# Wave Propagation in Laminated Cylinders with Internal Fluid and Residual Stress
## 1 Introduction  
Fluid-filled cylinders are components in a variety of systems such as chemical, petrochemical, gas, hydraulic, offshore plants and the human cardiovascular system. The simulation of their dynamic behaviour, together with the diagnosis of their structural health conditions, are important for design, safety, economic, environmental and medical reasons. Numerical prediction of wave propagation in cylindrical structures, both _in-vacuo_ and fluid-filled, provides information that is essential in many applications such as dynamics and shock response, noise transmission, material characterisation, non-destructive testing (NDT) and structural health monitoring (SHM). The prediction of waves that can propagate over long distances with low attenuation, together with their interaction with defects and inclusions, is fundamental for the implementation of ultrasonic guided wave techniques, which are commonly used for damage detection and long-range inspection of pipes, e.g., [1]. Characterisation of wave propagation in pipes, including fluid-structure interaction, is also important to detect failure or to predict noise propagation and fluid leakage in pipes. In [2], for example, theoretical and experimental results for noise and vibration propagation in a polyethylene pipe were presented. When leakage in a pipe occurs, acoustic waves are generated and propagate to both ends of the pipe, and their measurement is used to detect and locate leaks. These techniques are widely used for leak detection in buried pipes and benefit from an understanding ofwave propagation characteristics [3]. In [4], for example, a computational-fluid-dynamic simulation was used to model wave propagation in gas pipelines for leak detection, while in [5] the pressure wave velocity in fluid-filled pipes was analysed to detect solid deposits in pipes, which might need to be prevented or removed, especially in oil pipelines. As a further example, the prediction of pressure waves, including fluid-structure interaction, was investigated in [6] for the diagnosis of cladding failure of a nuclear fuel rod. Fuel rod cladding failure generates a pressure wave in the coolant fluid flowing around the fuel rod, which can be detected by a system of sensors, whose design depends on the precise understanding of wave propagation around the fuel rod. Simulation of wave propagation in human arteries can also indicate the physiological state of the cardiovascular system [7]. In particular, pressure wave propagation in the arterial system can indicate cardiovascular risk [8]. Although simplified models are typically assumed, the construction and dynamic behaviour of arteries is complicated, and refined models are required to both improve diagnostic techniques and develop a new generation of vascular prostheses. In [9], for example, segments of the aorta were modelled as laminated cylindrical shells, including residual stresses, while in [10] a 3D fluid-structure interaction model of the arteries was studied and results compared with simpler 1D and rigid wall models. Since [PERSON]'s pioneering work [11], numerous researchers have studied wave propagation in fluid-filled cylinders, as reviewed in the book by [PERSON] [12]. Although there is an extensive literature, the assumptions generally used to model flexible cylinders with an internal fluid often restrict the analysis to the so-called thin-wall theory and to beam-like motion of the pipe. Developing a continuum model in the framework of elasticity theory, including fluid-structure interaction (FSI), is a challenging task. Therefore, theoretical studies are often based on simplifying assumptions and approximations, resulting in an upper-frequency limit of applicability. In order to properly study elastic and acoustic wave propagation in fluid-filled cylinders, both the flexibility of the wall and the compressibility of the fluid must be taken into account, complicating the model and the analysis further [13].