Singularity analysis of response bifurcation for a coupled pitch–roll ship model with quadratic and cubic nonlinearity

Li, Xinye; Zhang, Lijuan; Zhang, Huabiao; Li, Kai

doi:10.1007/s11071-018-4714-z

Cited by 10 publications

(2 citation statements)

References 18 publications

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“…Hou et al [ 32 ] investigated the bifurcation modes of a periodic solution in a duffing system under constant force and harmonic excitation. Li et al [ 33 ] considered the bifurcation of a coupled pitch–roll ship model with quadratic and cubic nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of a Micro-Machined Gyroscope with Nonlinear Stiffness and Electrostatic Forces

Zhang

2021

Micromachines

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The bifurcation of the periodic response of a micro-machined gyroscope with cubic supporting stiffness and fractional electrostatic forces is investigated. The pull-in phenomenon is analyzed to show that the system can have a stable periodic response when the detecting voltage is kept within a certain range. The method of averaging and the residue theorem are employed to give the averaging equations for the case of primary resonance and 1:1 internal resonance. Transition sets on the driving/detecting voltage plane that divide the parameter plane into 12 persistent regions and the corresponding bifurcation diagrams are obtained via the singularity theory. The results show that multiple solutions of the resonance curves appear with a large driving voltage and a small detecting voltage, which may lead to an uncertain output of the gyroscope. The effects of driving and detecting voltages on mechanical sensitivity and nonlinearity are analyzed for three persistent regions considering the operation requirements of the micro-machined gyroscope. The results indicate that in the region with a small driving voltage, the mechanical sensitivity is much smaller. In the other two regions, the variations in the mechanical sensitivity and nonlinearity are analogous. It is possible that the system has a maximum mechanical sensitivity and minimum nonlinearity for an appropriate range of detecting voltages.

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Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of a Micro-Machined Gyroscope with Nonlinear Stiffness and Electrostatic Forces

Zhang

2021

Micromachines

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“…They nonetheless did not examine the effect of separation ratio on the cross flow at high Froude numbers (Fr > 0.75), as their investigation was limited up to Fr = 0.55. Regarding nonlinear dynamic response of the vessel, Li, Zhang, Zhang and Li [69] and Dash, Nagarajan…”

Section: Introductionmentioning

confidence: 99%

A new phenomenon in interference effect on catamaran dynamic response

Honaryar

Ghiasi

Liu

2021

International Journal of Mechanical Sciences

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Interference effect between catamaran demi-hulls has been considered as an adverse fluid-solid interaction; the narrower separation distance between the two hulls, the greater drag force acts upon the catamaran. However, this study is aimed at introducing a novel phenomenon contrasting outcome in semi-planing and planing regimes. As speed and accordingly the Froude number increase the catamaran transits across different modes, free surface profile becomes complicated and so does the interference effect as well as the prediction of catamaran dynamic response. The situation will be even more complex if demi-hull separation narrows where nonlinearity in interference effect is more pronounced. So, free-running tests in six degrees of freedom as well as obtaining fluid flow characteristics using computational fluid dynamics were conducted for a high-speed catamaran vehicle with asymmetric non-prismatic demi-hulls to tackle the problem. The results of catamaran dynamic response reveal that not only is drag reduced substantially up to 15%, but also trim angle diminishes by 30% as hulls separation distance decreases in semi-planing and planing modes. In other words, with increasing speed, and decreasing trim angle by 2.3 o , the current method achieved the goal of consequently reducing the risk of porpoising instability, without the increase of delivered power.

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Bifurcation analysis of quasi-periodic orbits of mechanical systems with 1:2 internal resonance via spectral submanifolds

Liang,

Jain,

2024

Nonlinear Dyn

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Singularity analysis of response bifurcation for a coupled pitch–roll ship model with quadratic and cubic nonlinearity

Cited by 10 publications

References 18 publications

Bifurcation Analysis of a Micro-Machined Gyroscope with Nonlinear Stiffness and Electrostatic Forces

Bifurcation Analysis of a Micro-Machined Gyroscope with Nonlinear Stiffness and Electrostatic Forces

A new phenomenon in interference effect on catamaran dynamic response

Bifurcation analysis of quasi-periodic orbits of mechanical systems with 1:2 internal resonance via spectral submanifolds

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