Research On Dynamic Characteristics Of Thin-walled Pipes Conveying Fluid

Pipes conveying fluid are widely used in modern industry,and has attracted many researchers' attentions due to the vibration and noise problem due to the combination of the fluid and other constraints in the system.Combined with functionally graded materials,the vibration characteristics and stability of thin-walled pipes conveying fluid are studied in this paper.The main contents and the main conclusions of the paperare listed as follows:1.The interval B-spline wavelet-based finite elements of fluid-conveying straight pipes and curved pipes are constructed,respectively.The wavelet-based finite element is applied to solve the frequency of the straight pipe and the curved pipe under various boundaries.And the critical flow velocity curves of the cantilever straight pipe conveying fluid are obtained by applying two different procedures and wavelet-based finite element method.The results show that The interval B-spline wavelet-based finite elements has certain advantages in solving the vibration problems of fluid-conveying pipes.The number of elements need is less,and the numerical results are accuracy and reliable.Under the same conditions such as program structure and PC,the computational time is less.The critical velocity curves obtained by applying Marzani's method are correct,monotonically increase and coincide with the Routh-Hurwitz stability criteria.2.Considering the shear effect,the differential equations of motion and the boundary conditions of FG thin-walled pipes conveying fluid are derived by applying the Hamiltonian method based on the thin-walled beam model.The govering equations of both models are discretized by wavelet-based finite element method.The wavelet-based stiffness matrix,wavelet-based damping matrix and wavelet-based mass matrix are deduced.The differences of vibration characteristics of FG pipes between two temperature distributions were studied.The results show that,considering or neglecting the shear effect,as the volume fraction or temperature gradient increases,the first six natrual frequencies have same trend and are decreased.The differences of the first six natural frequencies between two temperature distributions are not monotonous,and not always greater than zero.Neglecting the shear effect,the critical flow velocity curves of two cases of temperature distributions increase with the increase of mass ratio.The difference of the critical flow velocity of fluid-conveying pipes between two cases of temperature distributions is not always monotonic.As the mass ratio increases,the absolute value of the difference increases.3.Based on thin shell model,the differential equations of two coaxial circular cylindrical thin shells conveying fluid fixed at both ends are deduced.Combined with functionally graded material,the effects of volume fraction index on the dynamics of two coaxial circular cylindrical thin shells are studied by Galerkin's method and Fourier's transform.Two coaxial circular cylindrical thin shells,which one shell material is constructed with functionally graded material,and the other shell is metal,are considered.The results show that when the flow velocity is small,the smaller volume fraction index,the higher the frequency.When the flow velocity is high,the effects of volume fraction index on the frequency depend on the different flow area and the different materials of inner shell and outer shell.4.In order to study the effect of stochastic parameters and physical parameters,the dynamic characteristics of FG thin-walled pipes lying on random stiffness foundation are studied by using the stochastic finite element method.The effects of coefficient of variation,correlation length,volume fraction index and temperature gradient on the mean and standard deviation of critical flow velocity are analyzed.The results show that for fixed value of coefficient of variation,as the correlation length increases,the mean of the critical flow velocity curves of different volume fraction index and different temperature gradient has the same trend.For fixed values of volume fraction index and temperature gradient,when the coefficient of variation is small,the critical flow velocity of fluid-conveying thin-walled pipes increase as the the lenght of correlation increases.When the coefficient of variation is high,the variation of critical flow velocity of fluid-conveying thin-walled pipes are not monotonic as the the lenght of correlation increases.For fixed values of the coefficient of variation and failure probability,as the length of correlation increases,the limit of flow velocity decreases.5.For fluid-conveying thin-walled pipes constrained by clamps at both ends and lying on the elastic foundation,the wavelet-based finite element method is used to discretize the differential equations of the pipe,respectively.Considering the systematic error due to the uncertainty,the non-parametric method is applied to analysis the vibration problems of fluid-conveying thinwalled pipes.The results show for fluid-conveying pipes constrained by clamps at both ends,that the confidence interval of the frequency response curves of the nonparametric model contains that of the mean model perfectly.The higher the frequency,the greater the influence of the uncertainty.For the case of the frequencies as a function of fluid velocity,the confidence interval of the curves of nonparametric model also contain that of the mean model.With the increases of fluid velocity,the influence of the uncertainty on the real part of frequencies becomes smaller while the influence of the uncertainty on the imaginary part of frequencies becomes greater.However,the uncertainty has no effect on divergence and flutter instability.For fluid-conveying thin-walled pipes lying on the uniform elastic foundation,the confidence interval of the critical velocity curves of the nonparametric model contains that of the mean model perfectly.The higher the mass ration,the greater the influence of the uncertainty.6.In order to compare the dynamic response of standard clamps and new clamps in pipeline system,the random vibration test and hydraulic shock test are conducted.The effects of the new clamp on the dynamic characteristics of the pipe were obtained by comparisons of the test data.The result demonstrates that under the random vibration and hydraulic shock environment,the amplitude of the dynamic response of the pipe is significantly reduced when the new clamp constraints are adopted,which confirms the lifting effect of the new clamp on the dynamic characteristics of the pipe.In conclusion,the effects of FG material parameters,random elastic foundation,and the clamps on the dynamic characteristics of fluid-conveying thin-walled pipes are studied.The computational and experimental results in this study might be helpful for the design and applications of pipes conveying fluid.