General Analysis of Timoshenko Beams on Elastic Foundation

Abohadima, Samir; Taha, Marwa; Abdeen, Mostafa A. M.

doi:10.1155/2015/182523

Cited by 7 publications

(4 citation statements)

References 9 publications

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“…In addition, the effect of Winkler elastic foundation modulus, slenderness ratio and elastically restrained boundary conditions on the critical load of a Timoshenko beam subjected to an end follower force was investigated (Lee et al, 1992). The Recursive differentiation method was used to study the stability characteristics of axially loaded cantilever Timoshenko beam resting on two parameter foundation by Abohadima et al (Abohadima et al 2015). The obtained solutions were verified with published papers and good agreement was achieved.…”

Section: Introductionmentioning

confidence: 76%

Enhanced Damping Characteristics of Timoshenko Beam on Elastic and Metamaterial Foundations

Oyelade¹,

Sadiq²

2020

JSSCM

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An analytical model is developed for the flexural wave propagation of a continuous Timoshenko beam resting on elastic and metamaterial foundations. The metamaterial foundation consists of positive and negative springs with a damper. This added negative stiffness component is constructed in such a way to provide the same static stiffness and the same damping component with the equivalent reference beam on elastic foundation. Numerical examples are used to investigate the effect of the shear on wavenumber and damping for beam with elastic and metamaterial foundations. The effects of engineering safety, damping coefficient and resonating mass on the dissipative property of the beam is investigated analytically. The simulation results provide indication of an enhanced damping characteristics for the damping ratio of the flexural waves propagating within the beam.

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Section: Introductionmentioning

confidence: 76%

Enhanced Damping Characteristics of Timoshenko Beam on Elastic and Metamaterial Foundations

Oyelade¹,

Sadiq²

2020

JSSCM

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“…Vibrations of Timoshenko–Ehrenfest beams on an elastic foundation have been treated in several works, namely by Abohadima et al [3], Auciello [4], Avramidis and Morfidis [5], Atternejad et al [6], Calio and Greco [7], de Rosa [8], Hassan and Nassar [9], Manevich [10], Matsunaga [11], Obara [12], Sadeghian and Ekhterai Toussi [13], Wang and Gagnon [14], Wu [15], Yin [16], Yokoyama [17,18], and others. As example, in the work by de Rosa [8], the free vibration frequencies of Timoshenko–Ehrenfest beams on a two-parameter elastic foundation (Winkler and Pasternak) are examined; two variants of the equations of motion are deduced, and both axial flexibilities and rotational flexibilities of the constraints are taken in to account.…”

Section: Introductionmentioning

confidence: 99%

Three alternative versions of the theory for a Timoshenko–Ehrenfest beam on a Winkler–Pasternak foundation

Tonzani

Elishakoff

2020

Mathematics and Mechanics of Solids

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This paper analyzes the free vibration frequencies of a beam on a Winkler–Pasternak foundation via the original Timoshenko–Ehrenfest theory, a truncated version of the Timoshenko–Ehrenfest equation, and a new model based on slope inertia. We give a detailed comparison between the three models in the context of six different sets of boundary conditions. In particular, we analyze the most common combinations of boundary conditions deriving from three typical end constraints, namely the simply supported end, clamped end, and free end. An interesting intermingling phenomenon is presented for a simply-supported (S-S) beam together with proof of the ‘non-existence’ of zero frequencies for free-free (F-F) and simply supported-free (S-F) beams on a Winkler–Pasternak foundation.

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“…In 2015, Ghannadiasl and Mofid gave an analytical solution for free vibration of elastically restrained Timoshenko beam on elastic foundation under the action of axial load. In the same year, Abohadima, Taha and Abdeed used recursive differential method (RDM) to study the same problem under the action of a nonuniform lateral excitation. Again in 2015, Manevich analyzed some controversial and unclear issues in the Timoshenko‐Ehrenfest beam theory with emphasis on features of the two branches of frequencies.…”

Section: Introductionmentioning

confidence: 99%

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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General Analysis of Timoshenko Beams on Elastic Foundation

Cited by 7 publications

References 9 publications

Enhanced Damping Characteristics of Timoshenko Beam on Elastic and Metamaterial Foundations

Enhanced Damping Characteristics of Timoshenko Beam on Elastic and Metamaterial Foundations

Three alternative versions of the theory for a Timoshenko–Ehrenfest beam on a Winkler–Pasternak foundation

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

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