On the stability of the equilibrium of the double pendulum with follower force: Some new results

Puzyrov, Volodymyr; Awrejcewicz, Jan; Losyeva, Nataliya; Savchenko, Nina

doi:10.1016/j.jsv.2021.116699

Cited by 9 publications

(6 citation statements)

References 31 publications

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“…Since the critical parameters: r z , i z ,  and p , are theoretically evaluated, and agree well with its counterparts obtained by other methods, such as Routh-Hurwitz criteria and complex eigenvalues analysis method [1,12], thus the presented energy method and the parameters evaluation procedure can be validated to conduct the following flutter physical mechanism analysis.…”

Section: Non-conservative Energy Balance Principle and Critical Param...supporting

confidence: 62%

“…There exist two types of instability behaviors for lightweight structures in mechanics fields [1,2].…”

Section: Introductionmentioning

confidence: 99%

“…These complicated instability behaviors can occur in many engineering structures (brake squealing [4], panel flutter [5,6], wing/control surface flutter [7,8], conveying pipeline flutter and others [9,10,11]), and have been attracted much attentions till now. However, the above structures posing buckling or flutter instabilities can be treated as various variants of the simple Ziegler double pendulum model [1,2]. This model refers to a linked double pendulum with specific discrete mass, stiffness and damping, and under the follower type circular loading on its end, thus constitutes a nonlinear damped circular non-conservative system.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, the so-called MDGKN system (M, D, G, K, and N indicate the system inertia, dissipation, gyroscopic, potential and circulatory terms) was presented and investigated. Correspondingly, Volodymyr investigated the double pendulum flutter instability characteristics with arbitrary mass, stiffness and imperfect follower type loading by using Routh-Hurwitz criteria, and found the stiffness ratio induced destabilizing influences, but neglecting arbitrary mass induced destabilizing influences [1,22]. As from the experimental observation perspectives, although Koiter has noted that the "unrealistic follower forces" can not be directly achieved and exerted on the pendulum end, Bigoni et al have developed a significant breakthrough of the experimental devices, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…The upper rod is subjected to the follower tangential force p on its free end, and is connected with the lower rod through a visco-elastic joint with stiffness 1 k and damping 1 c . And the lower rod is ground supported by another visco-elastic joint with stiffness 2 k and damping 2 c .Different with the classical Ziegler's model ( , here the mass, stiffness and damping coefficients are assumed to be with arbitrary values[1,12].…”

mentioning

confidence: 99%

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Flutter instability characteristics and mechanisms of Ziegler double pendulum with arbitrary mass, stiffness and damping

Wang,

Fan,

Yang

et al. 2024

Preprint

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In this paper, the flutter instability characteristics and mechanisms of the weakly damped Ziegler double pendulum subjected to the follower type circular loading are investigated. The double pendulum is assumed to be with arbitrary masse, stiffness and damping. Different with the existed mathematical analysis methods, the pendulum flutter instability conditions and the corresponding critical parameters are theoretically deduced and evaluated based on an energy method with clear physical meanings. By introducing the ratio parameters of the structural mass, stiffness and damping coefficients, the complex influences of the structural mass, stiffness and damping are discussed in details. In addition to the counter-intuitive “damping Ziegler Paradox” influence, the stabilizing and destabilizing influences of the pendulum’s mass and stiffness are observed and investigated. To clarify these complex influences, the power flow characteristics on the pendulum flutter instability occurrence are investigated. The results indicate that the mass or stiffness related powers on each coordinate constitute the two “power exchange twins”, and can affect the related destabilizing or stabilizing influences of the pendulum mass and stiffness, while the “damping Ziegler Paradox” influence can be affected by the energy transmission efficiency between the stiffness related powers on each coordinate. Correspondingly the flutter instability physical mechanisms are clarified for the first time from the energy perspectives.

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Section: Non-conservative Energy Balance Principle and Critical Param...supporting

confidence: 62%

“…There exist two types of instability behaviors for lightweight structures in mechanics fields [1,2].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Flutter instability characteristics and mechanisms of Ziegler double pendulum with arbitrary mass, stiffness and damping

Wang,

Fan,

Yang

et al. 2024

Preprint

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Mechanics of delaminated composite beams subjected to retarded follower force with multiple time delay

Szekrényes

2024

Acta Mech

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In this work the problem of a delaminated composite cantilever beam subjected to a retarded periodically changing follower axial force is taken into consideration. The equation of motion is deduced based on a previous work including finite element discretization in space. On the other hand the delayed system is captured by the Chebyshev polynomials of the first kind in the time domain. The most important aspect of the model is that multiple time delay is considered, i.e., the principal period of the parametric excitation is not equal to the delay. Under these conditions the stability of the system is investigated using the Floquet theory and the unit circle criterion. The stability diagrams are determined for large number of cases focusing essentially on the effect of delamination on the stable domains. The main conclusion is that although the delamination length and thicknesswise position does not have an essential effect on the stability domains, the definite offset of the limit curves may be observed. In contrast, the relation of time delay and principal period influences substantially the shape and nature of limit curves on certain parameter planes.

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A double pendulum fixed at the L1 libration point: a precursor to a Mars–Phobos space elevator

Aslanov

2023

Nonlinear Dyn

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On the stability of the equilibrium of the double pendulum with follower force: Some new results

Cited by 9 publications

References 31 publications

Flutter instability characteristics and mechanisms of Ziegler double pendulum with arbitrary mass, stiffness and damping

Flutter instability characteristics and mechanisms of Ziegler double pendulum with arbitrary mass, stiffness and damping

Mechanics of delaminated composite beams subjected to retarded follower force with multiple time delay

A double pendulum fixed at the L1 libration point: a precursor to a Mars–Phobos space elevator

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