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Investigation of vibration characteristics for simply supported pipe conveying fluid bymechanical spring
Abstract
Finite element analysis was used in this study to analyse dynamically the stability of a pipe which is stiffened by linear spring and conveying an internal flow of fluid. Several effective parameters play an important role in stabilizes the system, such as stiffness addition. The effect of stiffness addition (linear spring) and effect of spring location with different diameter ratio were studied. Also, effect of the velocity of flowing on the dynamic stability of the system was taken into the consideration. There is a spring constant at which the dynamic behaviour becomes more sensitive and the spring offers best results for frequency of the system. Results show that the best spring's locations depend on the spring's constant and velocity of flowing.
... Thus, the analytical work included drive for the general equation of motion and solved its equation for simply supported pipe, and then, comparison the results calculated with experimental results calculated. After this, at 2018 S. N. Alnomani, [12], the finite element method used in this study was utilized to analyze the dynamic stability of the fluid-carrying pipe, which was changed in stiffness by the internal flow of the fluid and by the linear spring. Multiple effective parameters of great importance that play a key role in determining the stability, for example, the effect of location for the spring along the pipe in different locations and the effect of increased linear stiffness of the spring and the study of the proportion of diameters as well. ...
In spite of this widespread and critical importance of fluid conveying pipes, they suffer from major problems. One of these problems is the problem of vibrations that cause the collapse of the systems completely and cause significant economic losses if not avoided. Where, fluid conveying pipes are used in all hydraulic systems and enter in all industrial fields, such as water, petroleum products and gases of all kinds. For this reason, the researchers have dealt with this issue in all years, but the problem is not over. This research will highlight the problem of controlling the vibrations resulting from fluid flow inside the pipes, in addition to the study of reducing the vibrations of these pipes. This study is carried out by deriving differential equations for pipes and for different types of fixation. The research has studied the response and the natural frequency; the dynamic behavior of different types of stabilization of the pipes in the presence with no hydraulic damping (active control); and monitoring the response and stability of each case of stabilization. Where, in this paper using root locus technique to calculate the control for pipe conveying fluid. Thus, the investigation included calculated the effect for different damper parameters and fluid on the pipe stability. There, this work is expansion for previous study investigated the control for pipe vibration with using other stability and control theories, and comparison for presenting results with previous results, therefore, form comparison results found that the loot locus technique is a good technique can be using to investigation the stability and control for pipe fluid.
Keywords • fluid and thermal induced vibration • natural frequency • thermal loads • pressure • elastic foundation • finite element method Abstract The article aims to establish a coupled thermo-hydraulic numerical model for calculating the first natural frequencies and the first critical velocity corresponding to the appearance of buckling in the first mode, known as static instability of a hot fluid-conveying pipe. The circulating hot fluid has flexional motion as that of pipe structure. A dynamic characteristic of a pipe conveying internal fluid undergoes mechanical load due to the inertia effect of fluid, Coriolis effect, fluid kinetic force due to fluid flow velocity, dynamic load due to inertia effect, and thermal load due to hot fluid. A numerical modal analysis is realised in the fluid-structure interaction configuration. One-dimensional beam finite element is used for investigating the dynamic behaviour of the thin pipe, where the beam type has two degrees of freedom per node. According to the approved method, different elementary matrices are extracted, which are included into Matlab ®. Results are compared with those predicted by analytical , numerical, and experimental methods. Results are presented for cases: pinned-pinned pipe conveying fluid without foundation; with elastic foundation by Winkler-model; with pressure force, for varying values of fluid velocity and thermal effect. The study shows that increase in temperature negatively affects the stability of the system, as the critical velocity of the fluid decreases regularly and corresponds to the decrease in the frequencies. Ključne reči • fluid i toplotno izazvane vibracije • sopstvene frekvencije • termičko opterećenje • pritisak • elastičan oslonac • metoda konačnih elemenata Izvod Cilj rada je formulisanje spregnutog termohidrauličnog numeričkog modela za proračun prvih sopstvenih frekven-cija i prve kritične brzine koje se odnose na pojavu izvijanja u prvom modu, što je poznato kao statička nestabilnost cevo-voda sa toplim fluidom. Topli fluid koji protiče se pomera fleksiono kao i cevovodna konstrukcija. Dinamička karakte-ristika cevi kojom se transportuje fluid podrazumeva: meha-ničko opterećenje usled inercije fluida; uticaj Koriolisove sile; kinetičko opterećenje usled brzine kretanja fluida; dina-mičko opterećenje usled inercije; i termičko opterećenje usled toplog fluida u cevovodu. Urađena je numerička modalna analiza interakcije fluid-konstrukcija. Primenjen je konačni element jednodimenzionalnog nosača za određivanje dina-mičkog ponašanja tanke cevi, gde tip nosača ima dva stepena slobode u čvoru. Shodno datom postupku, dobijene su razli-čite elementarne matrice, koje su unete u Matlab ®. Rezultati su upoređeni sa rezultatima dobijenim analitički, numerički i eksperimentalno. Rezultati su predstavljeni za slučajeve: cev za transport fluida sa dva nepokretna oslonca bez pod-loge; sa elastičnom podlogom po Winkler modelu; sa silom pritiska, za promenljive brzine fluida i sa termičkim uticajem. Istraživanje pokazuje da porast temperature utiče negativ-no na stabilnost sistema, dok kritična brzina fluida redovno opada i odgovara opadanju frekvencija.
The influence of anchors on transient cavitating flow was not dealt with in detail, though there are limited studies on the effect of support on water hammer. This paper presents an experimental investigation into the influence of spacing of fixed anchors on the cavitation pressure generated in transient cavitating flows. The change in the fluid characteristics was studied along with the change in vibration of piping system. The study reveals that the occurrence of cavitation and resulting cavitation pressure are extremely influenced by the spacing of fixed anchors. As the spacing of fixed anchors is reduced; the cavitation pressure during a transient cavitating event increases severely without any change in other flow conditions while the acceleration induced on the pipe gets decreased drastically. Hence, the spacing of anchors in any piping system should be decided by balancing the lateral acceleration of the piping system and the pressure rise due to cavitation.
In this paper, the equations are discretized with standard finite element method (FEM), and are generalized to analyse the free vibration problem of clamped-clamped pipes carry-ing fluid flow with several parameters. The flow circulating has the flexional motion as that of pipe structure. We devel-oped a program under Matlab. The advantage of Matlab language by using standard functions is to present the first proper-modes of the system aspect interaction fluid-struc-ture for different parameters in complex planes. The numer-ical approach is based on some research and analytical models. Numerical results show the effect of mass ratio, length, pressure force and Winkler elastic foundation on instabilities regions and static instability range.
This paper deals with the mathematical model and Computational analysis of flow induced vibration of Rocket Engine Test Facility. In this set up, the main components of piping elements which causes vibration is angle type valve. Experimental study and analysis of flow induced vibration is to be carried out by study the effect of turbulence of gas flow in the piping system during the course of sub cooling of flight static fire test or flow trial. Mathematical Model of pinned-pinned pipe carrying fluid has been developed. Governing Equation of motion for pipe conveying fluid of real system has been derived. The critical fluid velocity has been calculated by analytical approach. The vibration structure of pipeline is modeled by using CATIA software as per specifications and the effect of turbulence of gas flow in the piping element is analysed by using Fluent and ANSYS software. The main piping element which causing Flow Induced Vibration is angle type valve. Analytically and computationally the dynamic behavior of fluid flow through this valve is studied. Modal Analysis has been carried out and found the natural frequency of six mode shape. Experimental studies/flow trials are to be carried out to validate the analytical and computational results.
The stability of fluid conveying welded pipe is of practical importance because the welding induced residual stresses which
affected on the vibration characteristics and stability. This paper deals with the vibration and stability of straight pipe made
of ASTM-214-71 mild steel, conveying turbulent steady water with different velocities and boundary conditions, the pipe
was welded on its mid-span by single pass fusion arc welding with an appropriate welding parameters. A new analytical
model was derived to investigate the effects of residual stresses at girth welds of a pipe on the vibration characteristics and
stability. The reaction components of the residual stresses at a single pass girth weld in a pipe was used in combination with
a tensioned Euler-Bernoulli beam and plug flow model to investigate the effect of welding on the vibration characteristics of
a pipe. The stability is studied employing a D-decomposition method. A finite element (FE) simulation was presented to
evaluate velocity and pressure distributions in a single phase fluid flow. A coupled field fluid-structure analysis was then
performed by transferring fluid forces, solid displacements, and velocities across the fluid-solid interface. A prestressed
modal analysis was employed to determine the vibration characteristics of a welded pipe conveying fluid. Experimental
work was carried out by built a rig which was mainly composed of a different boundary conditions welded pipes conveying
fluid and provided with the necessary measurement equipments to fulfill the required investigations. It has been proven
theoretically and experimentally that the residual stresses due to welding reducing natural frequencies for both clampedclamped
and clamped-pinned pipe conveying fluid. Also, we proved that for small fluid velocity (sub-critical), the clamped-clamped
and clamped-pinned welded pipes conveying fluid are stable. For relatively high fluid velocities (super-critical) the
clamped-pinned welded pipe loses stability by divergence.
Increasing advances in materials engineering and cost reduction in their testing have lead to the study of the stability of vibration of pipes conveying fluid an important problem to deal with. Currently, such analysis is done either by means of simulation with costly specialized software or by making laboratory tests of the selected material. One of the main issues with the last process is that if appears any trouble on the material selection, it is necessary to restart all the process, and it is happening each time there is a mistake on the material selection. In order to avoid such costly tests, a general mathematical description of the dynamic behavior of a clamped-pinned pipeline conveying fluid is presented. The system stability has been studied by means of the eigenvalues of a Hamiltonian linear system associated. From this analysis, characteristic expressions dependent on material constants have been developed as inequalities, which ensure the stability of the material if it matches all expressions. Finally, some specific materials are introduced as study cases to compare the mathematical description proposed with the results obtained from specialized software as ANSYS, in order to validate the results.
In this study, the natural frequency of a simply supported pipeline (hinged type) conveying one-dimension incompressible steady fluid flow set on viscoelastic foundation is investigated by using finite element analysis and the critical fluid velocity with different parameters such as stiffness and viscous coefficients of foundation are obtained. The foundation is simulated using the modified Winkler's model to introduce the effect of time dependent viscosity term. Some known results are confirmed and some new ones obtained. Two components of foundation, stiffness and viscosity, seemed to act on the critical flow velocity of the pipe in contrary trend. Where, increasing the foundation stiffness tended to increase the critical flow velocity in the pipe. While, increasing foundation viscosity attempted to decrease it. At some ranges of pipe length, the foundation viscosity effect seems to be more extreme. Increasing the fluid velocity leads to monotonic reduction in the system damping ratio. Two parameters, pipe length and fluid density which relate to the natural frequency of pipeline conveying fluid are studied in detail and the results indicate that the effect of Coriolis force on natural frequency is become more effective by increasing pipe length and fluid density besides increasing fluid flow velocity.
The first of two books concentrating on the dynamics of slender bodies within or containing axial flow, Fluid-Structure Interaction, Volume 1 covers the fundamentals and mechanisms giving rise to flow-induced vibration, with a particular focus on the challenges associated with pipes conveying fluid. This volume has been thoroughly updated to reference the latest developments in the field, with a continued emphasis on the understanding of dynamical behaviour and analytical methods needed to provide long-term solutions and validate the latest computational methods and codes.
The aim of this study is to clarify the discrepancy regarding the critical flow speed of straight pipes conveying fluids that appears to be present in the literature by using the Generalized Differential Quadrature method. It is well known that for a given “mass of the fluid” to the “mass of the pipe” ratio, straight pipes conveying fluid are unstable by a flutter mode via Hopf bifurcation for a certain value of the fluid speed, i.e. the critical flow speed. However, there seems to be lack of consensus if for a given mass ratio the system might lose stability for different values of the critical flow speed or only for a single speed value. In this paper an attempt to answer to this question is given by solving the governing equation following first the practical aspect related to the engineering problem and than by simply considering the mathematics of the problem. The
Generalized differential quadrature method is used as a numerical technique to resolve this problem. The differential governing equation is transformed into a discrete system of algebraic equations. The stability of the system is thus reduced to an eigenvalue problem. The relationship between the eigenvalue branches and the corresponding unstable flutter modes are shown via Argand diagram. The transfer of flutter-type instability from one eigenvalue branch to another is thoroughly investigated and discussed. The critical mass ratios, at which the transfer of the eigenvalue branches related to flutter take place, are determined.
In this paper, the nonlinear planar dynamics of a vertical cantilevered pipe conveying fluid are explored, in the presence of an intermediate spring support, by means of a two-degree-of-freedom Galerkin discretization of the flexible system. The stability of the original equilibrium is examined first, and the regions in the parameter space where the system is stable or loses stability by divergence or flutter are determined. Then, by examining the nonlinear equations of motion, the stability of the other fixed points that emerge with increasing flow velocity is studied, for various system parameters, revealing a very rich bifurcational behaviour. The nonlinear dynamics is also studied in the vicinity of various bifurcations by means of centre manifold theory and normal form reduction, as well by numerical simulation, in the vicinity of picthfork, Hopf and double degeneracy bifurcations; local and global behaviour are explored. Finally, the dynamics in the presence of harmonic perturbations in the flow is investigated numerically in the neighbourhood of the double degeneracy, where heteroclinic orbits arise, and chaotic regions are shown to exist.
In-plane and out-of-plane motions of a semi-circular pipe conveying fluid are analyzed in this paper. Assuming that the centerline of the semi-circular pipe is extensible, nonlinear equations of in-plane and out-of-plane motions are derived according to the extended Hamilton principle. The Lagrange nonlinear strain theory and the Euler–Bernoulli beam theory are used to derive the equations. The derived equations of motion are discretized by applying the Galerkin method. Linearized equations around the equilibrium position are obtained from the discretized equations, and then the dynamic characteristics of the pipe are investigated. In addition, some modelling issues, which are related to the nonlinearity of the circumferential strain and stress, are discussed. This study finds that a semi-circular pipe conveying fluid does not lose stability even at a high fluid velocity. Although a model using the Lagrange nonlinear strain and the corresponding nonlinear stress yields the most accurate computational results of the natural frequencies, a model using the Lagrange strain and a linearized stress is recommended to compute the natural frequencies efficiently while still maintaining accuracy.
This paper deals with the effect of an intermediate lateral spring support on the stability of a cantilevered tubular pipe conveying fluid. The governing equation of motion is cast into a matrix form by applying the Galerkin method. In the flutter analysis the material damping is taken into account. Comparisons are made between the theoretical and experimental results. It is shown that providing the cantilevered pipe with a spring support does not necessarily lead to stabilization and indeed is likely to have a destabilizing effect. In respect to its location a spring support at the free end may be most destabilizing. The stabilizing effect due to a spring can be caused by transition of the instability mechanism from flutter to divergence.
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