Dynamics Analysis Of Spinning Fluid-Conveying Pipes

The rotating motion(self-rotation)of the fluid pipeline around the axis will lead to complex dynamic characteristics.In this paper,based on Euler-Bernoulli beam theory,the dynamic model of rotating pipeline is established,and the system control equation is obtained based on Hamilton principle,and the free vibration,nonlinear parametric vibration and forced vibration of rotating pipeline are studied.In the free vibration part,the partial differential equation is discretized into ordinary differential equation by Galerkin method.The discrete complex modal function is introduced to obtain the characteristic frequency and periodic solution of the system,and then the stability of the system is analyzed according to the modal frequency Argand diagram,and the threedimensional spatial vibration mode is obtained The response of the system to the initial conditions is obtained by numerical method.In the part of parametric vibration,the ordinary differential control equation is obtained by Galerkin method by introducing single-mode trial function.Considering the single velocity perturbation,single rotational speed perturbation and double perturbation of rotational speed and velocity,the stability discriminant under subharmonic resonance and combined resonance is obtained by multi-scale method,and then the system stability and parameter influence are analyzed.The response of the system is analyzed and the stability boundary is verified by numerical method,and the threedimensional vibration mode and motion trajectory of the system are also studied.In the forced vibration part,considering the unidirectional external excitation,the ordinary differential control equation is also obtained by substituting the single-mode trial function.The critical state of the system is analyzed by numerical method,and the three-dimensional spatial vibration mode and motion trajectory are analyzed.The amplitude-frequency response of the system under nonlinear conditions is analyzed by multi-scale perturbation method.It is found that the rotation of the pipeline leads to two different frequency values of forward and reverse precession at the same speed of the system,and the three-dimensional spatial motion trajectory is a complex combination of rotation and precession(or similar precession).The rotation speed has a double influence on the stability of the system.Periodically disturbed rotating speed will strengthen the stability of the system,while constant rotating speed will weaken the stability of the system.In addition,the mass ratio has a great influence on the cantilever pipeline with low degree of freedom,which will weaken the stability of the system.Fluid velocity is an unstable factor of the system,and large velocity leads to system instability.In the forced vibrating pipeline system,periodic motion,almost periodic motion and chaotic motion are found.Only when rotating,the system has gyro coupling effect.The greater the rotating speed,the more obvious the gyro coupling effect of the system.In addition,the geometric nonlinearity of the pipeline affects the energy characteristics of the system,and more energy is transferred from the excitation direction to other directions at high speed.When the excitation amplitude is small,the gyro coupling effect is also obvious,while when the excitation amplitude is large,the response value of the system is large.The nonlinear parameter γ also plays a damping role,which keeps the system in a relatively stable state.