Based on the energy flow theory of nonlinear dynamical system,the stabilities,bifurcations,possible periodical/chaotic motions of nonlinear water-lubricated bearing-shaft coupled systems are investigated in this paper...Based on the energy flow theory of nonlinear dynamical system,the stabilities,bifurcations,possible periodical/chaotic motions of nonlinear water-lubricated bearing-shaft coupled systems are investigated in this paper.It is revealed that the energy flow characteristics around the equlibrium point of system behaving in the three types with different friction-para-mters.(a)Energy flow matrix has two negative and one positive energy flow factors,constructing an attractive local zero-energy flow surface,in which free vibrations by initial disturbances show damped modulated oscillations with the system tending its equlibrium state,while forced vibrations by external forces show stable oscillations,(b)Energy flow matrix has one negative and two positive energy flow factors,spaning a divergence local zero-energy flow surface,so that the both free and forced vibrations are divergence oscillations with the system being unstable,(c)Energy flow matrix has a zero-energy flow factor and two opposite factors,which constructes a local zero-energy flow surface dividing the local phase space into stable,unstable and central subspace,and the simulation shows friction self-induced unstable vibrations for both free and forced cases.For a set of friction parameters,the system behaves a periodical oscillation,where the bearing motion tends zero and the shaft motion reaches a stable limit circle in phase space with the instant energy flow tending a constant and the time averaged one tending zero.Numerical simulations have not found any possible chaotic motions of the system.It is discovered that the damping matrices of cases(a),(b)and(c)respectively have positive,negative and zero diagonal elements,resulting in the different dynamic behavour of system,which gives a giderline to design the water-lubricated bearing unit with expected performance by adjusting the friction parameters for applications.展开更多
Water entry problems represent complex multiphase flows involving air,water,and structure interaction,occurring rapidly in rough seas,and potentially effecting structural integrity of floating structures.This paper ex...Water entry problems represent complex multiphase flows involving air,water,and structure interaction,occurring rapidly in rough seas,and potentially effecting structural integrity of floating structures.This paper experimentally investigates asymmetric slamming loads acting on a 3-D elastic wedge section.The specimen,featuring two different bottom plates(stiffened and unstiffened),each 4 mm thick,aims to assess the effect of structural stiffness on dynamic loads.The experiments are conducted at different drop heights of 25 cm and 50 cm and varying heel angles from 5°to 25°.The paper describes the experimental conditions,including wedge geometry,material properties,and the test plan.The study explores the influence of heel angle on impact acceleration,revealing an increase in peak acceleration with a higher inclination angle,particularly in the vertical direction.Additionally,the hydrodynamic pressure resulting from asymmetric slamming is presented.The pressure results analyzed and compared at different locations along the length of the wedge.The experimental findings indicate that,despite the leeward side(stiffened)experiencing a smaller hydrodynamic load,the heel angle significantly affects pressure results on the windward side(unstiffened),leading to a more pronounced dynamic response.The time history of pressure results emphasizes the effect of elastic vibrations,particularly noticeable on the unstiffened bottom plate.This study contributes to a deeper understanding of asymmetric slamming on aluminum structures,facilitating the enhancement of mathematical models and the validation of numerical simulations.展开更多
基金We gratefully acknowledge NSFC(51509194)CSC for providing finacial support eanabling Li Qin and Hongling Qin to visit the University of Southampton to engage the related research.
文摘Based on the energy flow theory of nonlinear dynamical system,the stabilities,bifurcations,possible periodical/chaotic motions of nonlinear water-lubricated bearing-shaft coupled systems are investigated in this paper.It is revealed that the energy flow characteristics around the equlibrium point of system behaving in the three types with different friction-para-mters.(a)Energy flow matrix has two negative and one positive energy flow factors,constructing an attractive local zero-energy flow surface,in which free vibrations by initial disturbances show damped modulated oscillations with the system tending its equlibrium state,while forced vibrations by external forces show stable oscillations,(b)Energy flow matrix has one negative and two positive energy flow factors,spaning a divergence local zero-energy flow surface,so that the both free and forced vibrations are divergence oscillations with the system being unstable,(c)Energy flow matrix has a zero-energy flow factor and two opposite factors,which constructes a local zero-energy flow surface dividing the local phase space into stable,unstable and central subspace,and the simulation shows friction self-induced unstable vibrations for both free and forced cases.For a set of friction parameters,the system behaves a periodical oscillation,where the bearing motion tends zero and the shaft motion reaches a stable limit circle in phase space with the instant energy flow tending a constant and the time averaged one tending zero.Numerical simulations have not found any possible chaotic motions of the system.It is discovered that the damping matrices of cases(a),(b)and(c)respectively have positive,negative and zero diagonal elements,resulting in the different dynamic behavour of system,which gives a giderline to design the water-lubricated bearing unit with expected performance by adjusting the friction parameters for applications.
基金supported by the Estonian Research Council (Grant No.PRG1820).
文摘Water entry problems represent complex multiphase flows involving air,water,and structure interaction,occurring rapidly in rough seas,and potentially effecting structural integrity of floating structures.This paper experimentally investigates asymmetric slamming loads acting on a 3-D elastic wedge section.The specimen,featuring two different bottom plates(stiffened and unstiffened),each 4 mm thick,aims to assess the effect of structural stiffness on dynamic loads.The experiments are conducted at different drop heights of 25 cm and 50 cm and varying heel angles from 5°to 25°.The paper describes the experimental conditions,including wedge geometry,material properties,and the test plan.The study explores the influence of heel angle on impact acceleration,revealing an increase in peak acceleration with a higher inclination angle,particularly in the vertical direction.Additionally,the hydrodynamic pressure resulting from asymmetric slamming is presented.The pressure results analyzed and compared at different locations along the length of the wedge.The experimental findings indicate that,despite the leeward side(stiffened)experiencing a smaller hydrodynamic load,the heel angle significantly affects pressure results on the windward side(unstiffened),leading to a more pronounced dynamic response.The time history of pressure results emphasizes the effect of elastic vibrations,particularly noticeable on the unstiffened bottom plate.This study contributes to a deeper understanding of asymmetric slamming on aluminum structures,facilitating the enhancement of mathematical models and the validation of numerical simulations.
