Transverse vibration of a multiple-Timoshenko beam system with intermediate elastic connections due to a moving load

Ariaei, A.; Ziaei-Rad, Saeed; Ghayour, Mostafa

doi:10.1007/s00419-010-0410-2

Cited by 38 publications

(10 citation statements)

References 25 publications

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“…e advantages of the method developed in this study in terms of higher number of layers in this paper for specific performance are as follows: the system studied in this paper consists of n identical beams, in general, when much more layers are considered, the coupled partial equations are difficult to solve. Compared with the literature [12], this paper does not need to build a special relation of the stiffness of intermediate springs for decoupling the equation of motion; with the finite sine-Fourier transform, the equations can be uncoupled and solved. Compared with the literature [6], when studying the vibration of double-beam system, this paper does not need to divide into the vibration of two singlebeam systems subjected to the same force, interlayer stiffness, damping, material properties of each layer, and moving oscillator [19].…”

Section: Methods Validationmentioning

confidence: 99%

“…Using Timoshenko and high-order shear deformation theory, Stojanović et al [11] investigated a general procedure for the determination of the natural frequencies and buckling load for a set of beam system under compressive axial loading. Ariaei et al [12] investigated the dynamic behavior of n parallel identical elastically connected Timoshenko beams subjected to a moving load. A relatively new computed approach called the Adomian modified decomposition method has been used to analyze the free vibration problem for an elastically connected multiple beam with arbitrary boundary conditions [13].…”

Section: Introductionmentioning

confidence: 99%

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Vibration Theoretical Analysis of Elastically Connected Multiple Beam System under the Moving Oscillator

Feng

2019

Advances in Civil Engineering

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To investigate the vibration analysis of elastically connected multiple beam system (ECMB) under the moving oscillator, finite sine-Fourier transform has been applied to the dynamic partial differential equations of ECMB with respect to space coordinates. en, the numerical integration has been used to solve the equations. Finally, the expression for vibration analysis of ECMB under the moving oscillator has been derived based on finite sine-Fourier inverse transform. Using the method developed in this study and ANSYS numerical method, the vibration analysis of a four-layer beam system under moving oscillator with different speeds has been calculated. e results show that the calculated results from the method developed in this study are in good agreement with the ANSYS numerical calculation results, and the differences between the two calculation results are all less than 2%, which verified the correctness of the method developed in this study. e method developed in this study has been applied to the beamrail system on a railway line in China. e effect of the train speed and interlayer stiffness on the vibration of beam-rail system has been investigated. e results show that the maximum dynamic deflection of the rail under the train load is always near the midspan, while the maximum dynamic deflections of the track plate, base plate, and bridge occur after the train travel through the midspan. e interlayer stiffness has a larger impact on the vibration of the rail and the track plate and little impact on the vibration of the base plate and the bridge.

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Section: Methods Validationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vibration Theoretical Analysis of Elastically Connected Multiple Beam System under the Moving Oscillator

Feng

2019

Advances in Civil Engineering

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“…Assuming time harmonic motion and using separation of variables, the solutions to Eqs. 5 and 6 with the governing boundary conditions (8) can be written in the form…”

Section: Structural Model and Formulation Of The Problemmentioning

confidence: 99%

“…A specific example is given to show the effects of rotary inertia, shear deformation, and foundation constants on the natural frequencies of the beam. Ariaei et al [8] studied the dynamic response of an elastically connected multiple-beam. Identical prismatic Timoshenko beams are assumed to be parallel and connected by a finite number of springs.…”

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confidence: 99%

Effect of rotary inertia and shear on vibration and buckling of a double beam system under compressive axial loading

et al. 2011

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Free transverse vibration and buckling of a double-beam continuously joined by a Winkler elastic layer under compressive axial loading with the influence of rotary inertia and shear are considered in this paper. The motion of the system is described by a homogeneous set of two partial differential equations, which is solved by using the classical Bernoulli-Fourier method. The boundary value and initial value problems are solved. The natural frequencies and associated amplitude ratios of an elastically connected double-beam complex system and the analytical solution of the critical buckling load are determined. The presented theoretical analysis is illustrated by a numerical example, in which the effect of physical parameters characterizing the vibrating system on the natural frequency, the associated amplitude ratios and the critical buckling load are discussed.

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“…Modeling beams according to the Timoshenko assumptions is widely seen in the literature [9][10][11][12]. In Timoshenko beams, the cross sections are assumed to be undistorted after deformation, but they need not to remain perpendicular to the axial direction due to the consideration of the shear deformation.…”

mentioning

confidence: 99%

Investigation of the size effects in Timoshenko beams based on the couple stress theory

et al. 2010

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In this paper, a size-dependent Timoshenko beam is developed on the basis of the couple stress theory. The couple stress theory is a non-classic continuum theory capable of capturing the small-scale size effects on the mechanical behavior of structures, while the classical continuum theory is unable to predict the mechanical behavior accurately when the characteristic size of structures is close to the material length scale parameter. The governing differential equations of motion are derived for the couple-stress Timoshenko beam using the principles of linear and angular momentum. Then, the general form of boundary conditions and generally valid closed-form analytical solutions are obtained for the axial deformation, bending deflection, and the rotation angle of cross sections in the static cases. As an example, the closed-form analytical results are obtained for the response of a cantilever beam subjected to a static loading with a concentrated force at its free end. The results indicate that modeling on the basis of the couple stress theory causes more stiffness than modeling by the classical beam theory. In addition, the results indicate that the differences between the results of the proposed model and those based on the classical Euler-Bernoulli and classical Timoshenko beam theories are significant when the beam thickness is comparable to its material length scale parameter.Keywords Size-dependent behavior · Timoshenko beam · Couple stress theory · Material length scale parameter

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Transverse vibration of a multiple-Timoshenko beam system with intermediate elastic connections due to a moving load

Cited by 38 publications

References 25 publications

Vibration Theoretical Analysis of Elastically Connected Multiple Beam System under the Moving Oscillator

Vibration Theoretical Analysis of Elastically Connected Multiple Beam System under the Moving Oscillator

Effect of rotary inertia and shear on vibration and buckling of a double beam system under compressive axial loading

Investigation of the size effects in Timoshenko beams based on the couple stress theory

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