Green׳s functions for the forced vibrations of cracked Euler–Bernoulli beams

Zhao, Xingzhuang; Zhao, Yunshi; Gao, Xiaoyang; Li, X.Y.; Li, Y.H.

doi:10.1016/j.ymssp.2015.06.023

Cited by 58 publications

(10 citation statements)

References 38 publications

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“…ese effects must be considered in the serviceability analysis of existing cracked RC members [1,2]. Concrete cracking reduces the stiffness of a structure, which influences not only its static behavior but also its dynamic response [3,4]. Xu and Castel studied the effects of steel-concrete bond damage on the dynamic stiffness of cracked RC beams under low-amplitude vibration.…”

Section: Introductionmentioning

confidence: 99%

Full‐Scale Experimental Investigation of the Static and Dynamic Stiffness of Prestressed Concrete Girders

Zhou

Zhao

Yao

et al. 2019

Shock and Vibration

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Cracking damage influences the stiffness of the girders. Many articles in the literatures have studied the development of stiffness of the scale-down model; however, full-scale model testing cannot be completely replaced by scale-down testing because of material component characteristics and boundary effects. This paper deals with the effects of cracking damage on the structural static and dynamic stiffness based on three prestressed concrete (PC) girders which were removed from an old bridge. First, the equivalent flexural rigidity of cracked prestressed concrete girder was assessed using the measured load-deflection response under cycles of loading and unloading. Then, after unloading, the frequencies were measured on the PC girders supported by the elastomeric bearings. Next, the development of frequency under different damage was studied, and finally, the dynamic stiffness of PC girders with cracks was assessed. The results indicate that the first frequency is more sensitive to the cracking of concrete compared with the second frequency and that the mode shapes are not sensitive to girder damage. The test girders cannot be simplified as an ideal simply supported beam for the purpose of identifying frequencies. In addition, the “final” (the end of the ultimate load case) equivalent flexural rigidity of the girders is 30% of the “initial” (the beginning of the first load case) equivalent flexural rigidity, compared with 50% in the scale-down test; and the final dynamic stiffness is approximately 84% of the initial dynamic stiffness, whereas the scale-down test is 72%.

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Section: Introductionmentioning

confidence: 99%

Full‐Scale Experimental Investigation of the Static and Dynamic Stiffness of Prestressed Concrete Girders

Zhou

Zhao

Yao

et al. 2019

Shock and Vibration

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“…For example,Żur [15][16][17][18][19] presented a series of work over the free vibration analysis of thin circular plates and elastically supported functionally graded annular plates using the Green's functions. Zhao et al [20][21][22] analytically studied the vibration of a cracked Euler-Bernoulli beam induced by a heat flux or a harmonic force and that of Timoshenko beams due to a heat flux together with an external load. Chen et al [23] studied the dynamic behavior of an axially forced Timoshenko beam under different boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamic Response of Beams on Winkler Foundation Irradiated by Moving Laser Pulses

et al. 2018

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Abstract:In this paper, the exact analytical solutions are developed for the thermodynamic behavior of an Euler-Bernoulli beam resting on an elastic foundation and exposed to a time decaying laser pulse that scans over the beam with a uniform velocity. The governing equations, namely the heat conduction equation and the vibration equation are solved using the Green's function approach. The temporal and special distributions of temperature, deflection, strain, and the energy absorbed by the elastic foundation are calculated. The effects of the laser motion speed, the modulus of elastic foundation reaction, and the laser pulse duration time are studied in detail.

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“…Considering the low tensile strength of concrete, cracking may appear in reinforced concrete structures due to in-service loading, early age restrained shrinkage, and so on. Cracking-induced damages lead to a reduction in the stiffness of reinforced concrete members, which influences both static behavior and dynamic response of the structures (Deng et al, 2014; Zhao et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Influence of steel–concrete bond damage on the dynamic stiffness of cracked reinforced concrete beams

Huang

Castel

et al. 2018

Advances in Structural Engineering

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In this article, experiments focusing at the influence of steel-concrete bond damage on the dynamic stiffness of cracked reinforced concrete beams are reported. In these experiments, the bond between concrete and reinforcing bar was damaged using appreciate flexural loads. The static stiffness of cracked reinforced concrete beam was assessed using the measured load-deflection response under cycles of loading and unloading, and the dynamic stiffness was analyzed using the measured natural frequencies with and without sustained loading. Average moment of inertia model (Castel et al. model) for cracked reinforced beams by taking into account the respective effect of bending cracks (primary cracks) and the steel-concrete bond damage (interfacial microcracks) was adopted to calculate the static load-deflection response and the natural frequencies of the tested beams. The experimental results and the comparison between measured and calculated natural frequencies show that localized steel-concrete bond damage does not influence remarkably the dynamic stiffness and the natural frequencies both with and without sustained loading applied. Castel et al. model can be used to calculate the dynamic stiffness of cracked reinforced concrete beam by neglecting the effect of interfacial microcracks.

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Green׳s functions for the forced vibrations of cracked Euler–Bernoulli beams

Cited by 58 publications

References 38 publications

Full‐Scale Experimental Investigation of the Static and Dynamic Stiffness of Prestressed Concrete Girders

Full‐Scale Experimental Investigation of the Static and Dynamic Stiffness of Prestressed Concrete Girders

Thermodynamic Response of Beams on Winkler Foundation Irradiated by Moving Laser Pulses

Influence of steel–concrete bond damage on the dynamic stiffness of cracked reinforced concrete beams

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