• Steel and Composite Structures
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• 제44권3호
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• pp.353-369
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• 2022

This study attempts to shed light on the coupled impact of types of loading, thickness stretching, and types of variation of Winkler-Pasternak foundations on the flexural behavior of simply- supported FG plates according to the new quasi-3D high order shear deformation theory, including integral terms. A new function sheep is used in the present work. In particular, both Winkler and Pasternak layers are non-uniform and vary along the plate length direction. In addition, the interaction between the loading type and the variation of Winkler-Pasternak foundation parameters is considered and involved in the governing equilibrium equations. Using the virtual displacement principle and Navier's solution technique, the numerical results of non-dimensional stresses and displacements are computed. Finally, the non-dimensional formulas' results are validated with the existing literature, and excellent agreement is detected between the results. More importantly, several complementary parametric studies with the effect of various geometric and material factors are examined. The present analytical model is suitable for investigating the bending of simply-supported FGM plates for special technical engineering applications.

• Structural Engineering and Mechanics
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• 제67권5호
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• pp.517-525
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• 2018

In this study, we investigate the vibration of single-walled carbon nanotubes embedded in a polymeric matrix using nonlocal elasticity theories with account arbitrary boundary conditions effects. A Winkler type elastic foundation is employed to model the interaction of nanobeam and the surrounding elastic medium. Influence of all parameters such as nonlocal small-scale effects, Winkler modulus parameter, vibration mode and aspect ratio of nanobeam on the vibration frequency are analyzed and discussed. The mechanical properties of carbon nanotubes and polymer matrix are treated and an analytical solution is derived using the governing equations of the nonlocal Euler-Bernoulli beam models. Solutions have been compared with those obtained in the literature and The results obtained show that the non-dimensional natural frequency is significantly affected by the small-scale coefficient, the vibrational mode number and the elastic medium.

• 한국소음진동공학회논문집
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• 제11권5호
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• pp.101-107
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• 2001

This paper deals with the free vibrations of horizontally curved beams with mu1tiple elastic springs. Taking into account the effects of rotatory Inertia and shear deformation. differential equations governing the free vibrations of such beams are derived, In which each e1astic spring is modeled as a discrete Winkler foundation with very short longitudinal length. Differential equations are solved numerically to calculate natural frequencies and mode shapes. In numerical examples, the circular, Parabolic. sinusoidal and elliptic curved beams are considered. The parametric studies are conducted and the lowest four frequency parameters are reported In tables and figures as the non-dimensional forms. Also the typical mode shapes are presented.

• 한국소음진동공학회논문집
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• 제14권3호
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• pp.230-235
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• 2004

This paper deals with the free vibration analysis of circular strip foundations with the variable breadth. Taking into account effects of both rotatory inertia and shear deformation, differential equations governing free vibrations of such foundations are derived. The Winkler foundation is chosen as the model of soil foundation. The breadth of strip foundation is assumed to be a linear function. The differential equations are solved numerically to calculate natural frequencies. In numerical examples, the strip foundations with the hinged-hinged, hinged-clamped. clamped-hinged and clamped-clamped end constraints are considered. The parametric studies are conducted and the lowest four frequency parameters are reported in figures as the non-dimensional forms.

• Structural Engineering and Mechanics
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• 제40권4호
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• pp.583-594
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• 2011

In the present study, free vibration of an axially functionally graded (AFG) pile embedded in Winkler-Pasternak elastic foundation is analyzed within the framework of the Euler-Bernoulli beam theory. The material properties of the pile vary continuously in the axial direction according to the power-law form. The frequency equation is obtained by using Lagrange's equations. The unknown functions denoting the transverse deflections of the AFG pile is expressed in modal form. In this study, the effects of material variations, the parameters of the elastic foundation on the fundamental frequencies are examined. It is believed that the tabulated results will be a reference with which other researchers can compare their results.

• Advances in aircraft and spacecraft science
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• 제5권6호
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• pp.671-689
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• 2018

Bending, buckling and free vibration responses of functionally graded (FG) higher-order beams resting on two parameter (Winkler-Pasternak) elastic foundation are studied using a new inverse hyperbolic beam theory. The material properties of the beam are graded along the thickness direction according to the power-law distribution. In the present theory, the axial displacement accounts for an inverse hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the top and bottom surfaces of the beams. Hamilton's principle is employed to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending, bucking and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio and foundation parameter on the displacements, stresses, critical buckling loads and frequencies. Numerical results by using parabolic beam theory of Reddy and first-order beam theory of Timoshenko are specially generated for comparison of present results and found in excellent agreement with each other.

• Earthquakes and Structures
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• 제19권2호
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• pp.91-101
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• 2020

This work presents an efficient and original hyperbolic shear deformation theory for the bending and dynamic behavior of functionally graded (FG) beams resting on Winkler - Pasternak foundations. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present theory, the equations of motion are derived from Hamilton's principle. Navier type analytical solutions are obtained for the bending and vibration problems. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and vibration behavior of functionally graded beams.

• 소음진동
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• 제8권3호
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• pp.524-532
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• 1998

The purpose of this paper is to investigate the free vibrations of horizontally curved beams resting on Winkler-type foundations. Based on the classical Bernoulli-Euler beam theory, the governing differential equations for circular curved beams are derived and solved numerically. Hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered in numerical examples. The free vibration frequencies calculated using the present analysis have been compared with the finite element's results computed by the software ADINA. Numerical results are presented to show the effects on the natural frequencies of curved beams of the horizontal rise to span length ratio, the foundation parameter, and the width ratio of contact area between the beam and foundation.

• Structural Engineering and Mechanics
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• 제26권1호
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• pp.69-86
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• 2007

A four-noded plate bending quadrilateral (PBQ4) and an eight-noded plate bending quadrilateral (PBQ8) element based on Mindlin plate theory have been adopted for modeling the thick plates on elastic foundations using Winkler model. Transverse shear deformations have been included, and the stiffness matrices of the plate elements and the Winkler foundation stiffness matrices are developed using Finite Element Method based on thick plate theory. A computer program is coded for this purpose. Various loading and boundary conditions are considered, and examples from the literature are solved for comparison. Shear locking problem in the PBQ4 element is observed for small value of subgrade reaction and plate thickness. It is noted that prevention of shear locking problem in the analysis of the thin plate is generally possible by using element PBQ8. It can be concluded that, the element PBQ8 is more effective and reliable than element PBQ4 for solving problems of thin and thick plates on elastic foundations.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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• pp.852-857
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• 2003

This paper has the object of investigating natural frequencies of thick plates on inhomogeneous Pasternak foundation by means of finite element method and providing kinematic design data lot mat of building structures. This analysis was applied for design of substructure on elastic foundation. Mat of building structure may be consisdered as a thick plate on elastic foundation. Recently, as size of building structure becomes larger, mat area of building structure also tend to become target and building structure is supported on inhomogeneous foundation. In this paper, vibration analysis or rectangular thick plate is done by use or serendipity finite element with 8 nodes by considering shearing strain of plate. The solutions of this paper are compared with existing solutions and finite element solutions with 4${\times}$4 meshes of this analysis are shown the error of maximum 0.083% about the existing solutions. It is shown that natrural frequencies depend on not only Winkler foundation parameter but also shear foundation parameter.