# Influence of Dry Friction on the Dynamics of Cantilevered Pipes Conveying Fluid
## 1 Introduction  
Pipes conveying fluid have played an important role in aerospace, marine engineering, and the nuclear industry. For example, refueling aircraft through aviation refueling pipes will cause flow-induced vibrations of the pipe at higher flight speed, which will affect the practical application of pipes conveying fluid. The exploration and collection of deep-sea oil and gas require the use of kilometer-long pipes [1; 2]. Under the excitation of the internal and external flows, the pipe may vibrate and deform greatly. During vibration, harsh and harmful noise may be generated and the pipe system tends to be fatigued and damaged, which may cause economic losses and serious safety accidents [3]. Therefore, the dynamic analysis and vibration control of pipes conveying fluid have attracted much attention [4; 5; 6; 7]. [PERSON] et al. [8; 9; 10] reviewed the dynamical behavior of pipes conveying fluid under different boundary conditions and pointed out that a cantilevered pipe would be subjected to flutter instability when the internal flow velocity becomes sufficiently high. For heat-exchange bundle structures existing in the nuclear industry, beyond the onset of flutter instability, the pipe would be subjected to periodic motion and might contact the surrounding supporting plates or pipes [11; 12; 13]. In this case, the effect of contact and possible dry friction between the pipe and the surrounding structures may be pronounced. Therefore, it is inevitable to study the dynamical behavior of pipes conveying fluid with dry friction. In the past decades, many scholars have tried to establish nonlinear dynamical models for the basic system of pipes conveying fluid. For instance, [PERSON] et al. [14] derived the governing equations of straight pipes conveying fluid from different perspectives, which makes the longitudinal and transverse displacements of supported pipes be coupled with each other. [PERSON] et al. [15] were focused on the application of Timoshenko beam theoryunder supercritical conditions and showed that their theory is more advantageous at higher flow velocity. [PERSON] et al. [16] studied the flutter velocity and dynamical behavior of a fluid-conveying pipe under distributed random excitation. On the other hand, dry friction is a typical nonlinear force, which belongs to contact nonlinearity, and it is usually characterized by piecewise linearity [17; 18; 19]. Dry friction can generate damping in some cases and was also used in the manufacturing of brake pads [20] and clutches [21]. As one of the notable works on dry friction, [PERSON] et al. [22] applied dry friction to the support section of a simply supported beam. By using a refined model, the elastic deformation in the tangential direction of the friction surface was considered. [PERSON] et al. [23] performed a mode analysis of a beam with both ends supported under dry friction by using constraint conditions and Lagrange multipliers. [PERSON] et al. [24] studied the dynamical behavior of a mass system under dry friction and analyzed the influence of the different parameters of dry friction on the equilibrium position of the mass system. In this study, the stability and dynamic responses of a cantilevered pipe conveying fluid with a dry friction constraint somewhere along the length of the pipe is explored. It should be mentioned that, to the authors' knowledge, this may be the first study dedicated to the application of dry friction in non-conservative continuum system such as a cantilevered pipe conveying fluid. The equation of motion of the pipe system with dry friction is derived through the generalized Hamilton's principle. From a perspective of vibration control [25; 26; 27; 28; 29], by taking advantage of the energy-consumption characteristic of the dry friction, the dry friction is also expected to be effective at adjusting/controlling the stability and dynamics of the system of pipes conveying fluid. This paper is organized as follows.