МЕТОД ФУНКЦИИ ГРИНА В ИССЛЕДОВАНИИ ДИНАМИЧЕСКОЙ УСТОЙЧИВОСТИ ТРУБОПРОВОДА, ТРАНСПОРТИРУЮЩЕГО ЖИДКОСТЬ

Аннотация


Fluid-conveying pipes represent a fundamental dynamic problem within the realm of fluid-structure interaction. They find extensive applications in various industries, including petroleum, nuclear engineering, aviation, aerospace, and nanostructures. This paper applies the Green’s function method to solve the stability problem of a fluid-conveying pipe, hinged at both ends and supported by intermediate linear-elastic supports. The objective is to examine the influence of the number and rigidity of these supports on the critical fluid velocity, which is the velocity at which the pipe loses stability. A numerical solution was performed for a straight pipe conveying fluid with specified geometric and physical characteristics, where the number and rigidity of the elastic supports were considered as parameters. The numerical analysis presented herein includes graphs illustrating the dependence of the critical fluid velocity on the number of elastic supports for varying support rigidities. These results reveal that the elastic supports affect both the vibrational characteristics and the critical velocity of the conveyed fluid. The solution results are compared with those obtained using one of the most widely employed methods for analyzing the dynamic stability of pipe systems (Transfer Matrix Method – TMM). A good agreement between the results is observed. The paper aims at presenting a method for obtaining the exact solution to the differential equation governing the lateral displacements of a pipe system. This paper discusses the authors' perceived pros and cons of the Green's function method in comparison to the most popular methods for the dynamic investigation of fluid-conveying pipes.

Полный текст

Fluid conveying pipes represent a fundamental challenge in the field of fluid-structure interaction. The issue of dynamic stability of such structures has garnered significant attention in both scientific research and industry. Given that fluid-flowing pipes are integral components in numerous engineering facilities and serve as a primary means of transporting oil and gas, the stability of these pipes is of paramount importance. The loss of stability in a pipe can result in damages that have far-reaching consequences on the economy, the environment, and the well-being of the population. M. P. Paidoussis is a distinguished scientist renowned for numerous publications in the field of fluid-structure interaction. His research, particularly focused on the interaction between flowing fluids and pipes, is extensively discussed in [1] and [2]. In their works [3] and [4], R. Gregory and M. P. Paidoussis present numerical studies and results from experiments conducted on the dynamic stability of cantilevered pipes with flowing fluid. In [5], an approach is presented for determining the circular frequencies and oscillations of a pipe conveying fluid. The transverse displacements of the pipe axis are also calculated. Additionally, [6] explores the vibrations of a pipe with a transverse linear elastic support. A recent study on fluid-conveying pipes was conducted in [44]. Using the Euler-Bernoulli model, the authors investigated the stability of a pipe resting on a two-parameter elastic foundation, considering various boundary conditions. The Differential Transform Method was employed in the analysis. The results indicate that the elastic foundation has a stabilizing effect on the system, and increasing the foundation parameters leads to an increase in the system's critical velocity. In a further recent investigation [45], the dynamic stability of a cantilevered pipe subjected to a lateral distributed load was analyzed. The Differential Quadrature Method was utilized in the analysis. Ding and Ji [46] present a comprehensive review of the latest research in the field of vibration control for fluid-conveying pipes. The broad applicability of nanoscale tubes across various scientific and industrial domains has sparked considerable research, as demonstrated in [9-16] and more recently in [47-49]. To overcome the complexities and expenses of nanoscale experiments, fluid-structure interaction in carbon nanotubes is frequently studied using continuum elastic models, such as Euler and Timoshenko beam theories. Curved pipes represent another area of fluid-structure interaction. Research in this area has been conducted in [33-38]. Other aspects of the problem of fluid-conveying pipe dynamic stability include pipes under thermal loads [26], [27], submerged pipe systems [19-21], and pipes made of viscoelastic materials [23]. Common methods for dynamic analysis of fluid-conveying pipes include the Finite Element Method (FEM), the Transfer Matrix Method (TMM) [39], and the Generalized Differential Quadrature Method (GDQM). However, this paper proposes a different approach by suggesting the use of the Green’s Function Method to solve the stability problem. The objective is to demonstrate that this method can be competitive with the well-established techniques mentioned earlier in the dynamic stability investigations of fluid-conveying pipes. The study in this paper focuses on a fluid-conveying pipe supported by linear elastic springs. The results obtained shed light on the relationship between the critical fluid velocity and the rigidity, as well as the number of elastic supports. The critical fluid velocity is the speed at which the flowing fluid leads to the loss of stability in the pipe. The paper is structured as follows: first, we present the model of the pipe, including its static scheme, and the governing differential equation for eigen lateral vibrations. Second, we employ the Green’s function method to solve the problem, demonstrating the derivation of the frequency equation of the system. Conclusions about the system's stability can be drawn based on the roots of this equation. Finally, we present the results obtained from the numerical solution and summarize several key conclusions. To verify the results, they are compared to numerical results obtained using the Transverse Matrix Method for the same system. Furthermore, we offer our perspective on the key advantages and disadvantages of the Green’s function method compared to other methods for the dynamic investigation of pipe systems.

Об авторах

Д. С Лолов

Университет архитектуры, строительства и геодезии, София, Республика Болгария

С. В Лилкова-Маркова

Университет архитектуры, строительства и геодезии, София, Республика Болгария

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© Лолов Д.С., Лилкова-Маркова С.В., 2025

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