On discontinuous dynamics of a class of friction-influenced oscillators with nonlinear damping under bilateral rigid constraints

Dou, Chenjing; Fan, Jinjun; Li, Chunliang; Cao, Jing; Gao, Min

doi:10.1016/j.mechmachtheory.2019.103750

Cited by 22 publications

(5 citation statements)

References 55 publications

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“…Eq. (13) gives an equation of the form A = f (λ, δ), which can represent the saddle-node bifurcation boundary curve on the [λ, A] plane, the parameters are selected as ε = 0.1, k 1 = 1/3, k 3 = 4/3 [14,19,29], as shown in Fig. 2.…”

Section: Bifurcation Analysismentioning

confidence: 99%

“…Literature [26] considers the influence of frequency detuning on the vibration suppression of the coupled NES system, it is indicated that the value of the frequency detuning coefficient is related to the existence of SMR, however, no specific expression is given. Some scholars have found that the stiffness of nonlinear vibration absorbers is not purely cubic, they believe that the combined stiffness of some nonlinear vibration absorbers is more realistic [27][28][29]. However, their research is not thorough enough.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic analysis of 1-dof and 2-dof nonlinear energy sink with geometrically nonlinear damping and combined stiffness

et al. 2021

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Nonlinear energy sink (NES) refers to a typical passive vibration device connected to linear or weakly nonlinear structures for vibration absorption and mitigation. This study investigates the dynamics of 1-dof and 2-dof NES with nonlinear damping and combined stiffness connected to a linear oscillator. For the system of 1-dof NES, a truncation damping and failure frequency are revealed through bifurcation analysis using the complex variable averaging method. The frequency detuning interval for the existence of the strongly modulated response (SMR) is also reported. For the system of 2-dof NES, it is reported in a similar bifurcation analysis that the mass distribution between NES affects the maximum value of saddle-node bifurcation. To obtain the periodic solution of the 2-dof NES system with the consideration of frequency detuning, the incremental harmonic balance method (IHB) and Floquet theory are employed. The corresponding response regime is obtained by Poincare mapping, it shows that the responses of the linear oscillator and 2-dof NES are not always consistent, and 2-dof NES can generate extra SMR than 1-dof NES. Finally, the vibration suppression effect of the proposed NES with nonlinear damping and combined stiffness is analyzed and verified by the energy spectrum, and it also shows that the 2-dof NES system demonstrates better performance.

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Section: Bifurcation Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of 1-dof and 2-dof nonlinear energy sink with geometrically nonlinear damping and combined stiffness

et al. 2021

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show abstract

“…Eq. ( 13) gives an equation of the form A = f (λ, δ), which can represent the saddle-node bifurcation boundary curve on the [λ, A] plane, the parameters are selected as ε = 0.1, k 1 = 1/3, k 3 = 4/3 [14,19,29], as shown in Fig. 2.…”

Section: Bifurcation Analysismentioning

confidence: 99%

Dynamic Analysis of 1-Dof and 2-Dof Nonlinear Energy Sink With Geometrically Nonlinear Damping and Combined Stiffness

Zhang

Kong

Yue

et al. 2021

Preprint

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Nonlinear energy sink (NES) refers to a typical passive vibration device connected to linear or weakly nonlinear structures for vibration absorption and mitigation. This study investigates the dynamics of 1-dof and 2-dof NES with nonlinear damping and combined stiffness connected to a linear oscillator. For the system of 1-dof NES, a truncation damping and failure frequency are revealed through bifurcation analysis using the complex variable averaging method. The frequency detuning interval for the existence of the strongly modulated response (SMR) is also reported . For the system of 2-dof NES, it is reported in a similar bifurcation analysis that the mass distribution between NES affects the maximum value of saddle-node bifurcation. To obtain the periodic solution of the 2-dof NES system with the consideration of frequency detuning, the incremental harmonic balance method (IHB) and Floquet theory are employed. The corresponding response regime is obtained by Poincare mapping, it shows that the responses of the linear oscillator and 2-dof NES are not always consistent, and 2-dof NES can generate extra SMR than 1-dof NES. Finally, the vibration suppression effect of the proposed NES with nonlinear damping and combined stiffness is analyzed and verified by the energy spectrum, and it also shows that the 2-dof NES system demonstrates better performance.

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“…Third, the structural damping, resulting from Coulomb friction between parts within a structural system [ 9 ]. For damping characterization, several simplified models have been suggested; for instance, viscous damping, hysteretic damping, and Coulomb frictional damping models [ 10 ]. In real applications, equivalent viscous damping is commonly used to model the overall behavior of damped systems [ 11 ].…”

Section: Introductionmentioning

confidence: 99%

A Critical Review of Nonlinear Damping Identification in Structural Dynamics: Methods, Applications, and Challenges

Al-hababi

Cao

Saleh

et al. 2020

Sensors

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In recent decades, nonlinear damping identification (NDI) in structural dynamics has attracted wide research interests and intensive studies. Different NDI strategies, from conventional to more advanced, have been developed for a variety of structural types. With apparent advantages over classical linear methods, these strategies are able to quantify the nonlinear damping characteristics, providing powerful tools for the analysis and design of complex engineering structures. Since the current trend in many applications tends to more advanced and sophisticated applications, it is of great necessity to work on developing these methods to keep pace with this progress. Moreover, NDI can provide an effective and promising tool for structural damage detection purposes, where the changes in the dynamic features of structures can be correlated with damage levels. This review paper provides an overview of NDI methods by explaining the fundamental challenges and potentials of these methods based on the available literature. Furthermore, this research offers a comprehensive survey of different applications and future research trends of NDI. For potential development and application work for nonlinear damping methods, the anticipated results and recommendations of the current paper can assist researchers and developers worldwide to find out the gaps and unsolved issues in the field of NDI.

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On discontinuous dynamics of a class of friction-influenced oscillators with nonlinear damping under bilateral rigid constraints

Cited by 22 publications

References 55 publications

Dynamic analysis of 1-dof and 2-dof nonlinear energy sink with geometrically nonlinear damping and combined stiffness

Dynamic analysis of 1-dof and 2-dof nonlinear energy sink with geometrically nonlinear damping and combined stiffness

Dynamic Analysis of 1-Dof and 2-Dof Nonlinear Energy Sink With Geometrically Nonlinear Damping and Combined Stiffness

A Critical Review of Nonlinear Damping Identification in Structural Dynamics: Methods, Applications, and Challenges

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