Stability of modulated signals in the damped mechanical network of discontinuous coupled system oscillators with irrational nonlinearities

Kenmogné, Fabien; Noah, Pierre Marcel Anicet; Tafo, Joel  Bruneau Gonpe; Adoum, Danao Adile; Sali, Moussa; Abakar, Mahamat Tahir; Eno, Roger; Bell, Emmanuel Yamb

doi:10.1007/s00419-022-02259-2

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…For the practical applications of the oscillator, the multistability phenomenon that we focus on is the bistability within one potential well, as it can trigger a higher-amplitude response in a broad frequency band. Under the condition of three potential wells and α = 0.3, the structural parameter β ranges from 0 to 0.22, which is too small and impractical for the engineering applications of the oscillator [3,4,10]. Therefore, in the following parts of this study, by fixing the value of β at 0.85 and 0.5, respectively, the cases of mono-and double-potential wells are the main focus.…”

Section: Static Analysis Of the Irrationally Nonlinear Oscillatormentioning

confidence: 99%

“…By utilizing the allocation of two horizontal and four inclined linear springs, Han and Cao [8] designed a nonlinear oscillator that exhibited intricate equilibrium bifurcations and chaotic behaviors under the perturbations of viscous damping and the ambient excitation. A mechanical network with irrational nonlinearities was proposed in which each unit consisted of a lumped mass and two symmetric inclined springs [9,10]. Under the excitation of the network being loaded at one of its ends via the modulated signal, the conditions for modulational instability were found to be sensitive to the springs' angle of inclination as well as the dissipative coefficient.…”

Section: Introductionmentioning

confidence: 99%

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Global Dynamics and Bifurcations of an Oscillator with Symmetric Irrational Nonlinearities

Liu,

Shang

2023

Fractal Fract

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This study’s objective is an irrationally nonlinear oscillating system, whose bifurcations and consequent multi-stability under the circumstances of single potential well and double potential wells are investigated in detail to further reveal the mechanism of the transition of resonance and its utilization. First, static bifurcations of its nondimensional system are discussed. It is found that variations of two structural parameters can induce different numbers and natures of potential wells. Next, the cases of mono-potential wells and double wells are explored. The forms and stabilities of the resonant responses within each potential well and the inter-well resonant responses are discussed via different theoretical methods. The results show that the natural frequencies and trends of frequency responses in the cases of mono- and double-potential wells are totally different; as a result of the saddle-node bifurcations of resonant solutions, raising the excitation level or frequency can lead to the coexistence of bistable responses within each well and cause an inter-well periodic response. Moreover, in addition to verifying the accuracy of the theoretical prediction, numerical results considering the disturbance of initial conditions are presented to detect complicated dynamical behaviors such as jump between coexisting resonant responses, intra-well period-two responses and chaos. The results herein provide a theoretical foundation for designing and utilizing the multi-stable behaviors of irrationally nonlinear oscillators.

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Section: Static Analysis Of the Irrationally Nonlinear Oscillatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Global Dynamics and Bifurcations of an Oscillator with Symmetric Irrational Nonlinearities

Liu,

Shang

2023

Fractal Fract

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“…The geometric configuration of the springs causes irrational nonlinearity in the dynamic systems, hence causing difficulties in solving the analytical solutions of these systems. Theoretical and numerical approaches have been employed to investigate their nonlinear characteristics, including static bifurcations [20][21][22], approximative solutions [23][24][25], stochastic bifurcations [26] and global bifurcation analysis [27][28][29]. The SD oscillator subjected to harmonic excitation was found to possess the stiffness-hardening characteristics for a smooth parameter greater than one [23] but exhibited bistable potential wells and quad-stable responses for smooth parameters less than one [22,24].…”

Section: Introductionmentioning

confidence: 99%

Comparisons for Global Dynamics of a Geometrically Nonlinear Oscillator among Single-, Double- and Quadruple-Well Configurations

Sun,

Shang

2024

Fractal Fract

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This paper conducts a comparative analysis of the global dynamics of a harmonically excited oscillator with geometrical nonlinearities. Static analysis of the oscillatory system shows that adjusting the horizontal distance ratio from 1 to 0 can lead to single, double and quadruple well configurations successively. Intra-well and inter-well resonant responses are deduced analytically. Qualitative and quantitative results both reveal that the oscillator displays the stiffness–softening characteristic in cases of double and quadruple wells and the stiffness–hardening characteristic in the case of a single well. The initial-sensitive phenomenon jump is performed via fractal basins of attraction. Complex dynamical behaviors, including higher-order periodic responses and chaos, are also exhibited. The results demonstrate that the oscillator with a double or quadruple well configuration can achieve the inter-well response with large displacement, thus confirming its desirability in engineering applications of geometrically nonlinear oscillators.

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Propagation of the ordinary and extraordinary modulated optical pulses in a nonlinear Kerr-type birefringent optical waveguide: Analytical description

Donkeng,

Mabou,

kenmogne

et al. 2023

Results in Optics

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Stability of modulated signals in the damped mechanical network of discontinuous coupled system oscillators with irrational nonlinearities

Cited by 3 publications

References 19 publications

Global Dynamics and Bifurcations of an Oscillator with Symmetric Irrational Nonlinearities

Global Dynamics and Bifurcations of an Oscillator with Symmetric Irrational Nonlinearities

Comparisons for Global Dynamics of a Geometrically Nonlinear Oscillator among Single-, Double- and Quadruple-Well Configurations

Propagation of the ordinary and extraordinary modulated optical pulses in a nonlinear Kerr-type birefringent optical waveguide: Analytical description

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