Modified Vlasov Model for Beams on Elastic Foundations

Vallabhan, C. V. Girija; Das, Y. C.

doi:10.1061/(asce)0733-9410(1991)117:6(956)

Cited by 129 publications

(74 citation statements)

References 6 publications

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“…5 is considered. In evaluation of the foundation parameters, the analytical method studied by Vallabhan and Das [37] based on the modified 2-D Vlasov model is applied. This method uses experimentally determined values for the soil modulus of elasticity s E and the Poisson ratio ν .…”

Section: Curved Beam With Non-symmetric Open Sectionmentioning

confidence: 99%

A series solution for spatially coupled deflection analysis of thin-walled Timoshenko curved beam with and without elastic foundation

Kim

Shin

2009

J Mech Sci Technol

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The exact solutions for the spatially coupled deflection and the normal stress at an arbitrary location of a crosssection of the thin-walled Timoshenko curved beam with symmetric and non-symmetric cross-sections with and without two types of elastic foundations are newly presented using series solutions for the displacement parameters. The equilibrium equations and the force-deformation relations are derived from the elastic strain energy including the effects of shear deformation and the axial-flexural-torsional coupling, and the strain energy considering the foundation effects. The explicit expressions for displacement parameters are derived by applying the power series expansions of displacement components to the simultaneous ordinary differential equations. Next, the element stiffness matrix is determined by using the force-deformation relationships. The normal stress at any arbitrary location of the cross-section for a curved beam is evaluated from the stiffness matrix. To verify the validity and the accuracy of this study, the displacements and the normal stresses of curved beams are presented and compared with the analytical solutions, the finite element results using the isoparametric curved beam elements based on the Lagrangian interpolation polynomial, and the detailed three-dimensional analysis results using the shell elements of SAP2000.

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Section: Curved Beam With Non-symmetric Open Sectionmentioning

confidence: 99%

A series solution for spatially coupled deflection analysis of thin-walled Timoshenko curved beam with and without elastic foundation

Kim

Shin

2009

J Mech Sci Technol

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“…In these equations, (z) and u are the mode shapes de"ning the variation of the de#ection w N (x, z) in the z direction and the displacement of the subsoil in the x direction respectively [15,16].…”

Section: Evaluation Of the Stiffness Matrixmentioning

confidence: 99%

Application of Modified Vlasov Model to Free Vibration Analysis of Beams Resting on Elastic Foundations

Ayvaz

Özgan²

2002

Journal of Sound and Vibration

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“…On the other hand, when inertial properties of foundation are neglected while computing vertical vibrations of a plate-type engine, the seating may cause serious errors, as both experimental and numerical investigations as shown in Refs. [6][7][8][9][10][11]. Owing to the critical state-of-the art review carried out, the model proposed by Muravskii [11] seems to be one of the most appropriate ones for engineering as it exhibits high practical accuracy of the ground modeling with its simultaneous simplicity.…”

Section: Introductionmentioning

confidence: 99%