An Analytical Solution for Free Vibration of Elastically Restrained Timoshenko Beam on an Arbitrary Variable Winkler Foundation and Under Axial Load

Ghannadiasl, Amin; Mofid, Massood

doi:10.1590/1679-78251504

Cited by 25 publications

(27 citation statements)

References 27 publications

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“…Finally, Ghannadiasl and Mofid used the following data:

ν = 0.25

K = 2 / 3

and

r^{2} / L^{2} = 0.01 .

Results are reported in Table , for different values of

k_{w}

. The percentagewise difference between their results and those of current work is less than 0.03%.…”

Section: Discussionmentioning

confidence: 84%

“…Finally, Ghannadiasl and Mofid [16] used the following data: = 0.25, = 2∕3 and 2 ∕ 2 = 0.01. Results are reported in Table 22, for different values of .…”

Section: Discussionmentioning

confidence: 99%

“…The percentagewise difference between their results and those of current work is less than 0.03%. T A B L E 2 2 Comparison of natural frequency with paper of Ghannadiasl and Mofid [16]…”

Section: Discussionmentioning

confidence: 99%

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Contrasting three alternative versions of Timoshenko‐Ehrenfest theory for beam on Winkler elastic foundation – simply supported beam

et al. 2018

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In this paper the free vibration frequencies of beam on one‐parameter (Winkler) elastic foundation are analyzed via original Timoshenko‐Ehrenfest theory as well as two truncated versions of the Timoshenko‐Ehrenfest beam theory. The traditional version of Timoshenko‐Ehrenfest beam theory is contrasted with the truncated version that lacks the fourth‐order time derivative, as well as with the recently developed version that incorporates slope inertia effect. Advantages and disadvantages of each approach are indicated in the context of free vibrations of the beam on Winkler foundation. In addition an intriguing intermingling phenomenon is discussed in detail, and its implications on three theories.

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“…Finally, Ghannadiasl and Mofid used the following data:

ν = 0.25

K = 2 / 3

and

r^{2} / L^{2} = 0.01 .

Results are reported in Table , for different values of

k_{w}

. The percentagewise difference between their results and those of current work is less than 0.03%.…”

Section: Discussionmentioning

confidence: 84%

“…Finally, Ghannadiasl and Mofid [16] used the following data: = 0.25, = 2∕3 and 2 ∕ 2 = 0.01. Results are reported in Table 22, for different values of .…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Contrasting three alternative versions of Timoshenko‐Ehrenfest theory for beam on Winkler elastic foundation – simply supported beam

et al. 2018

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“…In this paper, the general boundary conditions associated with the beam theory are given below (Ghannadiasl and Mofid, 2015) [22]:…”

Section: Bending Relationships Between Euler-bernoulli and Timoshenkomentioning

confidence: 99%

Assessment of bending solution of beam with arbitrary boundary conditions: an accurate comparison of various approaches

Ghannadiasl

Mortazavi

2017

NMCE

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Bending responses are the important characteristics of structures. In this paper, the bending solution of the thin and thick beams which are elastically restrained against rotation and translation are presented using various theories. Hence, accurate and direct modeling technique is offered for modeling of the thin and thick beams. The effect of the values of the span-to-depth ratio and type of the beam supports are assessed to state accurate comparison of various theories. Finally, the numerical examples are shown in order to present the evaluation of the efficiency and simplicity of the various theories. The results of the theories are compared with the results of the finite element method (ABAQUS). Based on the results, using the Timoshenko beam theory, the obtained values are in good agreement with the Finite Element modeling for the values of the span-to-depth ratio (L/h) less than 3. On the other hands, due to ignoring the shear deformation effect, the Euler-Bernoulli theory underestimates the deflection of the moderately deep beams (L/h=5).

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“…The integral equations changed to a system of linear algebraic equations using the power series. Ghannadiasl and Mofid [17] presented the analytical solution for free vibration of TB with elastically restrained end conditions. In this study, the TB under axial load rests on the arbitrary variable elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

Free vibrations of non-uniform beams on a non-uniform Winkler foundation using the Laguerre collocation method

Ghannadiasl

Zamiri

Borhanifar

2020

J Braz. Soc. Mech. Sci. Eng.

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Natural frequencies and free vibration are important characteristics of beams with non-uniform cross section. Hence, the solution for free vibrations of non-uniform beams is presented using a Laguerre collocation method. The elastically restrained beam model is based on the Euler-Bernoulli theory. Also, the non-uniform beam is rested on a non-uniform foundation (Winkler type). The Laguerre collocation method is introduced for solving the differential equation. This approach reduces the governing differential equation to a system of algebraic equations, and finally, the problem is greatly simplified. Properties of Laguerre polynomials and the operational matrix of derivation are first presented. Eventually, the proposed method is applied for solving the governing differential equation subject to initial conditions, and the results are compared with other results from the literature.

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An Analytical Solution for Free Vibration of Elastically Restrained Timoshenko Beam on an Arbitrary Variable Winkler Foundation and Under Axial Load

Cited by 25 publications

References 27 publications

Contrasting three alternative versions of Timoshenko‐Ehrenfest theory for beam on Winkler elastic foundation – simply supported beam

Contrasting three alternative versions of Timoshenko‐Ehrenfest theory for beam on Winkler elastic foundation – simply supported beam

Assessment of bending solution of beam with arbitrary boundary conditions: an accurate comparison of various approaches

Free vibrations of non-uniform beams on a non-uniform Winkler foundation using the Laguerre collocation method

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