Parametric and internal resonance of axially accelerating viscoelastic beams with the recognition of longitudinally varying tensions

Tang, You-Qi; Zhang, Dengbo; Gao, Jia-Ming

doi:10.1007/s11071-015-2336-2

Cited by 66 publications

(15 citation statements)

References 33 publications

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“…Mao et al (2016a,b) firstly studied the forced vibration response of a pipe conveying fluid and super-harmonic resonances of a super-critical axially moving beam, with 3:1 internal resonance. Parametric and 3:1 internal resonance of axially moving viscoelastic beams on elastic foundation was analytically and numerically investigated by Tang et al (2016).…”

Section: Introductionmentioning

confidence: 99%

Magneto-elastic internal resonance of an axially moving conductive beam in the magnetic field

Wang

et al. 2019

Journal of Theoretical and Applied Mechanics

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The Hamiltonian principle is applied to the nonlinear vibration equation of an axially moving conductive beam in the magnetic field with consideration of the axial velocity, axial tension, electromagnetic coupling effect and complex boundary conditions. Nonlinear vibration characteristics of the free vibrating beam under 1:3 internal resonances are studied based on our approach. For beams with one end fixed and the other simply supported, the nonlinear vibration equation is dispersed by the Galerkin method, and the vibration equations are solved by the multiple-scales method. As a result, the coupled relations between the first-order and second-order vibration modes are obtained in the internal resonance system. Firstly, the influence of initial conditions, axial velocity and the external magnetic field strength on the vibration modes is analysed in detail. Secondly, direct numerical calculation on the vibration equations is carried out in order to evaluate the accuracy of the perturbation approach. It is found that through numerical calculations, in the undamped system, the vibration modes are more sensitive to the initial value of vibration amplitude. The amplitude changes of the first-order and second-order modes resulting from the increase of the initial amplitude value of the vibration modes respectively are very special, and present a "reversal behaviour". Lastly, in the damped system, the vibration modes exhibit a trend of coupling attenuation with time. Its decay rate increases when the applied magnetic field strength becomes stronger.

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Section: Introductionmentioning

confidence: 99%

Magneto-elastic internal resonance of an axially moving conductive beam in the magnetic field

Wang

et al. 2019

Journal of Theoretical and Applied Mechanics

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“…Ozhan and Pakdemirli [6][7] and Yang and Zhang [8] adopted the Kelvin model containing the partial time derivative for describing the viscoelastic behavior of beam materials. To study the nonlinear vibration of the traveling viscoelastic beams, Ding and Zu [9] , Yan et al [10] , and Tang et al [11] proved that the material time derivative should be contained in the Kelvin model. The standard linear solid model has been employed in modelling axially traveling viscoelastic beams.…”

Section: Introductionmentioning

confidence: 99%

“…By use of the direct multi-scale method, Sahoo et al [20] focused on the nonlinear transverse vibration of an axially moving beam subjected to two frequency excitations in the presence of internal resonance. By use of the direct multi-scale method to establish the solvability conditions, Tang et al [11] investigated the parametric and 3:1 internal resonance of the axially moving viscoelastic beams on the elastic foundation. Without internal resonance, the multi-scale method has been directly used to solve the nonlinear dynamics of the traveling beams.…”

Section: Introductionmentioning

confidence: 99%

Primary resonance of traveling viscoelastic beam under internal resonance

Ding

Huang

Mao

2016

Appl. Math. Mech.-Engl. Ed.

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Under the 3:1 internal resonance condition, the steady-state periodic response of the forced vibration of a traveling viscoelastic beam is studied. The viscoelastic behaviors of the traveling beam are described by the standard linear solid model, and the material time derivative is adopted in the viscoelastic constitutive relation. The direct multi-scale method is used to derive the relationships between the excitation frequency and the response amplitudes. For the first time, the real modal functions are employed to analytically investigate the periodic response of the axially traveling beam. The undetermined coefficient method is used to approximately establish the real modal functions. The approximate analytical results are confirmed by the Galerkin truncation. Numerical examples are presented to highlight the effects of the viscoelastic behaviors on the steady-state periodic responses. To illustrate the effect of the internal resonance, the energy transfer between the internal resonance modes and the saturation-like phenomena in the steady-state responses is presented.

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“…Ghayesh and Amabili 5,6 examined the nonlinear vibration of an axially moving beam with an intermediate spring support and a time-dependent axial speed. Tang et al 7 investigated the steady-state and oscillating responses and the stability and bifurcation of a beam using the method of multiple scales. Liu et al 8 developed an optimal delayed feedback control method to mitigate the primary and superharmonic resonances of a flexible simply supported beam using piezoelectric sensors and actuators.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration and stability of a moving printing web with variable density based on the method of multiple scales

Shao

Wang

et al. 2019

Journal of Low Frequency Noise, Vibration and Active Control

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An axially moving printing web with variable density in a printing process causes a geometric nonlinear vibration, and a nonlinear vibration system is established using the von Karman nonlinear plate theory and the D'Alembert principle. The time and displacement variables are separated using the Galerkin method. The ordinary differential equation of a web is solved using the method of multiple scales. The amplitude-frequency response equation of a moving web is obtained. The time histories, phase-plane portraits, and amplitude-frequency curves of the system are obtained by numerical calculations. The influence of different dimensionless speeds and variable density coefficients on the nonlinear vibration characteristics of the printing web is analyzed. The results show that the overprinting accuracy can be ensured by making a reasonable choice of web speed in the stable region.

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Parametric and internal resonance of axially accelerating viscoelastic beams with the recognition of longitudinally varying tensions

Cited by 66 publications

References 33 publications

Magneto-elastic internal resonance of an axially moving conductive beam in the magnetic field

Magneto-elastic internal resonance of an axially moving conductive beam in the magnetic field

Primary resonance of traveling viscoelastic beam under internal resonance

Nonlinear vibration and stability of a moving printing web with variable density based on the method of multiple scales

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