Abstract:In this paper, the Euler-Bernoulli beam model is used to predict the structural instability of rotating cantilever tubes conveying fluid and subjected to uniform distributed tangential compressive load. The governing equation of motion and boundary conditions of the system are derived using the Hamilton's principle. Then, Galerkin method is applied in order to transform the resulting equation into a general eigenvalue problem. The present analysis is validated by comparing the results with those available in l… Show more
“…Unexpected pipelines vibrations caused by various external and internal factors limit their application. Therefore, the vibration of pipelines has attracted the attention of a number of scientists and is still of interest (Andrzej and Jan, 2012;Paı €doussis, 2008;Karimi-Nobandegani et al, 2016;Jan and Andrzej, 2014;Siba et al, 2016;Kuiper et al, 2007;Chen and Jian, 2015;Marco et al, 2002;Xia et al, 2018;Zhi-Yuan et al, 2018;Kheiri, 2020;Jiang et al, 2020;Li et al, 2020a, b).…”
Section: Introductionmentioning
confidence: 99%
“…Unexpected pipelines vibrations caused by various external and internal factors limit their application. Therefore, the vibration of pipelines has attracted the attention of a number of scientists and is still of interest (Andrzej and Jan, 2012; Païdoussis, 2008; Karimi-Nobandegani et al. , 2016; Jan and Andrzej, 2014; Siba et al.…”
PurposeThe purpose of this study is to create a mathematical model, a numerical algorithm and a computer program for studying the vibration of composite pipelines based on the theory of beams used in the oil and gas industry, agriculture and water management, housing and communal services and other areas.Design/methodology/approachA mathematical model of vibration of a viscoelastic pipeline based on the theory of beams with a pulsating fluid flowing through it was developed. Using the Bubnov-Galerkin method, based on the polynomial approximation of deflections, the problem is reduced to the study of systems of ordinary integro-differential equations, the solution of which is found by a numerical method. A computational algorithm was developed for solving problems of vibrations of composite pipelines conveying pulsating liquid.FindingsThe stability and amplitude-time characteristics of vibration of composite pipelines with a pulsating fluid flowing in it are studied for wide range of changes in the parameters of deformable systems and fluid flow. The critical velocities of fluid flow at which the viscoelastic pipe loses its rectilinear equilibrium shape are found. The effect of singularity in the kernels of heredity on the vibrations of structures with viscoelastic properties was numerically studied. It is shown that with an increase in the viscosity parameter of the pipeline material, the critical flow velocity decreases. It was determined that an increase in the value of the fluid pulsation frequency and the excitation coefficient leads to a decrease in the critical velocity of the fluid flow. It was established that an increase in the parameters of the Winkler foundation and the rigidity parameter of the continuous layer leads to an increase in the critical flow velocity.Originality/valueThe study of the vibration of pipelines made of composite materials is of great theoretical and applied interest. The solution to this problem is an effective application of the theory of viscoelasticity to real processes. Therefore, the methods and problems of pipeline vibrations attract much attention from researchers. This study is devoted to solving the above problems and therefore its subject is relevant. The paper considers the results of numerical simulation of the processes of vibration of a composite pipeline based on the theory of shells during the flow of a pulsating liquid through it. A mathematical model of vibration of a composite pipeline was developed. A computational algorithm was developed for solving problems of vibrations of composite pipelines conveying pulsating liquid.
“…Unexpected pipelines vibrations caused by various external and internal factors limit their application. Therefore, the vibration of pipelines has attracted the attention of a number of scientists and is still of interest (Andrzej and Jan, 2012;Paı €doussis, 2008;Karimi-Nobandegani et al, 2016;Jan and Andrzej, 2014;Siba et al, 2016;Kuiper et al, 2007;Chen and Jian, 2015;Marco et al, 2002;Xia et al, 2018;Zhi-Yuan et al, 2018;Kheiri, 2020;Jiang et al, 2020;Li et al, 2020a, b).…”
Section: Introductionmentioning
confidence: 99%
“…Unexpected pipelines vibrations caused by various external and internal factors limit their application. Therefore, the vibration of pipelines has attracted the attention of a number of scientists and is still of interest (Andrzej and Jan, 2012; Païdoussis, 2008; Karimi-Nobandegani et al. , 2016; Jan and Andrzej, 2014; Siba et al.…”
PurposeThe purpose of this study is to create a mathematical model, a numerical algorithm and a computer program for studying the vibration of composite pipelines based on the theory of beams used in the oil and gas industry, agriculture and water management, housing and communal services and other areas.Design/methodology/approachA mathematical model of vibration of a viscoelastic pipeline based on the theory of beams with a pulsating fluid flowing through it was developed. Using the Bubnov-Galerkin method, based on the polynomial approximation of deflections, the problem is reduced to the study of systems of ordinary integro-differential equations, the solution of which is found by a numerical method. A computational algorithm was developed for solving problems of vibrations of composite pipelines conveying pulsating liquid.FindingsThe stability and amplitude-time characteristics of vibration of composite pipelines with a pulsating fluid flowing in it are studied for wide range of changes in the parameters of deformable systems and fluid flow. The critical velocities of fluid flow at which the viscoelastic pipe loses its rectilinear equilibrium shape are found. The effect of singularity in the kernels of heredity on the vibrations of structures with viscoelastic properties was numerically studied. It is shown that with an increase in the viscosity parameter of the pipeline material, the critical flow velocity decreases. It was determined that an increase in the value of the fluid pulsation frequency and the excitation coefficient leads to a decrease in the critical velocity of the fluid flow. It was established that an increase in the parameters of the Winkler foundation and the rigidity parameter of the continuous layer leads to an increase in the critical flow velocity.Originality/valueThe study of the vibration of pipelines made of composite materials is of great theoretical and applied interest. The solution to this problem is an effective application of the theory of viscoelasticity to real processes. Therefore, the methods and problems of pipeline vibrations attract much attention from researchers. This study is devoted to solving the above problems and therefore its subject is relevant. The paper considers the results of numerical simulation of the processes of vibration of a composite pipeline based on the theory of shells during the flow of a pulsating liquid through it. A mathematical model of vibration of a composite pipeline was developed. A computational algorithm was developed for solving problems of vibrations of composite pipelines conveying pulsating liquid.
“…It can be understood from their consequences that, unlike the fundamental vibrational frequency, the second natural frequency of the system descends by ascending the fluid velocity. Cantilevered rotating tubes containing flow subjected to distributed tangential loads are modeled by Karimi-Nobandegani et al 15 They illustrated that higher values of the mass ratio of the system yield higher transverse vibrational frequencies.…”
In the present investigation, with the aim of performance improvement of size-dependent bi-gyroscopic structures, the vibrational behavior of spinning small-scale tunes conveying fluid embedded in various foundations subjected to distributed tangential load and hygro-thermo-magnetic environments by including gravitational effect is investigated. The modified couple stress theory is used to study the microscale tube, and the modified nonlocal theory is utilized to model the nanoscale tubes. A parametric investigation is also conducted to highlight the impacts of various key factors such as gravity, flow profile modification factor, fluid velocity, spinning speed, substrate coefficients, boundary conditions, size-dependent parameters, and environmental attacks on divergence and flutter thresholds of the structure. The dynamical equations are solved using Laplace transformation as well as Galerkin discretization techniques, and forward and backward frequencies are identified accordingly. Meanwhile, the instability borders of the system are obtained analytically. Campbell and stability diagrams, and the time history of the system, are acquired. The results revealed that contrary to influences of gravity, magnetization, and size-dependent parameters, the compressive tangential load and humidity have decreasing effects on the vibrational frequencies and make the system prone to experience static and dynamical instabilities. Moreover, it is determined that applying the viscous foundation eliminates the re-stabilization zone in the system stability evolution, and after the occurrence of the divergence phenomenon, the system immediately undergoes the flutter instability.
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