• Title/Summary/Keyword: Elastic Foundations

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Free vibration analysis of tapered beam-column with pinned ends embedded in Winkler-Pasternak elastic foundation

  • Civalek, Omer;Ozturk, Baki
    • Geomechanics and Engineering
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    • v.2 no.1
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    • pp.45-56
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    • 2010
  • The current study presents a mathematical model and numerical method for free vibration of tapered piles embedded in two-parameter elastic foundations. The method of Discrete Singular Convolution (DSC) is used for numerical simulation. Bernoulli-Euler beam theory is considered. Various numerical applications demonstrate the validity and applicability of the proposed method for free vibration analysis. The results prove that the proposed method is quite easy to implement, accurate and highly efficient for free vibration analysis of tapered beam-columns embedded in Winkler- Pasternak elastic foundations.

On the elastic stability and free vibration responses of functionally graded porous beams resting on Winkler-Pasternak foundations via finite element computation

  • Zakaria Belabed;Abdelouahed Tounsi;Mohammed A. Al-Osta;Abdeldjebbar Tounsi;Hoang-Le Minh
    • Geomechanics and Engineering
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    • v.36 no.2
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    • pp.183-204
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    • 2024
  • In current investigation, a novel beam finite element model is formulated to analyze the buckling and free vibration responses of functionally graded porous beams resting on Winkler-Pasternak elastic foundations. The novelty lies in the formulation of a simplified finite element model with only three degrees of freedom per node, integrating both C0 and C1 continuity requirements according to Lagrange and Hermite interpolations, respectively, in isoparametric coordinate while emphasizing the impact of z-coordinate-dependent porosity on vibration and buckling responses. The proposed model has been validated and demonstrating high accuracy when compared to previously published solutions. A detailed parametric examination is performed, highlighting the influence of porosity distribution, foundation parameters, slenderness ratio, and boundary conditions. Unlike existing numerical techniques, the proposed element achieves a high rate of convergence with reduced computational complexity. Additionally, the model's adaptability to various mechanical problems and structural geometries is showcased through the numerical evaluation of elastic foundations, with results in strong agreement with the theoretical formulation. In light of the findings, porosity significantly affects the mechanical integrity of FGP beams on elastic foundations, with the advanced beam element offering a stable, efficient model for future research and this in-depth investigation enriches porous structure simulations in a field with limited current research, necessitating additional exploration and investigation.

Free Vibrations of Fluid-filled Cylindrical Shells on Partial Elastic Foundations (부분 탄성지지된 유체 저장 원통셸의 자유진동)

  • Jung, Kang;Kim, Young-Wann
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.22 no.8
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    • pp.763-770
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    • 2012
  • The free vibration characteristics of fluid-filled cylindrical shells on partial elastic foundations are investigated by an analytical method. The cylindrical shell is fully or partially surrounded by the elastic foundations, these are represented by the Winkler or Pasternak model. The motion of shell is represented by the first order shear deformation theory to account for rotary inertia and transverse shear strains. The steady flow of fluid is described by the classical potential flow theory. The fluid-structure interaction is considered in the analysis. The effect of internal fluid can be considered by imposing a relation between the fluid pressure and the radial displacement of the structure at the interface. To validate the present method, the numerical example is presented and compared with the available existing results.

Alternative plate finite elements for the analysis of thick plates on elastic foundations

  • Ozgan, K.;Daloglu, Ayse T.
    • Structural Engineering and Mechanics
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    • v.26 no.1
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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.

Vibration and Dynamic Stability of Pipes Conveying Fluid on Elastic Foundations

  • Ryu, Bong-Jo;Ryu, Si-Ung;Kim, Geon-Hee;Yim, Kyung-Bin
    • Journal of Mechanical Science and Technology
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    • v.18 no.12
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    • pp.2148-2157
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    • 2004
  • The paper deals with the vibration and dynamic stability of cantilevered pipes conveying fluid on elastic foundations. The relationship between the eigenvalue branches and corresponding unstable modes associated with the flutter of the pipe is thoroughly investigated. Governing equations of motion are derived from the extended Hamilton's principle, and a numerical scheme using finite element methods is applied to obtain the discretized equations. The critical flow velocity and stability maps of the pipe are obtained for various elastic foundation parameters, mass ratios of the pipe, and structural damping coefficients. Especially critical mass ratios, at which the transference of the eigenvalue branches related to flutter takes place, are precisely determined. Finally, the flutter configuration of the pipe at the critical flow velocities is drawn graphically at every twelfth period to define the order of the quasi-mode of flutter configuration.

Influence of Partial Elastic Foundations on Dynamic Stability of a Cantilevered Timoshenko Beam with a Tip Mass under a follower force (끝단 질량을 갖고 종동력을 받는 외팔 Timoshenko 보의 동적안정성에 미치는 부분 탄성기초의 영향)

  • Shin, Kwang-Bok;Kim, Hyo-Jun;Ryu, Bong-Jo
    • Journal of the Korean Society for Precision Engineering
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    • v.22 no.10 s.175
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    • pp.65-71
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    • 2005
  • This paper presents the dynamic stability of a cantilevered Timoshenko beam on partial elastic foundations subjected to a follower force. The beam with a tip concentrated mass is assumed to be a Timoshenko beam taking into account its rotary inertia and shear deformation. Governing equations are derived by extended Hamilton's principle, and finite element method is applied to solve the discretized equation. Critical follower force depending on the attachment ratios of partial elastic foundations, rotary inertia of the beam and magnitude and rotary inertia of the tip mass is fully investigated.

Buckling Stability of Timoshenko Beams on Two-Parameter Elastic Foundations under an Axial Force (축력을 받고 두 파라메타 탄성기초 위에 놓인 티모센코 보의 좌굴 안정성)

  • 정승호
    • Journal of the Korea Society for Simulation
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    • v.8 no.2
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    • pp.111-122
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    • 1999
  • The paper presents a stability analysis of uniform Timoshenko beams resting on two-parameter elastic foundations. The two-parameter elastic foundations were considered as a shearing layer and Winkler springs in soil models. Governing equations of motion were derived using the Hamilton's principle and finite element analysis was performed and the eigenvalues were obtained for the stability analysis. The numerical results for the buckling stability of beams under axial forces are demonstrated and compared with the exact or available confirmed solutions. Finally, several examples were given for Euler-Bernoulli and Timoshenko beams with various boundary conditions.

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On the resonance problems in FG-GPLRC beams with different boundary conditions resting on elastic foundations

  • Hao-Xuan, Ding;Yi-Wen, Zhang;Gui-Lin, She
    • Computers and Concrete
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    • v.30 no.6
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    • pp.433-443
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    • 2022
  • In the current paper, the nonlinear resonance response of functionally graded graphene platelet reinforced (FG-GPLRC) beams by considering different boundary conditions is investigated using the Euler-Bernoulli beam theory. Four different graphene platelets (GPLs) distributions including UD and FG-O, FG-X, and FG-A are considered and the effective material parameters are calculated by Halpin-Tsai model. The nonlinear vibration equations are derived by Euler-Lagrange principle. Then the perturbation method is used to discretize the motion equations, and the loadings and displacement are all expanded, so as to obtain the first to third order perturbation equations, and then the asymptotic solution of the equations can be obtained. Then the nonlinear amplitude-frequency response is obtained with the help of the modified Lindstedt-Poincare method (Chen and Cheung 1996). Finally, the influences of the distribution types of GPLs, total GPLs layers, GPLs weight fraction, elastic foundations and boundary conditions on the resonance problems are comprehensively studied. Results show that the distribution types of GPLs, total GPLs layers, GPLs weight fraction, elastic foundations and boundary conditions have a significant effect on the nonlinear resonance response of FG-GPLRC beams.

Vibration and Stability of Tapered Timoshenko Beams on Two-Parameter Elastic Foundations (두 파라미터 탄성기초를 갖는 테이퍼진 티모센코 보의 진동 및 안정성)

  • 류봉조;임경빈;윤충섭;류두현
    • Journal of KSNVE
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    • v.10 no.6
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    • pp.1075-1082
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    • 2000
  • The paper describes the vibration and stability of tapered beams on two-parameter elastic foundations. The two-parameter elastic foundations are constructed by distributed Winkler springs and a shearing layer as of ten used in soil models. The shear deformation and the rotatory inertia of a beam are taken into account. Governing equations are derived from energy expressions 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 of a beam with an axial force are presented and compared when other solutions are available. Vibration frequencies, mode shapes, and critical forces of a tapered Timoshenko beam on elastic foundations under an axial force are investigated for various thickness ratios, shear foundation parameters, Winkler foundation parameters and boundary conditions.

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