The ideally straight hydraulic pipe is inexistent in reality. The initial curve caused by the manufacturing or the creep deformation during the service life will change the dynamic character of the system. The current...The ideally straight hydraulic pipe is inexistent in reality. The initial curve caused by the manufacturing or the creep deformation during the service life will change the dynamic character of the system. The current work discusses the effect of the initial curve on the hydraulic pipe fixed at two ends for the first time. Based on the governing equation obtained via the generalized Hamilton’s principle,the potential energy changing with the height of the initial curve is discussed. The initial curve makes the potential energy curve asymmetric,but the system is always monostable. The initial curve also has very important influence on natural frequencies. It hardens the stiffness of the first natural mode at first and then has no effect on this mode after a critical value. On the contrast,the second natural frequency is constant before the critical value but increases while the height of the initial curve exceeds the critical value. On account of the initial value,the quadratic nonlinearity appears in the system. Forced resonance is very different from that of the ideally straight pipe under the same condition. Although the 2∶1 internal resonance is established by adjusting the height of the initial curve and the fluid speed,the typical double-jumping phenomenon does not occur under the initial curve given in the current work. This is very different from the straight pipe in the supercritical region. The work here claims that the initial curve of the hydraulic pipe should be taken into consideration. Besides,more arduous work is needed to reveal the dynamic characters of it.展开更多
A nonlinear torsional absorber,which can overcome the influence of the fluid velocity on the natural frequency,is employed at the boundary to restrain the bending vibration of a pipe for the first time.By using the ro...A nonlinear torsional absorber,which can overcome the influence of the fluid velocity on the natural frequency,is employed at the boundary to restrain the bending vibration of a pipe for the first time.By using the rotating angle at the end of the pipe,the bending vibration energy is pumped to the boundary absorber.The nonlinearly coupled pipe-absorber governing equations are obtained by the generalized Hamilton’s principle.Steady-state responses subjected to a basement excitation are discussed by the modal-correction-harmonic-balance-method.According to this method,the boundaries of the pipe are treated as the generalized governing equations.In this way,those nonlinearities and time-dependent terms in the boundary are involved in the response completely.A direct simulation method,called the differential quadrature element method(DQEM),is used to verify these analytical results.The investigation indicates that the nonlinear boundary absorber owns two outstanding advantages.The first one is that the natural characters remain the same and the absorber can capture the resonance of the pipe automatically.The second one is that the absorber works at all natural modes.Especially,by using the nonlinear damping,the absorber will not worsen the weak vibration in the non-resonance region.The parameters of the absorber are investigated to optimize the efficiency in detail.The result finds that good efficiency can be achieved with a tiny mass.Meanwhile,the efficiency becomes better as the damping increases.With the help of these investigations,the work provides a new strategy to protect pipes conveying fluids from being destroyed by the vibration.展开更多
基金supported by the National Natural Science Foundation of China(No.12002195)the National Science Fund for Distinguished Young Scholars (No.12025204)+1 种基金the Program of Shanghai Municipal Education Commission (No. 2019-01-07-00-09-E00018)the Pujiang Project of Shanghai Science and Technology Commission(No.20PJ1404000)。
文摘The ideally straight hydraulic pipe is inexistent in reality. The initial curve caused by the manufacturing or the creep deformation during the service life will change the dynamic character of the system. The current work discusses the effect of the initial curve on the hydraulic pipe fixed at two ends for the first time. Based on the governing equation obtained via the generalized Hamilton’s principle,the potential energy changing with the height of the initial curve is discussed. The initial curve makes the potential energy curve asymmetric,but the system is always monostable. The initial curve also has very important influence on natural frequencies. It hardens the stiffness of the first natural mode at first and then has no effect on this mode after a critical value. On the contrast,the second natural frequency is constant before the critical value but increases while the height of the initial curve exceeds the critical value. On account of the initial value,the quadratic nonlinearity appears in the system. Forced resonance is very different from that of the ideally straight pipe under the same condition. Although the 2∶1 internal resonance is established by adjusting the height of the initial curve and the fluid speed,the typical double-jumping phenomenon does not occur under the initial curve given in the current work. This is very different from the straight pipe in the supercritical region. The work here claims that the initial curve of the hydraulic pipe should be taken into consideration. Besides,more arduous work is needed to reveal the dynamic characters of it.
基金supported by the National Natural Science Foundation of China(Grant Nos.12025204 and 11872159)the Program of Shanghai Municipal Education Commission(Grant No.2019-01-07-00-09-E00018)。
文摘A nonlinear torsional absorber,which can overcome the influence of the fluid velocity on the natural frequency,is employed at the boundary to restrain the bending vibration of a pipe for the first time.By using the rotating angle at the end of the pipe,the bending vibration energy is pumped to the boundary absorber.The nonlinearly coupled pipe-absorber governing equations are obtained by the generalized Hamilton’s principle.Steady-state responses subjected to a basement excitation are discussed by the modal-correction-harmonic-balance-method.According to this method,the boundaries of the pipe are treated as the generalized governing equations.In this way,those nonlinearities and time-dependent terms in the boundary are involved in the response completely.A direct simulation method,called the differential quadrature element method(DQEM),is used to verify these analytical results.The investigation indicates that the nonlinear boundary absorber owns two outstanding advantages.The first one is that the natural characters remain the same and the absorber can capture the resonance of the pipe automatically.The second one is that the absorber works at all natural modes.Especially,by using the nonlinear damping,the absorber will not worsen the weak vibration in the non-resonance region.The parameters of the absorber are investigated to optimize the efficiency in detail.The result finds that good efficiency can be achieved with a tiny mass.Meanwhile,the efficiency becomes better as the damping increases.With the help of these investigations,the work provides a new strategy to protect pipes conveying fluids from being destroyed by the vibration.
