# Numerical Investigation of Excitation of Various Lamb Waves Modes in Thin Plastic Films
## 1 Introduction
In our previous investigations, we analyzed application of air-coupled linear phased ultrasonic arrays for excitation and reception of only the slow fundamental antisymmetric A\({}_{0}\) mode, in the frequency range in which the velocity of this mode is slower than the ultrasound velocity in air [16; 17]. For the analysis of propagation of the ultrasonic wave through the air gap, the impulse response method was used [16]. Propagation of the A\({}_{0}\) mode in a plastic film was calculated by the analytic time harmonic solution method [14; 16; 17]. However, exploitation of the symmetric S\({}_{0}\) mode enables not only detection of various defects, but also evaluation of elastic properties of the item under a test [20]. For example, simultaneously excited S\({}_{0}\) and A\({}_{0}\) guided wave modes enabled the measurement of thickness and Young's modulus of thin PVC films [21]. For practical applications, it would be very attractive to use it for the same ultrasonic air-coupled transducer or array. To our knowledge, a detailed analysis of the performance of such methods is still missing [21]. For this purpose, we propose instead a single ultrasonic transducer to use linear air-coupled arrays, which can be electronically readjusted to optimally excite and receive the required guided wave modes. For the solution of this problem, we used a numerical simulation based on the application of finite element modelling. The objective of this article was a numerical investigation of feasibility to excite different types of ultrasonic-guided waves, such as symmetrical S\({}_{0}\) and asymmetrical A\({}_{0}\) modes in thin plastic films with the same electronically readjusted linear phased array. First, we simulated propagation of two fundamental A\({}_{0}\) and S\({}_{0}\) Lamb wave modes in thin plastic films using a single ultrasonic transducer. Second, to improve the excitation of the S\({}_{0}\) mode, a linear phased array was proposed for use. Calculations were performed using finite element methods (FEM). FEM has many advantages such as [22]: it allows solving acoustic contact problems, to model bodies made of different materials; a curvilinear region can be approximated by means of finite elements of smaller dimensions, which enables the increase of modelling accuracy [23]. FEA's main advantage is that it produces a much more detailed set of results than experimental investigations and is often quickerand less expensive. Fundamentally, instead of tackling a big problem directly, we divided it into smaller and more easily solvable problems to attain a unique result for the system as a whole. The discrete model approximates the behavior of the real physical structure. However, provided that the discretization mesh is dense enough, the approximation is sufficient to accurately model reality [24; 25; 26]. The numerical modelling was performed using the commercially available finite element software, Abaqus. Two numerous calculation methods, 3D and 2D, were used. Numerous calculations showed that the 2D technique significantly improves the computational efficiency compared to the 3D technique [27; 28; 29]. The paper consists of four sections. In Section 2, the numerical simulation of propagation of A\({}_{0}\) and S\({}_{0}\) guided wave modes in thin PVC plastic film is presented. The finite elements modeling results of A\({}_{0}\) and S\({}_{0}\) guided wave modes are described in Section 3. In Section 4, conclusions and discussion of the obtained results are given.