1. Introduction
Pipeline systems are important transmission channels of energy and material in practical engineering applications. Pipelines are connected to each component and need to bear the highest pressure of the system. A pipeline system is mainly composed of a pipeline, clamps, valves, and so on. A pipeline system needs more manpower and material force in its maintenance because of the complex crisscrossed layout and the narrow space between the pipelines. When a pipeline works, it is excited by the pulsating excitation from the pump source and the foundation excitation of the structure. The pipeline resonates when the external excitation frequency is close to the modal frequency of the pipeline. At this point, the pipeline will produce large displacement, resulting in large stress. The action of long-term high stress will cause damage to and the failure of the pipeline. The forms of pipeline failure generally include pipeline collision, wear, burst, noise, and so on. With the development of the modernization of related industries, considering the safety and economy of pipeline systems, the industry has put forward higher requirements for the stability and reliability of pipeline systems. Composite materials are extensively used as key components in aerospace and mechanical engineering sectors owing to their high specific strength and specific stiffness [
1]. The most important problem to improve the stability and reliability of pipeline systems is the vibration of pipelines. Therefore, it is necessary for us to control the vibration of a pipeline using a more effective method.
Researchers have done a lot of research on the vibration of pipelines. Pipeline vibration is mainly due to the coupling effect of the liquid in the pipeline and the coupling vibration between the components in the hydraulic system. According to this vibration mechanism, the most commonly used vibration reduction methods are passive constrained layer damping control (PCLD) and active constrained layer damping control (ACLD). The passive control method pastes some inertia accessories on the structure to achieve the effect of vibration reduction [
2]. Passive constrained layer damping includes a viscoelastic material (VEM) layer and a constrained layer, and the damping capacity is controlled by changing the shear strain of viscoelastic materials [
3]. Gao et al. [
4] established a finite element model of a passive constrained layer damping pipeline under elastic boundary support, and studied the influence of key parameters such as support stiffness, fluid velocity and pressure, the thickness and the elastic modulus of VEM on pipeline vibration. The characteristics of PCLD include the structure being simple and without external energy input. However, the effect of PCLD treatment on low-frequency and large-amplitude vibration is not obvious. Compared with the PCLD technology, the ACLD uses a piezoelectric constraining layer instead of the conventional constraining layer of PCLD. ACLD has a stronger adaptive ability than PCLD. ACLD damping includes the advantages of the ability of passive damping in the high-frequency range and the control active damping in the low-frequency range [
5]. Zhao et al. [
6] adopted active constrained layer damping control for an aero pipeline, and analyzed the transmission of driving force under the harmonic voltage, the influence of control parameters and the structural parameters on pipeline vibration. The research methods of pipeline vibration have matured, and include the Galerkin-type method, the transfer matrix method, the characteristic line method, and the finite element method. Kheirl et al. [
7] used the Galerkin-type method to analyze the stability of a pipeline conveying fluid under flexible support, and verified the simplified motion equation. Li et al. [
8] obtained the analytical solution in the time domain by using the characteristic line method, and the effectiveness of the method was verified by their experiments. Gao et al. [
9] established the three-dimensional finite element modal, and discussed the influence of different voltages, control parameters, and structural parameters on pipeline vibration.
ACLD technology has been used widely in many fields of engineering. As early as 1993, Agnes [
10] proposed the concept of active constrained layer damping. Subsequently, Baz [
11], Shen [
12], Lesieutre [
13], and Liao [
14] optimized and extended the concept and treatment method of active constrained layer damping. The finite element model and vibration control of beams with active constrained layer damping was proposed by Balamurugan [
15]. Sonti [
16] proposed the application of the active constraint layer technique in a shell element model. In recent years, ACLD treatment has been developing steadily. With the development of ACLD treatment, many excellent research results about ACLD have been published at home and abroad [
17,
18,
19,
20,
21].
The parameters of ACLD have a great effect on vibration reduction. Therefore, it is necessary to study the influence of the parameters of ACLD to obtain the optimal value of treatment effect. The paper [
22] investigated the performances of four types of hybrid active-passive constrained layer damping treatment. The changes in parameters between active, passive, and hybrid treatment were studied in paper [
23]. In this paper, the influence of the damping length of the active constrained layer and the thickness of the viscoelastic material on the vibration of beam was obtained. The paper [
24] studied the influence of an ACLD patch for the vibration attenuation of a thin truncated conical shell. Considering the finite element model of an ACLD plate using the modal strain energy method, the location of ACLD was optimized [
25]. In paper [
26], open-loop and closed-loop dynamic models of active and passive constrained layer damping beams were established, and the effect of key parameters such as control gain, VEM thickness, ACLD axial coverage, and position change on the loss factors of beam system were studied in detail. Based on Timoshenko beam theory and the Hamilton principle, the vibration control equation of a beam with distributed internal viscous damping was established in paper [
27], and the frequency equation of the beam was gained by using transfer matrix method. There are some papers [
28,
29,
30,
31] which carried out a further exploration in improving and optimizing the active passive constrained layer damping structure. The purpose of these papers was to select the optimal parameters of an ACLD structure through the research and simulation, so that the vibration performance of the structure can reach the optimal state.
As mentioned above, the authors find that regarding active vibration control, most scholars paid attention to the application of beams and shells, while there are few studies on pipeline systems. Therefore, this is the first time that the vibration of an ACLD pipeline under fixed boundary supports is investigated. Due to the particularity of the pipeline structure and the complexity of the excitation, research on pipeline vibration is very important. So, this paper establishes the finite element model and deduces the dynamic equation of the pipeline. The influence of structural parameters and control parameters on pipeline vibration is discussed.
4. Conclusions
In this paper, the parametric characteristics of the partially covered active constrained layer damping pipeline is discussed. The ACLD pipeline motion equation is derived via the developed finite element method. The finite element method is used to simulate the vibration of the ACLD pipeline, and the results show that the technology can obtain the damping effect of the pipeline. The influence of thickness and the elasticity modulus of viscoelastic layer, the length of ACLD patch, and the voltage applied on the piezoelectric layer is illustrated. The conclusions are as follows.
The best damping capability can be obtained by selecting the elasticity modulus and the thickness of viscoelastic layer. When the variation range of the elasticity modulus is [106, 107] Pa and the thickness is around 1 mm, the pipeline can get the best damping performance. With the circumferential coverage of ACLD increases, the modal loss factors of the pipeline increase steadily.
The length and the location of the ACLD patch have a remarkable influence on the vibration reduction of the pipeline system. Compared the loss factors, the length of ACLD has little effect on natural frequencies. A longer ACLD patch can improve the loss factors dramatically. When the length of ACLD remains unchanged, the number of ACLD divided equally and the location of the ACLD patch also have a great influence on the vibration reduction of the system.
The different voltages applied on the piezoelectric layer also have a significant effect on the vibration reduction of the pipeline. The response of the pipeline first decreases and then increases with the increase in voltage. In terms of economy and high efficiency, 50 V voltage is the best choice. The smaller the base excitation acceleration applied to the pipeline, the better the damping effect of the pipeline. The above conclusions could be used in the design and maintenance of pipeline systems for active vibration control.