In this paper, a deterministic delay differential pantograph equation （DDPE） with an unbounded memory is stochastically perturbed by an Ito-type noise. The contribution of white noise to the oscillatory behaviour of...In this paper, a deterministic delay differential pantograph equation （DDPE） with an unbounded memory is stochastically perturbed by an Ito-type noise. The contribution of white noise to the oscillatory behaviour of the new stochastic delay differential pantograph equation （SDDPE） is investigated. It is established that under certain conditions and with a highly positive probability, the new stochastic delay differential pantograph equation has an oscillatory solution influenced by the presence of the noise. This is not possible with the original deterministic system which has a non-oscillatory solution due to the absence of noise.展开更多
As one of the main aerodynamic noise sources of high-speed trains, the pantograph is a complex structure containing many components, and the flow around it is extremely dynamic, with high-level turbulence. This study ...As one of the main aerodynamic noise sources of high-speed trains, the pantograph is a complex structure containing many components, and the flow around it is extremely dynamic, with high-level turbulence. This study analyzed the near-field unsteady flow around a pantograph using a large-eddy simulation(LES) with high-order finite difference schemes. The far-field aerodynamic noise from a pantograph was predicted using a computational fluid dynamics(CFD)/Ffowcs Williams-Hawkings(FW-H) acoustic analogy. The surface oscillating pressure data were also used in a boundary element method(BEM) acoustic analysis to predict the aerodynamic noise sources of a pantograph and the far-field sound radiation. The results indicated that the main aerodynamic noise sources of the pantograph were the panhead, base frame and knuckle. The panhead had the largest contribution to the far-field aerodynamic noise of the pantograph. The vortex shedding from the panhead generated tonal noise with the dominant peak corresponding to the vortex shedding frequency and the oscillating lift force exerted back on the fluid around the panhead.Additionally, the peak at the second harmonic frequency was associated with the oscillating drag force. The contribution of the knuckle-downstream direction to the pantograph aerodynamic noise was less than that of the knuckle-upstream direction of the pantograph, and the average sound pressure level(SPL) was 3.4 dBA. The directivity of the noise radiated exhibited a typical dipole pattern in which the noise directivity was obvious at the horizontal plane of θ=0°,the longitudinal plane of θ=120°,and the vertical plane of θ=90°.展开更多
文摘In this paper, a deterministic delay differential pantograph equation （DDPE） with an unbounded memory is stochastically perturbed by an Ito-type noise. The contribution of white noise to the oscillatory behaviour of the new stochastic delay differential pantograph equation （SDDPE） is investigated. It is established that under certain conditions and with a highly positive probability, the new stochastic delay differential pantograph equation has an oscillatory solution influenced by the presence of the noise. This is not possible with the original deterministic system which has a non-oscillatory solution due to the absence of noise.
基金supported by the High-Speed Railway Basic Research Fund Key Project of China(Grant No.U1234208)the National Key Research and Development Program of China(Grant No.2016YFB1200403)+1 种基金the National Natural Science Foundation of China(Grant Nos.51475394&51605397)the Research Project of State Key Laboratory of Traction Power(Grant No.2016TPL_T02)
文摘As one of the main aerodynamic noise sources of high-speed trains, the pantograph is a complex structure containing many components, and the flow around it is extremely dynamic, with high-level turbulence. This study analyzed the near-field unsteady flow around a pantograph using a large-eddy simulation(LES) with high-order finite difference schemes. The far-field aerodynamic noise from a pantograph was predicted using a computational fluid dynamics(CFD)/Ffowcs Williams-Hawkings(FW-H) acoustic analogy. The surface oscillating pressure data were also used in a boundary element method(BEM) acoustic analysis to predict the aerodynamic noise sources of a pantograph and the far-field sound radiation. The results indicated that the main aerodynamic noise sources of the pantograph were the panhead, base frame and knuckle. The panhead had the largest contribution to the far-field aerodynamic noise of the pantograph. The vortex shedding from the panhead generated tonal noise with the dominant peak corresponding to the vortex shedding frequency and the oscillating lift force exerted back on the fluid around the panhead.Additionally, the peak at the second harmonic frequency was associated with the oscillating drag force. The contribution of the knuckle-downstream direction to the pantograph aerodynamic noise was less than that of the knuckle-upstream direction of the pantograph, and the average sound pressure level(SPL) was 3.4 dBA. The directivity of the noise radiated exhibited a typical dipole pattern in which the noise directivity was obvious at the horizontal plane of θ=0°,the longitudinal plane of θ=120°,and the vertical plane of θ=90°.
