## 1 Introduction  
The hydraulic pipeline is considered the \"blood vessel\" of mechanical equipment used for hydraulic transmission. Its function is to transmit power and energy. Meanwhile, the pipeline system with excellent mechanical properties and a reasonable structure can also absorb the pressure pulsation in the hydraulic system [1]. These functions are particularly important in aviation equipment. \"High speed, high pressure and high power to weight ratio\" is one of the main development directions in the aviation hydraulic system and mobile machines [2]. Meanwhile, it also entails greater requirements for the stability and reliability of the hydraulic pipeline system. Due to the high speed and high pressure, as well as the complex spatial structure of the pipeline, the vibration mechanism for the aviation hydraulic system is complex, making vibration control more difficult [3]. Many scholars have conducted a lot of research on the vibration control of hydraulic systems. According to the mechanism, vibration control in the hydraulic pipeline includes passive control and active control. Passive control is realized by installing dampers, vibration absorbers, attenuators, and sticking damping materials. [PERSON] [4] studied the vibration absorption of a functionally graded materials fluid-conveying pipe coupled with NiTiNOL-steel, and the effects of structure parameters on the absorption performance. The results show that NiTi-steel is an effective means of vibration absorption. [PERSON] [5] designed a magnetic interaction-based vibration absorber for continuous beams, which has a significant role in the vibration suppression of continuous structures. [PERSON] [6] investigated the effectiveness of passive vibration suppression for an FSI system using a nonlinear energy sink. [PERSON] [7] proposed a vibration control method for the typical pipelines used in armored vehicles by changing the pipe diameter, bending the radius, and increasing the pipeline branches, etc. [PERSON] [8] used a beam-based dynamic vibration absorber (beam DVA) to analyze pipes with different sizes of harmonic excitation at different frequencies, which showed that the mass ratio and stiffness ratio, respectively, have the highest and lowest impact on pipe vibration absorption. Based on the sensitivity analysis method and the Pareto optimal multi-objective genetic algorithm, [PERSON] [9] optimized the parameters for the pipeline support and proposed an optimization method for the passive vibration control parameters in the aviation hydraulic pipeline. Although passive control has a clear damping mechanism, a simple structure, and easy implementation, its control frequency range is narrow, the effect of damping low-frequency vibration is limited, and the control parameters are not variable. Active control acquires vibration signals through sensing elements, obtains control signals through control algorithms, and applies them to actuators to achieve vibration control in the pipeline system. [PERSON] [10] designed a piezoelectric direct drive spool valve that could adjust the parameters with the adaptive optimal control method to reduce the pressure pulsation amplitude to a low level. [PERSON] [11] studied a noninvasive structure controller composed of piezoelectric laminated actuators. And the experiment proved that the controller could achieve around 20 dB of attenuation in the dominantly radiating modes. [PERSON] [12; 13] proposed an active constrained layer damping (ACLD) system with piezoelectric materials, with the aim of investigating the vibration and damping effect of an ACLD pipeline under fixed support. Active control technology has good characteristics for pipeline vibration and a good vibration suppression effect for low-frequency vibration, but its control algorithm is relatively complex, and the parallel structure makes the fluid flow state more complicated.