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

Ayvaz, Yusuf; Özgan, Korhan

doi:10.1006/jsvi.2001.4143

Cited by 26 publications

(14 citation statements)

References 16 publications

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“…The last model consists of an elastic layer resting on the non-deformable base. The analysis using Vlasov model was examined in Refs [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Vibrations And Stability Of Bernoulli-Euler And Timoshenko Beams On Two-Parameter Elastic Foundation

Obara

2014

Archives of Civil Engineering

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The vibration and stability analysis of uniform beams supported on two-parameter elastic foundation are performed. The second foundation parameter is a function of the total rotation of the beam. The effects of axial force, foundation stiffness parameters, transverse shear deformation and rotatory inertia are incorporated into the accurate vibration analysis. The work shows very important question of relationships between the parameters describing the beam vibration, the compressive force and the foundation parameters. For the free supported beam, the exact formulas for the natural vibration frequencies, the critical forces and the formula defi ning the relationship between the vibration frequency and the compressive forces are derived. For other conditions of the beam support conditional equations were received. These equations determine the dependence of the frequency of vibration of the compressive force for the assumed parameters of elastic foundation and the slenderness of the beam.

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“…The last model consists of an elastic layer resting on the non-deformable base. The analysis using Vlasov model was examined in Refs [21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Vibrations And Stability Of Bernoulli-Euler And Timoshenko Beams On Two-Parameter Elastic Foundation

Obara

2014

Archives of Civil Engineering

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“…This can be done by applying Equation (26), at grid points 3 X , 4 X ,…, 2 N X − . Substituting Equations (33), (35), (37) and (38) into Equation (26) gives the system of equations (39).…”

Section: Solution Of the Problemmentioning

confidence: 99%

“…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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“…This is due to the intractable mathematical nature of the problem. Numerical methods such as finite element method [1][2], transfer matrix method [3], differential quadrature element method (DQM) [4][5][6], perturbation techniques [7][8] are used to obtain the vibration behavior of different types of linear or nonlinear beams resting on linear or nonlinear foundations.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration Model for Initially Stressed Beam-Foundation System

Taha¹

2012

TOAMJ

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An analytical solution for nonlinear vibration of an initially stressed beam with elastic end restraints resting on a nonlinear elastic foundation is obtained. As a first step in solving nonlinear vibration equation, the linear vibration mode functions for a beam with elastic end restraints resting on a linear elastic foundation are obtained. Then, the nonlinear vibration equation is solved by employing the linear mode functions to obtain frequency equation and nonlinear response using Jacobi elliptic integral. The nonlinearity due to lateral vibrations, the nonlinearity of foundations and lateral displacement due to lateral elastic restraints at beam ends not included in previous analytical work are considered in the present work. The effects of spring stiffness at the beam ends, foundation stiffness, axial load and vibration amplitude on the frequency parameter are studied. The present solution can be used to measure the accuracy of approximate methods.

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

Cited by 26 publications

References 16 publications

Vibrations And Stability Of Bernoulli-Euler And Timoshenko Beams On Two-Parameter Elastic Foundation

Vibrations And Stability Of Bernoulli-Euler And Timoshenko Beams On Two-Parameter Elastic Foundation

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

Nonlinear Vibration Model for Initially Stressed Beam-Foundation System

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