Non-Linear Vibrations of a Beam on an Elastic Foundation

Coşkun, İrfan; Engin, Hasan

doi:10.1006/jsvi.1998.1973

Cited by 47 publications

(17 citation statements)

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“…Pellicano and Mastroddi (1997) studied nonlinear dynamics of beams resting on a nonlinear spring bed. Coskun and Engin (1999) presented the nonlinear vibration of a beam resting on nonlinear tensionless foundation subjected to a concentrated load at the center using the perturbation technique. Tsiatas (2010) presented the nonlinear problem of non-uniform beams.…”

Section: Introductionmentioning

confidence: 99%

Dynamic response of non-uniform beam subjected to moving load and resting on non-linear viscoelastic foundation

Abdelghany

Ewis

Mahmoud

et al. 2015

Beni-Suef University Journal of Basic and Applied Sciences

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Available online xxxKeywords: Dynamic response Non-uniform beam Viscoelastic foundation a b s t r a c t In this paper, it was purposed to comprehend the dynamic response of non-uniform EulereBernoulli simply supported beam which is subjected to moving load. The beam is rested on a nonlinear viscoelastic foundation. Galerkin with Runge-Kutta methods are employed. The influences of variations of the traveling velocity and the effect of increase in the magnitude of the moving load on the dynamic response are studied. A MATLAB code is designed to compute and plot the deflection.

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Section: Introductionmentioning

confidence: 99%

Dynamic response of non-uniform beam subjected to moving load and resting on non-linear viscoelastic foundation

Abdelghany

Ewis

Mahmoud

et al. 2015

Beni-Suef University Journal of Basic and Applied Sciences

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“…Coskun and Engin [13] investigated the non-linear vibration of an elastic beam on a linear unstretched Winkler foundation subjected to a concentrated stationary load at its midpoint. They found that in contrast to the linear cases, the position of the lift-off points will change depending on the magnitude of the load and also, the vertical displacements change with the square of the load in the non-linear case; the dynamic effect in the linear case, the dynamic effect and the non-linearity arising from the foundation modulus in the non-linear case affect the variation of the contact lengths and the vertical displacements of the beam.…”

Section: Introductionmentioning

confidence: 99%

Internal-external resonance of beams on non-linear viscoelastic foundation traversed by moving load

2010

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Vibration of a finite Euler-Bernoulli beam, supported by non-linear viscoelastic foundation traversed by a moving load, is studied and the Galerkin method is used to discretize the non-linear partial differential equation of motion. Subsequently, the solution is obtained for different harmonics using the Multiple Scales Method (MSM) as one of the perturbation techniques. Free vibration of a beam on non-linear foundation is investigated and the effects of damping and non-linear stiffness of the foundation on the responses are examined. Internal-external resonance condition is then stated and the frequency responses of different harmonics are obtained by MSM. Different conditions of the external resonance are studied and a parametric study is carried out for each case. The effects of damping and non-linear stiffness of the foundation as well as the magnitude of the moving load on the frequency responses are investigated. Finally, a thorough local stability analysis is performed on the system.

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“…Due to the difficulty of mathematical nature of the problem, a few analytical solutions limited to special cases for vibrations of non-uniform beams resting on non-linear elastic foundations are found. Many methods are used to obtain the vibration behavior of different types of linear or nonlinear beams resting on linear or nonlinear foundations such as finite element method [1][2][3], transfer matrix method [4], Rayleigh-Ritz method [5], differential quadrature element method (DQEM) [6][7][8][9][10], Galerkin procedure [11,12] and [13][14][15]. There are various types of foundation models such as Winkler, Pasternak, Vlasov, etc.…”

Section: Introductionmentioning

confidence: 99%

Vibration Analysis of Non-uniform Beams Resting on Two Layer Elastic Foundations Under Axial and Transverse Load Using (GDQM)

Abumandour¹

2017

IJMEA

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Abstract:The natural frequencies of non-uniform beams resting on two layer elastic foundations are numerically obtained using the Generalized Differential Quadrature (GDQ) method. The Differential Quadrature (DQ) method is a numerical approach effective for solving partial differential equations. A new combination of GDQM and Newton's method is introduced to obtain the approximate solution of the governing differential equation. The GDQ procedure was used to convert the partial differential equations of non-uniform beam vibration problems into a discrete eigenvalues problem. We consider a homogeneous isotropic beam with various end conditions. The beam density, the beam inertia, the beam length, the linear (k 1 ) and nonlinear (k 2 ) Winkler (normal) parameters and the linear (k 3 ) Pasternak (shear) foundation parameter are considered as parameters. The results for various types of boundary conditions were compared with the results obtained by exact solution in case of uniform beam supported on elastic support.

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Non-Linear Vibrations of a Beam on an Elastic Foundation

Cited by 47 publications

References 0 publications

Dynamic response of non-uniform beam subjected to moving load and resting on non-linear viscoelastic foundation

Dynamic response of non-uniform beam subjected to moving load and resting on non-linear viscoelastic foundation

Internal-external resonance of beams on non-linear viscoelastic foundation traversed by moving load

Vibration Analysis of Non-uniform Beams Resting on Two Layer Elastic Foundations Under Axial and Transverse Load Using (GDQM)

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