Analysis For Fluid Structure Interaction Vibration Characteristics And Resonance Reliability Of Fluid Conveying Pipe

Fluid conveying pipe is common in equipment or site needing transporting fluid medium,and it's an essential part in fluid machinery,once it loses efficacies due to vibration beyond tolerance,it will cause unnecessary losses.Hence,investigations with respect to its vibration characteristics,such as:natural frequency,shape function,critical velocity and steady-state displacement response under forced vibration et al.and resonance reliability appear of vital importance.The vibration differential equation based on Euler-Bernoulli beam theory,plug flow model and with the combination of Newton's second law of motion can describe one kind of typical fluid structure interaction vibration problem with respect to fluid conveying pipes.According to this equation,people have carried out enormous investigations like stability,bifurcation and chao,displacement response under forced vibration and resonance reliability et al.aiming at fluid conveying pipes characterized by different supporting types,spatial configurations and cross-section shapes up to now,and some conclusions promoting theoretical research and guiding production practice have been drawn.However,there still leaving many aspects related to fluid structure interaction vibration problem of fluid conveying pipe worthy of exploring,such as:effects of fluid model modification factor on the vibration characteristics and resonance failure probability of fluid conveying straight pipe;stability,steady-state displacement response under forced vibration and critical velocity under changeable material property et al.of fluid conveying straight pipe with elastic supports;in-plane forced vibration steady-state displacement response of fluid conveying curved pipe with both ends supported,and critical velocity,changeability of combined force of curved pipe with elastic supports;analysis model for fluid structure interaction vibration and its related vibration characteristics of combined straight-curved pipe;calculation methods for resonance failure probability of fluid conveying pipe et al,therefore,deep researches on the above problems have been proceeded in this paper,and maj or works are listed below:(1)Diffrential transformation method(DTM)is used to estabilish flow-induced vibration analysis models of fluid conveying straight pipe with both ends supported under laminar and plug flow models,then changing curve of natural frequency following flow velocity and concrete values of critical velocity are obtained after calculation.The method is extended to the flow-induced vibration problems of clamped-elastically supported straight pipe and curved pipe with both ends supported,for the former,it's found that the instability mode will no longer be only flutter,but divergence,coupled divergence-flutter and coupled-mode flutter may appear.While for the latter,the pipe will never lose stability on the basis of modified inextensible or extensible theories,DTM lays a foundation for subsequent research on resonance reliability of fluid conveying pipe.(2)For the problem that the pipe has too long span,it's put forward that adding an extra elastic support to guarantee the vibration to still keep linear,its related vibration differential equation is established by introducing the additional term caused by the elastic support into the basic one.The advantage of the Galerkin method based on a shape function different from that of beam lies in that the shape function has simple form,and hence can simplify the derivation process.According to the above differential equation,the method is used to establish analysis models of both flow-induced and forced vibrations of clamped-elastically supported-clamped straight pipe conveying fluid.After calculation,it's found that change of elastic support installation position can cause the natural frequency to fluctuate,Galerkin method can be a foundation in designing supporting types,and can be radiated to study fluid structure interaction vibration problem of pipes with other forms.(3)A new transfer matrix method based on Laplace transform(abbreviated by L-TMM in the paper)is put forward,and the characteristic equation related to the state vectors of two ends of fluid conveying pipe(including straight and curved pipes)is established.Its advantage lies in that it can guarantee the computing precision and simutalneously reduce orders of the characteristic equation,and hence can save computing time.L-TMM is used to study the relationships between critical velocity of periodic cantilevered straight pipe conveying fluid and number of elements,length ratio;critical velocity of cantilevered fluid conveying pipe with movable elastic supports and elastic supports;natural frequency of clamped-elastically supported curved pipe conveying fluid and flowing velocity,elastic supports(during the process,the concept that the steady combined force is changeable is firstly put forward,and the influence of this force on the system's natural frequency is investigated).The results show that,the installation positions of elastic supports that promoting the system to obtain the maximum and minimum critical velocities can be received with the aid of L-TMM;change of the steady combined force can affect the judgement of the system's stability.L-TMM can be radiated to study other dynamic problems of structure characterized by chain.(4)Green function method(GFM)is used to establish the forced vibration analysis model of clamped-elastically supported straight pipe conveying fluid and its analytical solution of steady-state displacement response is deduced,the concrete positions and values of displacement response under different parameter levels are received after calculation.Aiming at fluid conveying curved pipe,its in-plane forced vibration differential equation is established on the basis that the external force with random direction and format is introduced directly into the existing flow-induced vibration differential equation,then GFM is used to establish its related forced vibration analysis model,and influences of some key parameters on the displacement response are studied.GFM plays a very intuitional guiding role in the configuration of pipes,espically when the installation space is exactly limited.(5)On the basis of 'replace curved by straight',the governing equation characterizing flexural motion(with the consideration of flow model modification)of combined straight-curved pipe is established by introducing steady combined force into the flow-induced vibration differential equation of fluid conveying straight pipe,L-TMM is used to calculate the system's natural frequency,after the comparison with FEM,the efficiency of the governing equation is verified.(6)The anti-resonance performance function of fluid conveying pipe is established from the angle of preventing resonance,on the basis of moment method,its calculation model of resonance failure probability is given out.One method that on the basis of the natural frequency obtained by DTM,moment combined with point-estimate methods are used to calculate the resonance failure probabilities of fluid conveying straight pipe under four typical supporting types is put forward,during this process,the flow model modification factor is taken into consideration for the first time.Subsequently,the resonance failure probabilities of fluid conveying curved pipe under four typical supporting types are calculated by moment method based on the results by DTM and L-TMM,all methods here can be programmed uniformly in Matlab,embodying the high portability and generalization of the whole method proposed.