The Stability And Bifurcations Of Pipes Conveying Fluid With Complex Restricted Conditions

The stability and bifurcations of pipes conveying fluid with complex restricted conditions are investigated.The concrect content of this research comprises some aspects as follows:The govering equation which is established by analysis the transverse vibrations of the pipe with complex elastic support at both ends.The nature frequency and crisis velocity is determined by applicating differencial quadrature method(DQM) and separated variables method to the govering equation. The laws of frequency changes are discussed with the some boundaries and some combinations of elastic supports.Then,the numerical result of DQM is cmpared with separated variables method,It turns out that their results match so satisfactorily.Further, The parameter resonates caused by variable flows are investigated.The direct mulit-scale method is applied to the governing equation of the pipe.The instability boundary is obtained by calculation.It is found that the system parameters can destabilize the pipe.The harmonious equilibrium method is used to comfirmed the results.The non-linear frequency obtained by considering the geometry non-linearity. In the problem of non-linear vibration caused by pulstile flows and non-linearity,stabiliy and bifurcations of steady-state solutions are analyzed .At last of this paper.the response of resonates and its change rule in force vibration is investigated.