Instability inspection of parametric vibrating rectangular Mindlin plates lying on Winkler foundations under periodic loading of moving masses

Torkan, Ehsan; Pirmoradian, Mostafa; Hashemian, Mohammad

doi:10.1007/s10409-018-0805-9

Cited by 13 publications

(1 citation statement)

References 29 publications

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“…The problem of parametric resonance arises in many branches of physics and engineering. For example, pendulum with a moving support system [15], [16], two-link flexible manipulator [17], [18], flexible structures such as beams and plates under periodic motion or loads [19]- [22], etc. In contrast to the external excitations in which a small excitation produces a large response only if the frequency of the excitation is close to a linear natural frequency, however, a small parametric excitation may produce a large response when the frequency of the excitation is away from the linear natural frequencies of the system [23].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamics Analysis of a Large Flexible Slender Truss-Structure Carrying a Manipulator for On-Orbit Assembly

et al. 2022

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Nonlinear dynamic of a flexible slender truss-structure mounted manipulator for on-orbit assembly, which can be simplified as a beam-rotating link interaction system, is theoretically investigated. The governing partial differential equations (PDEs) of beam with time-varying coefficients is established by using the D'Alembert principle incorporated with the moment balance method where the beam is of a Euler-Bernoulli type and the influence of slope is considered. Such system is a typical parametrically excited system. The multiple scales method is used to determine the approximate solution and the conditions of the primary resonance (ω 1 ≈ ω ref ) and sub-harmonic resonance (ω 1 ≈ 2ω ref , ω 1 ≈ 3ω ref and ω 1 ≈ 4ω ref ) are obtained. In addition, the nonlinear response, stability and bifurcations for primary and sub-harmonic resonance conditions have also been investigated by varying system parameters. Moreover, the results of some specific conditions by the perturbation analysis are compared with the numerical solution and are found to be in good agreement. This work has certain guiding significance for autonomous on-orbit assembly task and the method can be extended to the more general three-dimensional case.INDEX TERMS On-orbit assembly, flexible slender truss-structure mounted manipulator, parametric excitation, method of multiple scales, primary resonance, sub-harmonic resonance.

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