foundation parameters on the thermomechanical behavior of functionally graded plates. It can be concluded that the proposed theory is accurate and efficient in predicting the thermomechanical bending response of functionally graded plates.

• Steel and Composite Structures
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• v.27 no.3
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• pp.311-325
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• 2018

This article presents the bending analysis of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment. Theoretical formulations are based on a recently developed refined shear deformation theory. The displacement field of the present theory is chosen based on nonlinear variations in the in-plane displacements through the thickness of the plate. The present theory satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the present refined shear deformation theory contains only four unknowns as against five in case of other shear deformation theories. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The elastic foundation is modeled as non-uniform foundation. The results of the shear deformation theories are compared together. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and elastic foundation parameters on the thermo-mechanical behavior of functionally graded plates. Numerical results show that the present theory can archive accuracy comparable to the existing higher order shear deformation theories that contain more number of unknowns.

• Earthquakes and Structures
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• v.26 no.4
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• pp.251-259
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• 2024

In this paper, the thermal post-buckling behavior of graphene platelets reinforced metal foams (GPLRMFs) plate with initial geometric imperfections on nonlinear elastic foundations are studied. First, the governing equation is derived based on the first-order shear deformation theory (FSDT) of plate. To obtain a single equation that only contains deflection, the Galerkin principle is employed to solve the governing equation. Subsequently, a comparative analysis was conducted with existing literature, thereby verifying the correctness and reliability of this paper. Finally, considering three GPLs distribution types (GPL-A, GPL-B, and GPL-C) of plates, the effects of initial geometric imperfections, foam distribution types, foam coefficients, GPLs weight fraction, temperature changes, and elastic foundation stiffness on the thermal post-buckling characteristics of the plates were investigated. The results show that the GPL-A distribution pattern exhibits the best buckling resistance. And with the foam coefficient (GPLs weight fraction, elastic foundation stiffness) increases, the deflection change of the plate under thermal load becomes smaller. On the contrary, when the initial geometric imperfection (temperature change) increases, the thermal buckling deflection increases. According to the current research situation, the results of this article can play an important role in the thermal stability analysis of GPLRMFs plates.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.826-831
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• 2005

In this paper the effect of moving mass on dynamic behavior of cracked cantilever beam on elastic foundations is presented. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. That is, the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory. The crack is assumed to be in the first mode of fracture. As the depth of the crack is increased, the tip displacement of the cantilever beam is increased. When the crack depth is constant the frequency of a cracked beam is proportional to the spring stiffness.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.10 s.103
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• pp.1195-1201
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• 2005

In this paper, the effect of a moving mass on dynamic behavior of the cracked cantilever beam on elastic foundations is presented. Based on the Euler-Bernoulli beam theory, the equation of motion can be constructed by using the Lagrange's equation. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. That is, the crack is modelled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section and is derived by applying fundamental fracture mechanics theory The crack is assumed to be in the first mode of fracture. As the depth of crack is increased, the tip displacement of the cantilever beam is Increased. When the depth of crack is constant, the frequency of a cracked beam is proportional to the spring stiffness.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 2000.10a
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• pp.213-218
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• 2000

This paper deals with the free vibrations of shallow arches resting on elastic foundations. Foundations are assumed to follow the hypothesis proposed by Pasternak. The governing differential equation is derived for the in-plane free vibration of linearly elastic arches of uniform stiffness and constant mass per unit length. Sinusoidal arches with hinged-hinged and clamped-clamped end constraints are considered in analysis. The frequency equations (lowest symmetical and antisymmetrical natural frequency equations) are obtained by Galerkin's method. The effects of arch rise, Winkler foundation parameter and shear foundation parameter on the lowest two natural frequencies are investigated.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.3
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• pp.261-267
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• 2014

The free vibration characteristics of cylindrical shells on inclined partial elastic foundations are investigated by an analytical method. The cylindrical shell is partially surrounded by the elastic foundations, these are represented by the Winkler or Pasternak model. The area of elastic foundation is not uniform and varies along the axial direction of the shell. The motion of shell is represented by first-order shear deformation theory(FSDT) to account for rotary inertia and transverse shear strains. The governing equation is obtained using the Rayleigh-Ritz method and a variation approach. To validate the present method, the numerical example is presented and compared with the present FEA results. The numerical results reveal that the elastic foundation has significant effect on vibration characteristics.

• Structural Engineering and Mechanics
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• v.57 no.6
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• pp.969-988
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• 2016

Vibration analysis of the beams on elastic foundation has gained the great interest of many researchers. In the literature, there are many studies that focus on the free vibration analysis of the beams on one or two parameter elastic foundations. On the other hand, there are no sufficient studies especially focus on the comparison of dynamic response including the bending moment and shear force of the beams resting on Winkler and two parameter foundations. In this study, dynamic response of the axially loaded Timoshenko beams resting on modified Vlasov type elastic soil was investigated by using the separation of variables method. Governing equations were obtained by assuming that the material had linear elastic behaviour and mass of the beam was distributed along its length. Numerical analysis were provided and presented in figures to find out the differences between the modified Vlasov model and conventional Winkler type foundation. Furthermore, the effect of shear deformation of elastic soil on the dynamic response of the beam was investigated.

• Structural Engineering and Mechanics
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• v.28 no.6
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• pp.635-658
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• 2008

An application is presented of a modified Vlasov model to the free vibration analysis of plates resting on elastic foundations. The effects of the subsoil depth, the ratio of the plate dimensions, the ratio of the subsoil depth to the plate dimension in the longer direction, and the value of the vertical deformation parameter within the subsoil on the frequency parameters of plates on an elastic foundation are investigated. This analysis has been caried out by the aid of a computer program. The first ten frequency parameters are presented in tabular and the graphical forms to evaluate the effects of the parameters considered in this study. Then mode shapes corresponding to the first six of the frequency parameters are given in graphs. It is concluded that the effect of the subsoil depth on the frequency parameters of the plates on an elastic foundation is generally larger than those of the other parameters considered in this study.

• Advances in nano research
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• v.5 no.2
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• pp.179-192
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• 2017

The transverse vibration of double walled carbon nanotube (DWCNT) embedded in elastic medium with an initial imperfection is considered. In this paper, Timoshenko beam theory is employed. However the nonlocal theory is used for modeling the nano scale of nanotube. In addition, the governing Equations of motion are obtained utilizing the Hamilton's principle and simply-simply boundary conditions are assumed. Furthermore, the Navier method is used for determining the natural frequencies of DWCNT. Hence, some parameters such as nonlocality, curvature amplitude, Winkler and Pasternak elastic foundations and length of the curved DWCNT are analyzed and discussed. The results show that, the curvature amplitude causes to increase natural frequency. However, nonlocal coefficient and elastic foundations have important role in vibration behavior of DWCNT with imperfection.