Analysis Of Free Vibration Of Piping System Conveying Fluid Based On Isogeometric Method

Piping is a significant ingredient in the industry and has been widely used in many fields,such as aerospace,petrochemical,energy nuclear power and so forth.The dynamic analysis of the piping system has drawn increasing attention in engineering in recent decades.One of the reasons is that the vibration of piping system could make itself broken,bringing damage to piping accessories and impacting on other equipment.Especially in the piping conveying fluid,the changes induced by the uncertainty of the flow state of the fluid inside the piping system have a great influence on the vibration of the system,which can lead to the water hammer,system oscillation and so on.If the piping layout is unreasonable,the low-order natural frequency of the piping system is close to the frequency generated by the exciting force,which could result in resonance and have extremely bad effects on the system.Therefore,it is quite meaningful to analyze the dynamic performance of piping under the reasonable assumptions,proposing the appropriate models and using more accurate and efficient numerical calculation method for theoretical research and engineering applications.Recently,researchers from all over the world have studied the vibration characteristics of the piping systems conveying fluid through theoretical derivation,experiments and numerical simulations.A large quantity of theoretical,experimental and numerical methods have been proposed,and many research results have been obtained.However,difficulties still exist in the study of free vibration of the piping system conveying fluid:(1)In order to improve the accuracy and efficiency of the solution in the analysis of vibration of piping system conveying fluid,it is necessary to establish or select the suitable mechanical models that are consistent with the real situation and are appropriately simplified.(2)The complexity of the structure and layout of the piping system in engineering make it difficult to obtain analytical solutions by theoretical analysis.Generally,numerical calculation methods including the finite element method(FEM),the transfer matrix method(TMM),the differential quadrature method(DQM)and so forth are applied by engineers and researchers to deal with such complicated vibration problems.Finite element method is the most versatile approach among those mentioned methods.To ensure the accuracy of the calculation,refinements in the process of meshing is essential,which spend a large amount of time.Furthermore,this time-consuming work has to be done for several times for obtaining enough precise results.Moreover,Lagrangian polynomials are employed in FEM to build the approximate geometrical description instead of the exact one,making some evitable errors.(3)On the basis of the finite element method,many researchers have proposed the Isogeometric analysis based on the Euler beam model to study the vibration problem of the piping system conveying fluid.The method applies the non-uniform rational B-spline curve to ensure that the geometric shape of piping system do not change after refinements in the modeling.Not only the time cost can be reduced but also can the calculation accuracy be improved.But it does not satisfy the real situation,as the effect of shear on the free vibration of the piping system is neglected.The classical analytical models include beam model,shell model and tube model in the dynamic analysis of piping system in order to simplify the calculation.The influence of fluid on piping is seldom considered,which makes the model have a large deviation from the real condition.For solving above problems,the vibration characteristics of piping system conveying fluid are studied from three aspects: theoretical derivation,numerical simulation and experimental verification.The specific research contents are as follows:(1)Based on Timoshenko beam model,the pipe element model is proposed.The principle of virtual work is used to derive the dynamic differential equation of the piping system conveying fluid,which provides a theoretical basis for the dynamic analysis of the piping system.(2)According to the Hamilton’s principle,the mass matrix and stiffness matrix of discrete systems coped with isogeometric analysis(IGA)are derived.The subspace iteration method is used to calculate the natural frequencies and mode of the discrete system.The calculation and iterative process including modeling and establishment of mass matrix and stiffness matrix are implemented in MATLAB 2014 a.(3)The isogeometric method based on Timoshenko beam model is verified in this paper.The results analyzed by the Timoshenko beam model and the Euler beam model in pipes with different sizes and restrictions are compared.It is found that the model based on the Timoshenko beam is more accurate for the free vibration analysis of elbows.The verification results show that a small number of calculation elements are needed by IGA in the dynamic analysis of the piping system conveying fluid and obtain satisfactory results.This method reduces the calculation error by considering the fluid impact and applying the precise geometric description of the piping system.In this algorithm,the solution efficiency grows rapidly,which has strong practical value in engineering.(4)Based on the isogeometric method,the free vibration of different types of straight pipes and elbows in different restrictions are analyzed to obtain the natural frequencies.The conclusion is that the natural frequencies of piping conveying fluid decrease with the increase of the length of the pipes and he natural frequencies of piping conveying fluid increase when the diameter of the pipes grow.(5)A vibration damping device for piping system based on piezoelectric materials is proposed,and its feasibility is analyzed.The free vibration analysis for the straight pipe,the curved pipe and the piping system conveying fluid before and after the installation of the pipe damping device is finished.The scheme of vibration reduction of piping system conveying fluid is designed,and the vibration reduction device of piping system is applied in the straight pipe,the curved pipe and the piping system,and the corresponding conclusions are obtained.