Dynamic stability of an axially transporting beam with two-frequency parametric excitation and internal resonance

Zhang, Dengbo; Tang, You-Qi; Liang, Ruquan; Liu, Yang; Chen, Liqun

doi:10.1016/j.euromechsol.2020.104084

Cited by 26 publications

(10 citation statements)

References 40 publications

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“…Ghadiri and Hosseini [1] studied the nonlinear dynamic behavior of a nanobeam modeled by Bernoulli-Euler beam theory; in this work, the authors sought the influence of parametric excitation, axially imposed and generated by thermo-magnetic load, on the stability of a beam. Zhang et al [2] analyzed the stability of a parametrically excited viscoelastic beam. In this study the time -varying axial tension is the source of parametric excitation and its effect on the principal parametric frequencies, close to twice the value of each natural frequency, is investigated.…”

Section: Introductionmentioning

confidence: 99%

Numerical and Experimental Stability Investigation of a Parametrically Excited Cantilever Beam at Combination Parametric Resonance

2022

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Background The presence of parametric excitation in dynamic structures, caused by friction, crack, varying compliance, electromagnetic field, etc. may generate unbounded responses. In the literature there exist several numerical analyses of systems affected by parametric excitation, while experimental studies are less frequent. Objective The goal of the paper is to create a demonstrator of a parametrically excited system, whose stability can be modified through a controlled physical parameter. This work also investigates the applicability of the recently developed stability analysis method named Jacobian Based Approach (JBA). Methods This paper studies a simple experimental set-up comprising of a cantilever beam mounted on a spring with time – varying stiffness, achieved through the use of an electromagnet. The test rig allows measuring directly the magnetic force without any preknowledge of the values of electrical parameters. Results obtained from the test rig are compared with numerical results obtained from the Finite Element model. In this study, Hill’s method and JBA are employed to obtain the stability plot highlighting the regions of parametric instabilities. Results Good agreement is found between experimental and numerical data and the presence of unstable behavior is verified through the use of the well – known Hill’s method and the JBA. Furthermore, this study demonstrates that the stability plot, highlighting the unstable regions, computed by JBA is in complete agreement with the one obtained by Hill’s method. Conclusions It is shown how the parametric instability can be triggered through the regulation of a simple physical parameter, i.e. the gap between the electromagnet and the beam. The numerical model analyzed by the ad – hoc technique proposed by the authors i.e. JBA has been proven to have predictive capabilities in studying a system under parametric excitation and could be a potential substitution for state-of-the-art stability analysis techniques such Hill’s method.

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Section: Introductionmentioning

confidence: 99%

Numerical and Experimental Stability Investigation of a Parametrically Excited Cantilever Beam at Combination Parametric Resonance

2022

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“…A relatively more appropriate approach is to assume the velocity as well as tension to be variable. Few works [36][37][38][39][40][41][42] are available to fill up this lack of research gap for a nonlinear traveling system. Chen and tang [36][37][38] investigated the vibrational analysis of axially accelerating viscoelastic beam with nonhomogeneous boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…Further, Tang and coworkers carried out similar studies on moving beams by introducing 3:1 internal resonance [37] and considering the velocity and longitudinal tension as a function of time and interdependence [38]. Zhang et al [39] analyzed the effect of two frequency excitations on the stability boundary of the traveling beam.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of traveling beam with longitudinally varying axial tension and variable velocity under parametric and internal resonances

et al. 2022

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In this investigation, the nonlinear dynamics of an axially accelerating viscoelastic beam on a pully mounting system have been analyzed. The axial tension of the beam is modeled as a function of the traveling velocity, support stiffness parameter as well as spatial coordinate. Geometric cubic nonlinearity appeared in the equation of motion due to elongation set in the neutral axis of the beam. The integropartial differential equation of motion of the axially accelerating beam associated with the simplysupported end conditions is solved analytically by adopting the direct perturbation method of multiple time scales (MMS). As a result, a set of complex variable modulation equations are generated, which governs the modulation of amplitude and phase. This set of modulated equations is numerically solved to explore the influence of the support stiffness parameter upon the stability and bifurcation of the beam which has not been addressed in the existing literature. Apart from this, the impact of fluctuating velocity component, viscoelastic coefficient, longitudinal stiffness parameter, internal and parametric detuning parameters on the stability and bifurcation analysis is studied, revealing significant dynamic characteristics of the traveling system. The Fourth-order Runge-Kutta method is applied is to find the dynamic solution of the system. The system displays stable periodic, quasi-periodic, and mixed-mode dynamic responses along with the unstable chaotic behavior for a specific set of system parameters. The results obtained through an analytical-numerical approach may help the design and operation of an axially moving beam.

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“…Nonlinear dynamics of an axially accelerating viscoelastic sandwich beam with a two-frequency parametric excitation and a 3:1 internal resonance were investigated by Zhu et al [36] . Zhang et al [37] studied the dynamic stability of an axially transporting beam with the internal resonance and two-frequency parametric excitation. So far, the nonlinear dynamic behavior of axial variable tension beam models with the internal resonance and two-frequency parametric excitation has not been understood.…”

Section: Introductionmentioning

confidence: 99%

Internal resonance of an axially transporting beam with a two-frequency parametric excitation

Zhang

Tang

Liang

et al. 2022

Appl. Math. Mech.-Engl. Ed.

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This paper investigates the transverse 3:1 internal resonance of an axially transporting nonlinear viscoelastic Euler-Bernoulli beam with a two-frequency parametric excitation caused by a speed perturbation. The Kelvin-Voigt model is introduced to describe the viscoelastic characteristics of the axially transporting beam. The governing equation and the associated boundary conditions are obtained by Newton’s second law. The method of multiple scales is utilized to obtain the steady-state responses. The Routh-Hurwitz criterion is used to determine the stabilities and bifurcations of the steady-state responses. The effects of the material viscoelastic coefficient on the dynamics of the transporting beam are studied in detail by a series of numerical demonstrations. Interesting phenomena of the steady-state responses are revealed in the 3:1 internal resonance and two-frequency parametric excitation. The approximate analytical method is validated via a differential quadrature method.

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Dynamic stability of an axially transporting beam with two-frequency parametric excitation and internal resonance

Cited by 26 publications

References 40 publications

Numerical and Experimental Stability Investigation of a Parametrically Excited Cantilever Beam at Combination Parametric Resonance

Numerical and Experimental Stability Investigation of a Parametrically Excited Cantilever Beam at Combination Parametric Resonance

Nonlinear dynamics of traveling beam with longitudinally varying axial tension and variable velocity under parametric and internal resonances

Internal resonance of an axially transporting beam with a two-frequency parametric excitation

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