Free vibrations of Timoshenko beams on two-parameter elastic foundation

Rosa, M.A. De

doi:10.1016/0045-7949(94)00594-s

Cited by 87 publications

(50 citation statements)

References 6 publications

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“…The second foundation parameter is a function of the total rotation of the beam, like in Ref. [29]. The effects of the shear deformation, rotatory inertia and the foundation parameters on the frequency and critical loads of the beam are discussed in detail.…”

Section: Introductionmentioning

confidence: 99%

“…The analysis of a beam resting on two-parametrical elastic foundation has been conducted by many authors [24][25][26][27][28][29][30][31][32][33]. A majority of them employed a fi nite element formulation to perform analyses.…”

Section: Introductionmentioning

confidence: 99%

“…The static, dynamic and stability behavior of framed structures made of beam-columns were analyzed in that paper. Free vibration frequencies of Timoshenko beams on two-parameter elastic foundation were examined by Rosa [29] for two different models. In the fi rst model, the second foundation parameter is assumed to be a function of the fl exural rotation, whereas in the second model, it is assumed to be a function of the global cross-section rotation.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Obara

2014

Archives of Civil Engineering

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“…Lin [1] was among the first who dealt with the vibration of a beam on elastic supports. Valsangkar and Pradhanang [2] and Franciosi and Masi [3] investigated Euler-Bernoulli beam on two-parameter model soil foundation, while De Rosa [4] and Ruta [5] did the same for Timoshenko beams. Chen employed the differential quadrature element method (DQEM), to investigate the vibration of beams on Winkler [6] and Pasternak [7] foundations.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of a tapered beam with exponentially varying thickness resting on Winkler foundation using the differential transform method

Boreyri

Mohtat

Ketabdari

et al. 2014

International Journal of Physical Research

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In this paper, free vibration of a new type of tapered beam, with exponentially varying thickness, resting on a linear foundation is analyzed. The solution is based on a semi-analytical technique, the differential transform method (DTM). Applying DTM, nonlinear partial differential equations of the varying thickness beam are transformed into algebraic equations, which are then solved to obtain the solution. An Euler-Bernoulli beam with a number of boundary conditions and different exponential factor is taken into account. Results have been compared to the 4th order Runge-Kutta, and where possible with DQEM and analytical solution. These comparisons prove the preciseness of this method, based on which DTM can be considered as a powerful framework for eigenvalue analysis of new type of tapered beams.

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“…De Rosa [1995] studied the free vibration frequencies of Timoshenko beams on a two-parameter elastic layer. Two variants of the equation of motion were deduced, in which the second-layer parameter was a function of the total rotation of the beam or a function of the rotation due to bending only.…”

Section: Introductionmentioning

confidence: 99%

Untitled

2012

J. Mech. Mater. Struct.

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This paper presents an analytical method for determining deflection of fully clamped thin circular plates. The plates are made from a rigid perfectly plastic material and subjected to a transverse localized and uniform blast loading. The essence of the model is to describe the deformation profile with the aid of a zero-order Bessel function and to perform energy analysis. This provides a method for predicting the plastic deformation of circular plates under impulsive loading. It can be also regarded as an attempt to use the energy method for different impulsive loading conditions. Calculations of the cases indicate that the proposed analytical models are based on reasonable assumptions. The solutions obtained are in very good agreement with different sets of experimental results.A list of symbols can be found on page 320.

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Free vibrations of Timoshenko beams on two-parameter elastic foundation

Cited by 87 publications

References 6 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 a tapered beam with exponentially varying thickness resting on Winkler foundation using the differential transform method

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