On the effects of linear damping on the nonlinear Ziegler’s column

D’Annibale, Francesco; Ferretti, Manuel

doi:10.1007/s11071-020-05797-y

Cited by 12 publications

(4 citation statements)

References 58 publications

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“…et.al. [35] had explained the effect of nonlinearity in case of mean wind force for the shallow cables that is very in term of inherent nonlinearity present with in a system. In this research article they also described the process of removing the effect of nonlinearity which makes a system more stable.…”

Section: Dynamics Of Mechanical System-a Literature Reviewmentioning

confidence: 99%

Analytical Study of Series Solutions for the ‘Nonlinear Mechanical System’ with Stability Analysis

Chakraborty¹,

Bhattacharjee²,

Roy³

et al. 2022

YMER

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Any mechanical system can easily be analyzed with the help of proper designing or modeling. All kinematical constrains are also been considered at the time of modeling. Generally the traditional dynamical differential equations are solved to predict the nature of the system. In this work, some typical types of dynamical mechanical system in taken into consideration and further the dynamical equations are being solved using ‘Series Solutions Technique’ for the analysis of the nonlinear system. The solution is consisting of two sections. Using frequency response analysis via simulation, which section of the solution is more suitable or effective for the designing purpose has also been explained in detail. Finally, the local stability analysis of the entire system is studied in detail with proper numerical simulation. Keywords: Nonlinearity, Series Solution, Stability Analysis, Phase Portrait, Frequency Response Function.

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Section: Dynamics Of Mechanical System-a Literature Reviewmentioning

confidence: 99%

Analytical Study of Series Solutions for the ‘Nonlinear Mechanical System’ with Stability Analysis

Chakraborty¹,

Bhattacharjee²,

Roy³

et al. 2022

YMER

View full text Add to dashboard Cite

show abstract

“…In addition to the above analysis, Krillov applied the perturbation methods to derive the necessary and sufficient conditions for the asymptotic stability of the damped circulatory system [19]. Luongo developed the asymptotic multiple scales method (MSM) to study the complex damping influences on the pendulum's nonlinear post-flutter behaviors [20,21]. These studies have indicated that the damping paradox influences can be complicated by the pendulum mass and the follower type loading with imperfections.…”

Section: Introductionmentioning

confidence: 99%

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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“…Finally, the influence of nonlinear damping on the limit cycle amplitude for various linearly damped columns is studied. In study of Luongo et al, 38 the effect of linear damping on the postcritical behavior of a Ziegler column is discussed. For this purpose, the well-known double pendulum loaded at the free end with a repeating force, first introduced by Ziegler, is considered in the regime of finite displacements.…”

Section: Introductionmentioning

confidence: 99%

Dynamic modeling of a non-ideal gyroscopic rotor system with nonlinear damping and nonlinear rigidity of an elastic support

Iskakov¹,

Jamalov

Bissembayeb

et al. 2022

Advances in Mechanical Engineering

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The article considers the effect of joint linear and nonlinear cubic damping on dynamics of a gyroscopic rigid rotor interacting with an electric motor with a rectilinear characteristic, taking into account the nonlinear rigidity of the support material. The method of regulating the control parameter (voltage on the motor), the amplitude of vibration, and the angular velocity of the shaft in the frequency equation, depending on the value of the coefficient of nonlinear cubic damping of the support, offers the most effective options for controlling resonant oscillations of large amplitudes. It is shown that the greater the value of the coefficient of nonlinear cubic damping, the easier it is to control these oscillations. Moreover, it is proved that the Sommerfeld effect (of the first kind) can also be weakened and eliminate with the help of joint linear and nonlinear damping. To do this, in the case of a rigid characteristic of the nonlinear elasticity of the support material, in a rotor system with a nonideal energy source to eliminate the bistability region, that is, jumping effects, more nonlinear damping of support or energy from a nonideal energy source will be required than in the case of an ideal rotor system.

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On the effects of linear damping on the nonlinear Ziegler’s column

Cited by 12 publications

References 58 publications

Analytical Study of Series Solutions for the ‘Nonlinear Mechanical System’ with Stability Analysis

Analytical Study of Series Solutions for the ‘Nonlinear Mechanical System’ with Stability Analysis

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

Dynamic modeling of a non-ideal gyroscopic rotor system with nonlinear damping and nonlinear rigidity of an elastic support

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