Advanced composite materials such as Carbon Fibre Reinforced Polymers (CFRP) tend to be used in aerospace industry to keep the weight at its minimum and yet retain a great strength. CFRP have a strong, stiff fibres in a matrix. The resulting material is very strong as it has the best strength to weight ratio of all construction materials. However, aircraft structures such as wings can break due to Fluid-Structure Interaction (FSI) oscillations or material fatigue. Material inspection by piezoelectric induced ultrasonic waves is a relatively new and an intelligent technique to monitor the health of CFRP for a damage detection in the Non-Destructive Test (NDT). To design a Structural Health Monitoring (SHM) system, it is important to understand phenomenologically and quantitatively the wave propagation in CFRP and the influence of the geomaterial and mechanical properties of the structures. The principal aim of this research is to explore and understand the design and operation from safety and economic points of view. To accelerate the design of SHM systems, the FSI effect on the wave propagation has to be considered. This research will focus on the mathematical modeling and numerical analysis of Navier-Stokes, elastodynamics and elastic waves equations in the arbitrary Lagrangian-Eulerian (ALE) framework in order to determine the wave propagation in moving domains and optimum locations for sensors. Since analytical solutions are only available in special cases, the equations need to be solved by numerical methods. For the implementation we chose the finite element library package deal.ii and DOpElib due to its special characteristics.