• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 춘계학술대회논문집A
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• pp.596-601
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• 2000

The paper presents free vibration and stability analyses of a non-uniform Timoshenko beam resting on a two-parameter elastic soil. The soil parameters can vary along the spat and is assumed to be two-parameter model including the effects of both transverse shear deformation and elastic foundation Governing equations related to the vibration and the stability of the beam are derived from Hamilton's principle, and the resulting eigen-value problems can be solved to give natural frequencies and critical force by finite element method. Numerical results for both vibration and stability of beams under an axial force are presented and compared with other available solutions. Finally, vibration frequencies, mode shapes and critical forces are investigated for various thickness ratios, shear foundation parameter, Winkler foundation parameter and boundary conditions of tapered Timoshenko beams.

• Structural Engineering and Mechanics
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• 제69권5호
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• pp.511-525
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• 2019

This paper presents an analytical study of wave propagation in simply supported graduated functional plates resting on a two-parameter elastic foundation (Pasternak model) using a new theory of high order shear strain. Unlike other higher order theories, the number of unknowns and governing equations of the present theory is only four unknown displacement functions, which is even lower than the theory of first order shear deformation (FSDT). Unlike other elements, the present work includes a new field of motion, which introduces indeterminate integral variables. The properties of the materials are assumed to be ordered in the thickness direction according to the two power law distributions in terms of volume fractions of the constituents. The wave propagation equations in FG plates are derived using the principle of virtual displacements. The analytical dispersion relation of the FG plate is obtained by solving an eigenvalue problem. Numerical examples selected from the literature are illustrated. A good agreement is obtained between the numerical results of the current theory and those of reference. A parametric study is presented to examine the effect of material gradation, thickness ratio and elastic foundation on the free vibration and phase velocity of the FG plate.

• Earthquakes and Structures
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• 제3권3_4호
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• pp.495-506
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• 2012

An elasto-dynamic model for pile-soil-pile interaction together with a simple plate model is used in this study to assess the effect of flexible foundation slabs on the dynamic response of pile groups. To this end, different pile configurations with various slab thicknessesare considered in two soil media with low and high elastic moduli. The analyses include dynamic impedances and seismic responses of pile-group foundations. The presented results indicate that the stiffness and damping of pile foundations increase with thickness of the foundation slab; however, the results approach those for rigid slab as the slab thickness approaches twice the pile diameter for the cases considered in this study. The results also reveal that pile foundations with flexible slabs may amplify the earthquake motions by as much as 10 percent in the low to intermediate frequency ranges.

• Geomechanics and Engineering
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• 제10권2호
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• pp.189-205
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• 2016

Soils are subjected to additional stresses due to the loads transferred by the foundations of the buildings. The distribution of stress in soil has great importance in geotechnical engineering projects such as stress, settlement and liquefaction analyses. The purpose of this study is to examine the shear stresses on horizontal plane below the rectangular foundations subjected to biaxial bending on an elastic soil. In this study, closed-form analytical solutions for shear stresses in x and y directions were obtained from Boussinesq's stress equations. The expressions of analytical solutions were simplified by defining the shear stress influence values ($I_1$, $I_2$, $I_3$), and solution charts were presented for obtaining these values. For some special loading conditions, the expressions for shear stresses in the soil below the corners of a rectangular foundation were also given. In addition, a computer program was developed to calculate the shear stress increment at any point below the rectangular foundations. A numerical example for illustrating the use of the presented solution charts was given and, finally, shear stress isobars were obtained for the same example by a developed computer program. The shear stress expressions obtained in this work can be used to determine monotonic and cyclic behavior of soils below rectangular foundations subjected to biaxial bending.

• Geomechanics and Engineering
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• 제11권2호
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• pp.289-307
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• 2016

A simple hyperbolic shear deformation theory taking into account transverse shear deformation effects is proposed for the free flexural vibration analysis of thick functionally graded plates resting on elastic foundations. By considering further supposition, the present formulation introduces only four unknowns and its governing equations are therefore reduced. Hamilton's principle is employed to obtain equations of motion and Navier-type analytical solutions for simply-supported plates are compared with the available solutions in literature to check the accuracy of the proposed theory. Numerical results are computed to examine the effects of the power-law index and side-to-thickness ratio on the natural frequencies.

• 한국해양공학회지
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• 제3권2호
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• pp.570-570
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• 1989

The natural frequencies of a rectangular plate on non-homogeneous elastic foundations were obtained by using the Ritz method and Galerkin method. The results of both methods using the different type of trial functions were also compared. Furthermore, the effects of the variation of boundary conditions, the stiffness of the foundation spring, the dimension ratio of the plate were investigated. As a result, the Galerkin method can be used to obtain the accurate solution and can be effectively used to design the foundation bed.

• 한국해양공학회지
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• 제3권2호
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• pp.70-76
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• 1989

The natural frequencies of a rectangular plate on non-homogeneous elastic foundations were obtained by using the Ritz method and Galerkin method. The results of both methods using the different type of trial functions were also compared. Furthermore, the effects of the variation of boundary conditions, the stiffness of the foundation spring, the dimension ratio of the plate were investigated. As a result, the Galerkin method can be used to obtain the accurate solution and can be effectively used to design the foundation bed.

• Steel and Composite Structures
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• 제28권5호
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• pp.541-557
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• 2018

This paper presents the influence of carbon nanotubes (CNTs) waviness and aspect ratio on the vibrational behavior of functionally graded nanocomposite sandwich annular sector plates resting on two-parameter elastic foundations. The carbon nanotube-reinforced (CNTR) sandwich plate has smooth variation of CNT fraction along the thickness direction. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of Pasternak's elastic foundation coefficients, sandwich plate thickness, face sheets thickness and plate aspect ratio are investigated on the free vibration of the sandwich plates with wavy CNT-reinforced face sheets. The study is carried out based on three-dimensional theory of elasticity and in contrary to two-dimensional theories, such as classical, the first- and the higher-order shear deformation plate theories, this approach does not neglect transverse normal deformations. The sandwich annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free.

• Steel and Composite Structures
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• 제25권6호
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• pp.649-661
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• 2017

This paper is motivated by the lack of studies in the technical literature concerning to the influence of carbon nanotubes (CNTs) waviness and aspect ratio on the vibrational behavior of functionally graded nanocomposite annular sector plates resting on two-parameter elastic foundations. The carbon nanotube-reinforced (CNTR) plate has smooth variation of CNT fraction based on the power-law distribution in the thickness direction, and the material properties are also estimated by the extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. Parametric studies are carried out to highlight the influence of CNTs volume fraction, waviness and aspect ratio, boundary conditions and elastic foundation on vibrational behavior of FG-CNT thick sectorial plates. The study is carried out based on three-dimensional theory of elasticity and in contrary to two-dimensional theories, such as classical, the first- and the higher-order shear deformation plate theories, this approach does not neglect transverse normal deformations. The annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. For an overall comprehension on 3-D vibration of annular sector plates, some mode shape contour plots are reported in this research work.

• Structural Engineering and Mechanics
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• 제89권2호
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• pp.103-119
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• 2024

The present research investigates the thermodynamically bending behavior of FG sandwich plates, laying on the Winkler/Pasternak/Kerr foundation with various boundary conditions, subjected to harmonic thermal load varying through thickness. The supposed FG sandwich plate has three layers with a ceramic core. The constituents' volume fractions of the lower and upper faces vary gradually in the direction of the FG sandwich plate thickness. This variation is performed according to various models: a Power law, Trigonometric, Viola-Tornabene, and the Exponential model, while the core is constantly homogeneous. The displacement field considered in the current work contains integral terms and fewer unknowns than other theories in the literature. The corresponding equations of motion are derived based on Hamilton's principle. The impact of the distribution model, scheme, aspect ratio, side-to-thickness ratio, boundary conditions, and elastic foundations on thermodynamic bending are examined in this study. The deflections obtained for the sandwich plate without elastic foundations have the lowest values for all boundary conditions. In addition, the minimum deflection values are obtained for the exponential volume fraction law model. The sandwich plate's non-dimensional deflection increases as the aspect ratio increases for all distribution models.