Green’s function for uniform Euler–Bernoulli beams at resonant condition: Introduction of Fredholm Alternative Theorem

Hozhabrossadati, Seyed Mojtaba; Sani, Ali Mohamadi; Mehri, B.; Mofid, Massood

doi:10.1016/j.apm.2014.11.038

Cited by 18 publications

(5 citation statements)

References 8 publications

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“…They notice that for S near zero, it is the equivalent of 0 →  , in the absence of resonance L n S /    , the dynamic Green function reduced to the static Green function of a supported beam such explained in the paper (Hozhabrossadati SM et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

“…(1) With L being the length of the beam and the 8 coefficients from A to H being constant functions of u, these coefficients are calculated by evaluating the boundary and continuity conditions and shear force. The solution can be simplified, and solving the system with 8 equations, given this form, is developed in detail (Hozhabrossadati SM et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

“…Another work by Mehri et al (2009) studied the beam's dynamic response under moving loads with different boundary conditions, based on the Euler-Bernouli theory and using the simplified Green function in the work of (Hozhabrossadati SM et al, 2015). The effect of the type of support conditions, the velocity of the passage of the load on the beam, and other parameters were presented in this study; the boundary conditions are supports with longitudinal and transversal springs with stiffness values that encompass all supports conditions of extreme values starting from zero to infinity in theory.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Green Function Solution of Beams Under Moving Loads With Elastically Supports

Ouchenane*

Lassoued²

2023

Aceh Int. J. Sci. Technol

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The dynamic analysis of bridges simulated as Euler-Bernoulli beam models with elastic supports subjected to mobile loads are analyzed by conventional methods to obtain a new solution for displacement. Generally, these beam supports can be characterized by springs with a given stiffness, which considerably influence the structure's dynamic behavior and even attenuate the dynamic amplification. The solutions proposed until now are defined only on span but not supports. In this paper, we used Green's function, considering boundary and continuity conditions and shear force to study the global behavior of the beam. A new displacement formula is proposed for the beam to support a span according to the velocity of the mobile load, the beam rigidity, and the stiffness of supports. A further study leads to the present two new formulas, which directly give displacements at the level of supports according only to the beam rigidity and supports stiffness and to the load value at any time. The result of this analysis shows that several combined factors influence the vibratory behavior of the beam when it is supported on elastically supports, namely the stiffness of the supports, the rigidity of the beam, its length, the value of the mobile load, and its velocity. The evolution of support stiffness leads to classical boundary conditions. A study of coupling between the beam and supports is presented, with the study of the comportment in function to the ratio between the beam rigidity and spring stiffness.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic Green Function Solution of Beams Under Moving Loads With Elastically Supports

Ouchenane*

Lassoued²

2023

Aceh Int. J. Sci. Technol

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“…The Green's functions were obtained by using the techniques of separation of variables and the Laplace transformation. Hozhabrossadati et al [24] analyzed the Bernoulli beams under the resonant condition and they developed a Green's function procedure by constructing the proper Green's function and adopting the pertinent boundary conditions. Mohammad et al [25] studied the thermoelastic static behaviors of a curved circular beam through Green's function technique.…”

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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“…In the past decades, there are many other works related to frequency analysis of interactive system consisting of a beam with several attachments. The analytical approaches used to solving this problem included assumed-modes method (Cha, 2005(Cha, , 2007, the Green's function method (Hozhabrossadati et al, 2015;Kukla, 1994;Kukla & Posiadala, 1994) x x x  , the beam is split into 1 n  segments, and the two boundaries are denoted as spring 0 and n. The first i -1 segments are between the spring j-1 to j ( 1, , 1 ji    ); the ji   segment is between the spring 1 i  to the sensor; the ji   segment is between the sensor and the spring i; and the rest segments are between the spring j-1 to j ( 1, ., j i n The compatibility conditions at each spring location can be written as For the sensor location, the compatibility conditions can be written as…”

Section: Analysis Of Quasi-static Moving Mass Problemmentioning

confidence: 99%

Vibration based moving inspection method to detect loose fasteners and damaged supports in a rail system

Wang¹

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CHAPTER 2 LITERATURE REVIEW 13 2.1 CURRENT INSPECTION METHODS FOR SUPPORTING SYSTEMS 13 2.1.1 Inspection of damaged sleepers and blasters 13 2.1.2 Inspection of damaged joints and fasteners 14 2.1.3 Discussion on current inspection methods of degraded supports 20 2.2 DAMAGE DETECTION METHODS BASED ON DYNAMIC PROPERTIES 20 2.2.1 Frequency based methods 21 2.2.2 Mode shape based methods 22 2.2.3 Other vibration based methods 23 2.2.4 Vibration based damage detection method using moving device 25

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Green’s function for uniform Euler–Bernoulli beams at resonant condition: Introduction of Fredholm Alternative Theorem

Cited by 18 publications

References 8 publications

Dynamic Green Function Solution of Beams Under Moving Loads With Elastically Supports

Dynamic Green Function Solution of Beams Under Moving Loads With Elastically Supports

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

Vibration based moving inspection method to detect loose fasteners and damaged supports in a rail system

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