Combination, principal parametric and internal resonances of an accelerating beam under two frequency parametric excitation

Sahoo, Bamadev; Panda, L. N.; Pohit, G.

doi:10.1016/j.ijnonlinmec.2015.09.017

Cited by 44 publications

(8 citation statements)

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“…Based on the generalized integral transform technique (GITT), Yan et al (2015) investigated nonlinear dynamic behavior in the transverse vibration of an axially accelerating viscoelastic Timoshenko beam with an external harmonic excitation. Sahoo et al (2015Sahoo et al ( , 2016 analyzed the nonlinear transverse vibration of an axially moving beam subject to two-frequency excitation. Analytical and numerical approach was applied to find the steady-state and dynamic behavior of an axially accelerating viscoelastic beam subject to two-frequency parametric excitation in the presence of internal resonance.…”

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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“…Substituting Eqs. (19), (20), and (21) into Eq. (11) and equalizing the coefficients of ε 0 and ε 2 in the obtained equations yield…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The nonlinear dynamics of the traveling beams have also been studied by the direct perturbation method. 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.…”

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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“…Finally, it is worth mentioning that any application using dual-frequency driving can benefit (at least indirectly) from the results presented in this study due to the very detailed investigation. Some possible applications are acoustic cavitation [80][81][82][83], Faraday waves [84], stability of traveling beams [85,86] or laser-driven dissociation of molecules [87].…”

Section: Discussionmentioning

confidence: 99%

Non-feedback technique to directly control multistability in nonlinear oscillators by dual-frequency driving

et al. 2018

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A novel method to control multistability of nonlinear oscillators by applying dual-frequency driving is presented. The test model is the Keller-Miksis equation describing the oscillation of a bubble in a liquid. It is solved by an in-house initial-value problem solver capable to exploit the high computational resources of professional graphics cards. Dur-Electronic supplementary material The online version of this article (

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Combination, principal parametric and internal resonances of an accelerating beam under two frequency parametric excitation

Cited by 44 publications

References 50 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

Non-feedback technique to directly control multistability in nonlinear oscillators by dual-frequency driving

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