Free vibration analysis of elastically connected multiple-beams by using the Adomian modified decomposition method

Mao, Qibo

doi:10.1016/j.jsv.2012.01.028

Cited by 56 publications

(31 citation statements)

References 11 publications

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“…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]. rough a differential transform method, a new procedure for determining natural frequencies and mode shapes of a system of elastically connected multiple rotating tapered beams has been presented [14].…”

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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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: 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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“…Rao [33] investigated the natural vibrations of elastically connected multi-Timoshenko beams. Mao [34] used the Adomian modified decomposition method (AMDM) to investigate the free vibrations of N elastically connected parallel Euler-Bernoulli beams continuously joined by a Winkler-type elastic layer, and a general solution for the free vibration problem of elastically connected beams under general boundary conditions was obtained. Stojanović developed a general procedure for the determination of natural frequencies and buckling load for a set of beam system under compressive axial load using Timoshenko and high-order shear deformation theory [35].…”

Section: Introductionmentioning

confidence: 99%

An Analytical Study on Dynamic Response of Multiple Simply Supported Beam System Subjected to Moving Loads

Lai

Jiang

Zhou

2018

Shock and Vibration

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Based on Euler–Bernoulli beam theory, first, partial differential equations were established for the vibration of multiple simply supported beams subjected to moving loads. Then, integral transforms were conducted on the spatial displacement coordinate and time in the partial differential equations, and the frequency-domain response of multiple simply supported beams subjected to moving loads was obtained. Next, by conducting the corresponding inverse transforms on the displacement frequency-domain responses of multiple simply supported beams, the spatial displacement time-domain responses were obtained. Finally, to validate the analytical method reported in this paper, the dynamic response of a typical double simply supported rail-bridge beam system of high-speed railway in China subjected to a moving load was carried out. The results show that the analytical solution proposed in this paper is consistent with the results obtained from a finite element analysis, validating and rationalizing the analytical solution. Moreover, the system parameters were analyzed for the dynamic response of double simply supported rail-bridge beam system in high-speed railway subjected to a moving load with different speeds; the conclusions can be beneficial for engineering practice.

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“…Firstly, mode shapes for a beam with an arbitrary number of cracks under general boundary conditions are determined by the Adomian decomposition method (ADM). [18][19][20][21][22] Using the Figure 1. The coordinate system for a multiple-cracked beam, elastically restrained at both ends.…”

Section: Introductionmentioning

confidence: 99%

Vibration Analysis of Cracked Beams Using Adomian Decomposition Method and Non-Baseline Damage Detection via High-Pass Filters

Mao¹

2016

IJAV

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The Adomian decomposition method (ADM) and high-pass filters are employed in this study to investigate the free vibrations and damage detection of cracked Euler-Bernoulli beams. Based on the ADM and employing some simple mathematical operations, the closed-form series solution of the mode shapes can be determined for beams consisting of an arbitrary number of cracks under general boundary conditions in a recursive way. Then, a highpass filter is used to extract the irregularity profile from the corresponding mode shape. The location and size of the cracks in the beam can be determined by the peak value of the irregularity profile. The numerical results for different locations and depths of cracks on the damaged beam under different boundary conditions are presented. The results show that the proposed method is effective and accurate. The experimental work for aluminium cantilever beams with one and two cracks was performed to verify the proposed method. The successful detection of cracks in the beam demonstrates that the proposed method has great potential in crack detection of beam-type structures, as it is simple and does not require the mode shapes of an uncracked beam as a baseline.

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Free vibration analysis of elastically connected multiple-beams by using the Adomian modified decomposition method

Cited by 56 publications

References 11 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

An Analytical Study on Dynamic Response of Multiple Simply Supported Beam System Subjected to Moving Loads

Vibration Analysis of Cracked Beams Using Adomian Decomposition Method and Non-Baseline Damage Detection via High-Pass Filters

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