## 1 Introduction  
High-speed, high-pressure and high power-to-weight ratio are the strategic development direction of modern aircraft hydraulic system, which can reduce the weight and volume of aircraft hydraulic system effectively, but the Fluid-Structure Interaction (FSI) vibration of aircraft hydraulic pipeline will be enhanced at the same time. Moreover, the aircraft hydraulic pipeline system is subjected to superposition effect and coupling action of pressure, temperature, body deformation, vibration, and acceleration loading, which causes the flow state of the fluid in the pipeline to be extremely complicated. For instance, over 21% of about 800 hydraulic pipelines have a higher Reynolds number than the critical Reynolds number of 2320 in all hydraulic pipelines of Advanced Regional Jet for the 21 st Century (ARJ21-700) aircraft developed by Commercial Aircraft Corporation of China Ltd. (COMAC), which shows that turbulence phenomenon exists in the pipelines [1]. When the fluid is in a laminar flow state, the coupling vibration between the fluid and the pipe has been studied extensively. However, the turbulence is a random, unsteady three-dimensional flow with strong nonlinearities, making it hard to obtain a friction model between the fluid and the tube wall. Hence, establishing a more accurate friction model to study FSI vibration characteristics of high-speed high-pressure hydraulic pipelines is of significant theoretical value and practical significance. Numerous researchers have proposed and improved FSI vibration models to investigate the vibration characteristics of hydraulic pipeline. [PERSON] presented water hammer theory, which laid a theoretical foundation for the research of the Fluid-Structure Interaction mechanism of pipeline [2], [PERSON] expanded water hammer theory and given the 4-equation model [3]. [PERSON] and [PERSON] perfected the 4-equation model. Besides, [PERSON] proposed the 8-equation model and solved it using frequency-domain transfer matrix method [4; 5]. [PERSON] presented the 6-equation model without considering poisson coupling [6]. [PERSON] put forward the 14-equation model ignored friction coupling and bound coupling [7]. On the basis of [PERSON]'s 14-equation model, [PERSON] consummated the 14-equation model and verified the effectiveness of this method by testing [8]. [PERSON] and [PERSON] further improved the FSI vibration model, which makes the calculated value more accurate [9; 10]. In addition, various numerical and analytical methods were developed to predict FSI vibration. Frequency-domain transfer matrix method of 14 equation model was discussed and verified in detail by [PERSON] [11; 12]. [PERSON] analyzed the FSI vibration of the pipeline under different support conditions and proposed the 14-equation model based on the elastic support condition [13]. A frequency modeling and solving method considering complex constraints is proposed to analyze the vibrational characteristics of complex pipelines by [PERSON] [14]. Numerous scholars have investigated friction coupling models. The first group of models was given by [PERSON] in 1968, which is applicable for transient laminar flow and has a great calculation precision [15]. In this model, the friction term will be influenced by instantaneous flow acceleration or the past velocity changes. [PERSON] obtained a simplified friction model by adding a weight function into the [PERSON] model, but calculation accuracy of this model is decreased [16]. [PERSON] and [PERSON] postulated that the fluid inside the pipeline split into laminar flow layer and turbulent flow layer and [PERSON] assumed that the fluid inside the pipeline separated into four layers, in order to develop a model that could be applied to a wide range of Reynolds numbers and frequencies [17; 18; 19; 20]. Apart from the models above, another group of empirical formula model was proposed by [PERSON], he thought the shear friction force depended on the velocity of unsteady flow and local instantaneous acceleration [21].