Non-Linear Vibrations of a Beam Resting on a Tensionless Winkler Foundation

Coşkun, İrfan

doi:10.1006/jsvi.2000.2982

Cited by 31 publications

(8 citation statements)

References 21 publications

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“…Explicit expressions for the natural frequencies and the associated amplitude ratios of a double-beam system and the analytical solution of its critical buckling were also derived by Zhang et al [6]. Moreover, semi-analytical closed form solutions [7] and numerical methods such as the method of power series expansion of displacement components employing Hamilton's principle [8], the Galerkin method [9], the differential quadrature element method [10], a combination between the state space and the differential quadrature methods [11], double Fourier transforms [12] and the finite element technique [13][14][15] have also been used for the vibration and buckling analysis of beam-columns on one or two-parameter linear or nonlinear (tensionless) elastic foundations taking into account or ignoring shear deformation effect.…”

Section: Introductionmentioning

confidence: 96%

Nonlinear dynamic analysis of Timoshenko beam-columns partially supported on tensionless Winkler foundation

Sapountzakis

Kampitsis

2010

Computers & Structures

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Section: Introductionmentioning

confidence: 96%

Nonlinear dynamic analysis of Timoshenko beam-columns partially supported on tensionless Winkler foundation

Sapountzakis

Kampitsis

2010

Computers & Structures

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“…As the soil essentially reacts only in compression, the above consideration contradicts the actual scenario where the rail is found to show a tendency to lift off the ground at rear as well as in front of applied load. Some of the works that considers this tensionless behavior for unreinforced earth beds include Rao (1974), Torby (1975), Lin and Adams (1987), Coşkun (2000), Chen and Chen (2011) and He et al (2016) among others. For reinforced earth beds, Maheshwari et al (2004Maheshwari et al ( , 2005 considered the tensionless foundations for geosynthetic membrane reinforced earth bed.…”

Section: Introductionmentioning

confidence: 99%

Modeling of Rail Tracks on Stone Column Reinforced Tensionless Foundations

Bhatra

Maheshwari

2019

Front. Built Environ.

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This research investigates the response of rails on geocell-stone column composite reinforced foundation beds under a moving load. Improved earth bed has been considered to respond only to compressive forces. The granular mat below the rail has been idealized as a Pasternak shear layer and geocell reinforcement as an infinite beam with finite bending stiffness. Soft soil and stone columns have been symbolized by Winkler springs of different stiffnesses. Analysis has been carried out with due consideration to viscous damping in the system. The governing differential equations have been established and simplified for general use with the help of dimensionless parameters. These equations have been solved in presence of appropriate boundary conditions by utilizing Finite difference method in combination with iterative Gauss-Seidel procedure. Inclusion of stone columns has been observed to significantly affect the onset of separation between rail and the soil layer underneath. Various parameters namely, applied load and its velocity, stiffnesses of top, bottom soil layers and stone columns, damping ratio, relative flexural rigidity, depth of placement of geocell, configuration of stone columns have been found to affect the response of soil-foundation system significantly. Improvement in the properties of soil by means of higher value of relative compressibility resulted in typical reduction of 50% in maximum deflection. It has been observed that the region of detachment reduces on increasing the depth of placement of the bottom beam. Sensitivity analysis highlighted the greater sensitivity of upward deflection as compared to the downward deflection of rail with respect to all the parameters except for relative compressibility of the soil and relative stiffness of the stone columns.

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“…Zhang and Murphy [6] developed a general analytical model for the static response of a beam resting on a tensionless elastic foundation subjected to a lateral point load. The forced vibrations of an elastic beam resting on a non-linear tensionless Winkler foundation subjected to a concentrated dynamic load at its centre are considered in [7]. A Hamiltonian variational formulation to determine the energy minimizing boundary conditions of the tensionless contact problem for an Euler-Bernoulli beam resting on a Pasternak or a Reissner two-parameter foundation is given in [8].…”

Section: Introductionmentioning

confidence: 99%

Dynamic stability of Timoshenko beams on Pasternak viscoelastic foundation

Pavlović

2018

Theor appl mech (Belgr)

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The dynamic stability problem of a Timoshenko beam supported by a generalized Pasternak-type viscoelastic foundation subjected to compressive axial loading, where rotary inertia is neglected, is investigated. Each axial force consists of a constant part and a time-dependent stochastic function. By using the direct Liapunov method, bounds of the almost sure asymptotic stability of a beam as a function of viscous damping coefficient, variance of the stochastic force, shear correction factor, parameters of Pasternak foundation, and intensity of the deterministic component of axial loading are obtained. With the aim of justifying the use of the direct Liapunov method analytical results are firstly compared with numerically obtained results using Monte Carlo simulation method. Numerical calculations are further performed for the Gaussian process with a zero mean as well as a harmonic process with random phase. The main purpose of the paper is to point at significance damping parameter of foundation on dynamic stability of the structure.2010 Mathematics Subject Classification: 74H55.

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Non-Linear Vibrations of a Beam Resting on a Tensionless Winkler Foundation

Cited by 31 publications

References 21 publications

Nonlinear dynamic analysis of Timoshenko beam-columns partially supported on tensionless Winkler foundation

Nonlinear dynamic analysis of Timoshenko beam-columns partially supported on tensionless Winkler foundation

Modeling of Rail Tracks on Stone Column Reinforced Tensionless Foundations

Dynamic stability of Timoshenko beams on Pasternak viscoelastic foundation

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