Dynamic response of a multi-span Timoshenko beam with internal and external flexible constraints subject to a moving mass

Ariaei, A.; Ziaei-Rad, Saeed; Malekzadeh, Maryam

doi:10.1007/s00419-013-0745-6

Cited by 15 publications

(10 citation statements)

References 17 publications

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“…Each estate is described in Table 1, and the parameters k ti , k θi , k te and k θ e are the stiffness of internal extensional, internal rotational, external extensional and external rotational spring, respectively [22]. If there are two or more springs in every connection point, a combination component of the above estates can be used for modeling.…”

Section: Intermediate Flexible Connectionsmentioning

confidence: 99%

“…In Eqs. (1) and (2), θ i (x, t) is the rotation cross section angle and w i (x, t) is the vertical displacement of the beam and can be expressed as [22] …”

Section: Fig 1 Rotating Tapered Timoshenko Beammentioning

confidence: 99%

“…(19)(20)(21)(22)(23)(24)(25)(26)(27) at x 0 = 0, and using the correlations defined in Table 2, the following equations are obtained Table 3 DTM theorems adopted for boundary conditions…”

Section: Solutionmentioning

confidence: 99%

“…This approach has some limitations, while it is applicable if one is interested in the general rather than the local behavior of the cracked beam. Nevertheless, many authors have applied this approach [22,23]. As the analysis of local effect is not within the scope of this article, it will therefore be logical to apply this approach.…”

mentioning

confidence: 98%

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Vibration analysis of a rotating Timoshenko beam with internal and external flexible connections

Talebi

Ariaei

2014

Arch Appl Mech

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An analytical method is presented to determine the vibration characteristics of a rotating Timoshenko beam with variable cross section and intermediate flexible connections using the differential transform method. Based on the application of Timoshenko beam theory on separate beams and the compatibility requirements on each connection point, the correlations between every two adjacent spans are obtained. The formulation is extended to a point where it would be able to evaluate the cases with internal and external flexible connections. The results will be validated against those reported in the literature and compared with the ones from the modal test. A number of parametric studies are conducted to assess the stiffness of elastic connections, rotating speed, hub radius and tapered ratio effects on the beam natural frequencies and mode shapes. It is observed that by changing the stiffness of the intermediate springs, the general formulation developed here can cover a large array of problems such as cracked or intermediately constrained beams.

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Section: Intermediate Flexible Connectionsmentioning

confidence: 99%

“…In Eqs. (1) and (2), θ i (x, t) is the rotation cross section angle and w i (x, t) is the vertical displacement of the beam and can be expressed as [22] …”

Section: Fig 1 Rotating Tapered Timoshenko Beammentioning

confidence: 99%

“…(19)(20)(21)(22)(23)(24)(25)(26)(27) at x 0 = 0, and using the correlations defined in Table 2, the following equations are obtained Table 3 DTM theorems adopted for boundary conditions…”

Section: Solutionmentioning

confidence: 99%

mentioning

confidence: 98%

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Vibration analysis of a rotating Timoshenko beam with internal and external flexible connections

Talebi

Ariaei

2014

Arch Appl Mech

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“…There are not so many papers focused on the dynamic response problem of a multispan beam due to a moving load [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. The vibrations of a multispan Bernoulli-Euler beam with an arbitrary geometry in each span subjected to moving forces [13][14][15][16][17][18][19], or moving masses [24,25], or moving oscillators [26] have been considered. Also the vibrations of a multispan Timoshenko beam due to moving load have been considered [27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Application of Volterra Integral Equations in Dynamics of Multispan Uniform Continuous Beams Subjected to a Moving Load

Zakęś

Śniady

2016

Shock and Vibration

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The dynamic behavior of multispan uniform continuous beam arbitrarily supported on its edges subjected to various types of moving noninertial loads is studied. Problem is solved by replacing a multispan structure with a single-span beam loaded with a given moving load and redundant forces situated in the positions of the intermediate supports. Redundant forces are obtained by solving Volterra integral equations of the first or the second order (depending on the stiffness of the intermediate supports) which are consistent deformation equations corresponding to each redundant. Solutions for the beam arbitrarily supported on its edges (pinned or fixed) due to a moving concentrated force and moving distributed load are given. The difficulty of solving Volterra integral equations analytically is bypassed by proposing a simple numerical procedure. Numerical examples of two- and three-span beam have been included in order to show the efficiency of the presented method.

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Vibrations of a Multi-span Beam Subjected to a Moving Stochastic Load

Zakęś

Śniady

2018

Springer Proceedings in Mathematics &Amp; Statistics

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Dynamic response of a multi-span Timoshenko beam with internal and external flexible constraints subject to a moving mass

Cited by 15 publications

References 17 publications

Vibration analysis of a rotating Timoshenko beam with internal and external flexible connections

Vibration analysis of a rotating Timoshenko beam with internal and external flexible connections

Application of Volterra Integral Equations in Dynamics of Multispan Uniform Continuous Beams Subjected to a Moving Load

Vibrations of a Multi-span Beam Subjected to a Moving Stochastic Load

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