Static and dynamic nonlinear behavior of a multistable structural system consisting of two coupled von Mises trusses

de Castro, Carlos H.L.; Orlando, Diego; Gonçalves, Paulo B.

doi:10.1016/j.ijnonlinmec.2023.104510

Cited by 3 publications

(1 citation statement)

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“…Accordingly, it is necessary for researchers to extend the investigation of the effects of initial conditions on achieving the largest-amplitude final response. Castro et al [28] carried out a specific analysis of a structural system composed by a pair of coupled bistable von Mises trusses and found that the fractal basins of attraction of the attractors could trigger the loss of dynamic integrity and thus the reliability of the structure. Regarding the SD oscillator under harmonic excitation, Wang and Shang [29] investigated jump among periodic attractors, period-three responses and chaos caused by variations in the excitation level and initial states.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%