Nonlinear dynamics of the quasi-zero-stiffness SD oscillator based upon the local and global bifurcation analyses

Hao, Zhifeng; Cao, Qingjie; Wiercigroch, Marian

doi:10.1007/s11071-016-3093-6

Cited by 121 publications

(24 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The Duffing oscillator is a typical nonautonomous system, which has been modeled in various fields of physics, mechanics and engineering. It can exhibit different periodic motions and chaotic phenomena due to the periodically excitation [1]- [4]. For instance, the strange attractors of Duffing oscillator with negative linear stiffness and damping were discussed through Poincaré map and the positive maximal Lyapunov exponent [5].…”

Section: Introductionmentioning

confidence: 99%

Discontinuous Dynamic Analysis of a Modified Duffing-Rayleigh System With a Piecewise Quadratic Function

et al. 2020

View full text Add to dashboard Cite

The discontinuous dynamical behavior of a modified Duffing-Rayleigh system with a piecewise quadratic function is studied. The necessary and sufficient conditions for motion switchability at the velocity boundary are investigated through the theory of discontinuous dynamical systems. Various motions through the boundary are demonstrated by the parameter maps and coexisting bifurcation diagrams. The coexistence of an example system under different initial conditions is illustrated by attraction basins, and the trajectories in phase plane. The periodic and chaotic motions with different mapping structures are analyzed for a better understanding of the motion switching mechanism. Through Multisim, the circuit experiment proves the effectiveness of the theoretical analysis.

show abstract

Section: Introductionmentioning

confidence: 99%

Discontinuous Dynamic Analysis of a Modified Duffing-Rayleigh System With a Piecewise Quadratic Function

et al. 2020

View full text Add to dashboard Cite

show abstract

“…(The model is often named 'smooth and discontinuous' SD oscillator, too.) In the smooth regime the system bears significant similarities to the Duffing oscillator, but at the discontinuous limit there is a substantial departure in dynamics from the standard one [5]. In the paper [6] the model is extended by introducing of a damper.…”

Section: Introductionmentioning

confidence: 99%

“…The authors obtained the result that this type of slider-spring-damper system gives benefits of using a nonlinear stiffness in an energy harvesting device. In [4][5][6] it is shown that regulating the smooth parameter the control of the dynamics of the system is possible. The systems are produced and experimental measurements on the real systems are done [7].…”

Section: Introductionmentioning

confidence: 99%

Variable Preloading Force in an Archetypal Oscillator

et al. 2019

View full text Add to dashboard Cite

In this paper, the influence of the time variable preloading force on the vibration of an archetypal oscillator is investigated. The oscillator is modeled as a slider-string system which is mathematically described with a second order nonlinear differential equation with time variable parameters. An approximate procedure for solving the equation is introduced. It is based on the exact solution of the pure nonlinear equation in the form of the Ateb function. The obtained result gives the vibration amplitude and phase variation of the oscillator depending on the preloading force variation. Based on this result, the procedure for regulation of the preloading force as the function of the required vibration amplitude decrease is developed. It is concluded that the preloading force may be used as a control parameter of the oscillator.

show abstract

“…Nonlinear geometrically arranged elements have been considered previously, the concept of snapthrough mechanism to provide the conditions HSLDS (high-static low-dynamic stiffness) has been considered in many works [2,4,12,15,24]. Tang and Brennan [30] studied the vibration transmissibility characteristics of geometrically arranged viscous damper.…”

Section: Introductionmentioning

confidence: 99%

On the dynamics of a vibration isolator with geometrically nonlinear inerter

2018

View full text Add to dashboard Cite

The inerter is a two-terminal mechanical element that produces forces directly proportional to the relative acceleration between these terminals. The linear behaviour of this element has already been described in the literature. In this work, the nonlinear effects of the geometrical arrangement of the inerter are investigated in terms of vibration isolation and compared to the traditional arrangement. The analysis comprises the use of harmonic-balanced method applied to the exact equation, as well as approximations for low amplitude and high amplitude. Numerical analysis is used to complement the investigation. Comparison with classic vibration isolators shows possible benefits for high frequency regimes. The effects from the geometrical nonlinearity vanish when the amplitude of motion is large.

show abstract

Nonlinear dynamics of the quasi-zero-stiffness SD oscillator based upon the local and global bifurcation analyses

Cited by 121 publications

References 61 publications

Discontinuous Dynamic Analysis of a Modified Duffing-Rayleigh System With a Piecewise Quadratic Function

Discontinuous Dynamic Analysis of a Modified Duffing-Rayleigh System With a Piecewise Quadratic Function

Variable Preloading Force in an Archetypal Oscillator

On the dynamics of a vibration isolator with geometrically nonlinear inerter

Contact Info

Product

Resources

About