Unified Green's functions of forced vibration of axially loaded Timoshenko beam: Transition parameter

Chen, T.; Shen, Yu-Sheng; Gao, Bo; Li, Xiangyu; Müller, Ralf

doi:10.1016/j.ijmecsci.2016.05.003

Cited by 33 publications

(12 citation statements)

References 30 publications

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“…where the symbol α is the transition coefficient (Chen et al, 2016). Hence, the first-order variation of the total work done by the external forces reads…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…By introducing two characteristic parameters, Li et al (2014a) discussed the influence of damping on the vibration of Timoshenko beam. Chen et al (2016) derived the unified Green’s function for forced vibration of Timoshenko beams under axially load by introducing the transition parameter. Su et al (2018) obtained the exact analytic solutions of forced and free vibrations of nanowires on an elastic substrates.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…Then it is unnecessary to treat the ordinary differential equation separately on the intervals 0 ≤ x ≤ x 0 and x 0 ≤ x ≤ L . The justification of the Laplace transform corresponded to the spatial variable defined on a definite interval has been discussed by Chen et al (2016). Performing transform to the coordinate x in equation (41) gives rise to…”

Section: Formulation Of the Problemmentioning

confidence: 99%

See 2 more Smart Citations

Steady-state forced vibrations of magneto-electro-elastic Timoshenko nanobeams

Wang

et al. 2022

Journal of Intelligent Material Systems and Structures

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This paper aims to investigate forced vibrations of Timoshenko nanobeam, which is under axially loaded. The material is assumed to be magneto-electro-elastic coupling and surface effect is considered. The governing equations and the corresponding boundary conditions are derived, with the Hamilton principle. For steady-state forced vibrations, the variable separation and the Laplace transform methods are employed to obtain the Green’s function, for three typical kinds of beams, namely Hinged-Hinged, Clamped-Clamped, and Clamped-Free. Numerical examples are performed to check the validity of the present solutions and to evaluate the influence of magneto-electric coupling and surface effect on the forced vibration of the beams.

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“…where the symbol α is the transition coefficient (Chen et al, 2016). Hence, the first-order variation of the total work done by the external forces reads…”

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Formulation Of the Problemmentioning

confidence: 99%

See 1 more Smart Citation

Steady-state forced vibrations of magneto-electro-elastic Timoshenko nanobeams

Wang

et al. 2022

Journal of Intelligent Material Systems and Structures

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“…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. The Green's functions were obtained by using the techniques of separation of variables and the Laplace transformation.…”

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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“…Li et al (2014) discussed damping effects on the vibrations of Timoshenko beams by introducing two characteristic parameters. Chen et al (2016), considering two assumptions on the directions of the axial force in the process of deforming, obtained the unified Green's functions of forced vibration of axially loaded Timoshenko beam. Zhao et al (2016) provided the explicit expressions of the steady-state responses of a cracked Euler-Bernoulli beam excited by a harmonic force and investigated the influences of crack geometry on the mechanical behavior of beam.…”

Section: Introductionmentioning

confidence: 99%

Closed-form solutions for vibrations of a magneto-electro-elastic beam with variable cross section by means of Green’s functions

Zhang

Chen

Yang

et al. 2018

Journal of Intelligent Material Systems and Structures

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In this article, closed-form solutions are obtained for vibrations of a magneto-electro-elastic beam with variable cross section. Based on Timoshenko beam assumptions, governing equation for the non-uniform beam with exponentially varying width is obtained. Laplace transform approach applied to the governing equation results in the corresponding Green’s functions for the beams with various boundary conditions. The equations, which are solved to obtain Green’s functions, are degenerated for the analyses of the characters of free vibration. For free vibrations of the beams under different mechanical boundary conditions, the effects of the non-uniformly cross-sectional parameters and magneto-electric boundary conditions on the dynamic characters are studied. In addition, the magneto-electric potential modal variables’ distributions through the thickness are presented. In the discussions of forced vibration, two points in the beam are selected to investigate frequency responses in terms of displacement and magneto-electric potential. Moreover, the influences of excitation frequency and cross-sectional parameter on through-the-thickness distributions of electric potentials are investigated.

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Unified Green's functions of forced vibration of axially loaded Timoshenko beam: Transition parameter

Cited by 33 publications

References 30 publications

Steady-state forced vibrations of magneto-electro-elastic Timoshenko nanobeams

Steady-state forced vibrations of magneto-electro-elastic Timoshenko nanobeams

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

Closed-form solutions for vibrations of a magneto-electro-elastic beam with variable cross section by means of Green’s functions

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