• Journal of KSNVE
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• v.9 no.4
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• pp.828-834
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• 1999

The paper describes the vibration and the stability of nonuniform tapered beams resting on two-layered elastic foundations. The two-layered elastic foundations are constructed by discributed Winkler springs and shearing layers as ofen used in oil models. Governing equations are derived from energy experssions using Hamilton's Principle. The associated eigenvalue problems are solved to obtain the free vibration frequencies or the buckling loads. Numerical results for the vibration and the stability of beams under an axial force are presented and compared with other available solutions. Finally, vibration frequencies and critical forces are investigated for various thickness ratios, shear foundation parameters, Winkler foundation parameters, and boundary conditions of tapered beams.

• Structural Engineering and Mechanics
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• v.64 no.1
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• pp.1-10
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• 2017

The present paper deals with the free vibration and buckling problem with consideration of surface properties of circular nanobeams and nanoarches. The Gurtin-Murdach theory is used for investigating the surface effects parameters including surface tension, surface density and surface elasticity. Both linear and nonlinear elastic foundation effect are considered on the circular curved nanobeam. The analytically Navier solution is employed to solve the governing equations. It is obviously detected that the natural frequencies of a curved nanobeams is substantially influenced by the elastic foundations. Besides, it is revealed that by increasing the thickness of curved nanobeam, the influence of surface properties and elastic foundations reduce to vanished, and the natural frequency and critical buckling load turns into to the corresponding classical values.

• Structural Engineering and Mechanics
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• v.4 no.2
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• pp.149-162
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• 1996

A postbuckling analysis is presented for a simply supported, moderately thick rectangular plate subjected to combined axial compression and uniform temperature loading and resting on a two-parameter elastic foundation. The two cases of thermal postbuckling of initially compressed plates and of compressive postbuckling of initially heated plates are considered. The initial geometrical imperfection of the plate is taken into account. The formulations are based on the Reissner-Mindlin plate theory considering the first order shear deformation effect, and including the plate-foundation interaction and thermal effect. The analysis uses a deflection-type perturbation technique to determine the buckling loads and postbuckling equilibrium paths. Numerical examples cover the performances of perfect and imperfect, moderately thick plates resting on Winkler or Pasternak-type elastic foundations. Typical results are presented in dimensionless graphical form.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.911-916
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• 2004

The paper deals with the dynamic stability of a cantilevered Timoshenko beam on partial elastic foundations subjected to a follower force. The beam is assumed to be a Timoshenko beam with a concentrated mass taking into account its rotary inertia and shear deformation. Governing equations are derived by extended Hamilton's principle, and FEM is applied to solve the discretized equation. Critical follower force depending on the attachment ratios of partial elastic foundations, concentrated mass and rotary inertia of the beam is fully investigated.

• Advances in aircraft and spacecraft science
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• v.6 no.3
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• pp.207-223
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• 2019

Current investigation deals with the thermal stability characteristics of carbon nanotube reinforced composite beams (CNTRC) on elastic foundation and subjected to external uniform temperature rise loading. The single-walled carbon nanotubes (SWCNTs) are supposed to have a distribution as being uniform or functionally graded form. The material properties of the matrix as well as reinforcements are presumed to be temperature dependent and evaluated through the extended rule of mixture which incorporates efficiency parameters to capture the size dependency of the nanocomposite properties. The governing differential equations are achieved based on the minimum total potential energy principle and Euler-Bernoulli beam model. The obtained results are checked with the available data in the literature. Numerical results are supplied to examine the effects of numerous parameters including length to thickness ratio, elastic foundations, temperature change, and nanotube volume fraction on the thermal stability behaviors of FG-CNT beams.

• Geomechanics and Engineering
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• v.6 no.2
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• pp.173-194
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• 2014

Laboratory and field data showed that deep mixed (DM) columns accelerated the rate of consolidation of the soft foundations. Most analyses of consolidation of DM column-improved foundations so far have been based on the elastic theory. In reality, the DM columns may yield due to the stress concentration from the soft soil and its limited strength. The influence of column yielding on the degree of consolidation of the soft foundation improved by DM columns has not been well investigated. A three-dimensional mechanically and hydraulically-coupled numerical method was adopted in this study to investigate the degree of consolidation of the DM column foundation considering column yielding. A unit cell model was used, in which the soil was modeled as a linearly elastic material. For a comparison purpose, the DM column was modeled as an elastic or elastic-plastic material. This study examined the aspects of stress transfer, settlement, and degree of consolidation of the foundations without or with the consideration of the yielding of the DM column. A parametric study was conducted to investigate the influence of the column yielding on the stress concentration ratio, settlement, and average degree of consolidation of the DM column foundation. The stress concentration ratio increased and then decreased to reach a constant value with the increase of the column modulus and time. A simplified method was proposed to calculate the maximum stress concentration ratios under undrained and drained conditions considering the column yielding. The simplified method based on a composite foundation concept could conservatively estimate the consolidation settlement. An increase of the column modulus, area replacement ratio, and/or column permeability increased the rate of consolidation.

• Steel and Composite Structures
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• v.39 no.1
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• pp.95-107
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• 2021

In this work, the dynamic response of functionally graded beams on variable elastic foundations is studied using a novel higher-order shear deformation theory (HSDT). Unlike the conventional HSDT, the present one has a new displacement field which introduces undetermined integral variables. The FG beams were assumed to be supported on Winkler-Pasternak type foundations in which the Winkler modulus is supposed to be variable in the length of the beam. The variable rigidity of the elastic foundation is assumed to be linear, parabolic and sinusoidal along the length of the beam. The material properties of the FG porous beam vary according to a power law distribution in terms of the volume fraction of the constituents. The equations of motion are determined using the virtual working principle. For the analytical solution, Navier method is used to solve the governing equations for simply supported porous FG beams. Numerical results of the present theory for the free vibration of FG beams resting on elastic foundations are presented and compared to existing solutions in the literature. A parametric study will be detailed to investigate the effects of several parameters such as gradient index, thickness ratio, porosity factor and foundation parameters on the frequency response of porous FG beams.

• Structural Engineering and Mechanics
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• v.37 no.4
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• pp.367-383
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• 2011

In this paper, nonlinear partial differential equations of motion for a hybrid composite plate subjected to initial stresses on elastic foundations are established to investigate its nonlinear vibration behavior. Pasternak foundation and Winkler foundations are used to represent the plate-foundation interaction. The initial stress is taken to be a combination of pure bending stress plus an extensional stress in the example problems. The governing equations of motion are reduced to the time-dependent ordinary differential equations by the Galerkin's method. Then, the Runge-Kutta method is used to evaluate the nonlinear vibration frequency and frequency ratio of hybrid composite plates. The nonlinear vibration behavior is affected by foundation stiffness, initial stress, vibration amplitude and the thickness ratio of layer. The effects of various parameters on the nonlinear vibration of hybrid laminated plate are investigated and discussed.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.301-308
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• 1998

This paper deals with the influence of elastic foundations on natural frequencies of curved beams. Taking into account the effects of rotatoy inertia and shear deformation, the differential equations governing free, out-of-plane vibrations of circular curved beams resting on Winkler-type foundations are derived and solved numerically. Hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered in numerical examples. The lowest three natural frequencies are claculated over a range of non-dimensional system parameters: the horizontal rise to span length ratio, the slenderness ratio, the foundation parameter, and the width ratio of contact area between the beam and foundation. The effects of rotatory inertia and shear deformation are also analyzed.

• Steel and Composite Structures
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• v.34 no.1
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• pp.75-89
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• 2020

The current paper illustrates the effect of in-plane varying compressive force on critical buckling loads and buckling modes of sandwich composite laminated beam rested on elastic foundation. To generalize a proposed model, unified higher order shear deformation beam theories are exploited through analysis; those satisfy the parabolic variation of shear across the thickness. Therefore, there is no need for shear correction factor. Winkler and Pasternak elastic foundations are presented to consider the effect of any elastic medium surrounding beam structure. The Hamilton's principle is proposed to derive the equilibrium equations of unified sandwich composite laminated beams. Differential quadrature numerical method (DQNM) is used to discretize the differential equilibrium equations in spatial direction. After that, eigenvalue problem is solved to obtain the buckling loads and associated mode shapes. The proposed model is validated with previous published works and good matching is observed. The numerical results are carried out to show effects of axial load functions, lamination thicknesses, orthotropy and elastic foundation constants on the buckling loads and mode shapes of sandwich composite beam. This model is important in designing of aircrafts and ships when non-uniform compressive load and shear loading is dominated.