# Numerical Investigation of Excitation of Various Lamb Waves Modes in Thin Plastic Films
## 1 Introduction  
Ultrasonic-guided wave-based inspection techniques are very promising for non-destructed testing (NDT) and structural health monitoring (SHM) and are the primary techniques for long-range damage detection and characterization of plate-like structures. The guided Lamb waves propagate within the interior of the objects under investigation. The Lamb wave's fundamental A\({}_{0}\) and S\({}_{0}\) modes are widely used as they can be relatively easy to excite and are sensitive to various types of defects, which are found especially in composite materials. Contemporary technologies include the employing of thin films and composite plate materials. There is a special class of widely used, very thin (-0.1 mm) materials--plastic tapes and films such as clear polyvinyl chloride films [1]. polyvinyl, also known as poly (vinyl chloride) or PVC, is the third-most widely produced synthetic plastic. The production of polyvinyl chloride films in Europe reaches five million tons annually [2]. During the manufacturing of PVC films, various defects such as wrinkles, holes, rough surfaces, and thickness variations can arise. Ultrasonic methods using guided waves enable the investigation of key elastic properties of materials that cannot be assessed by merely using other methods, for example excitation by lasers [3, 4], electrostatic excitation methods [3], or electromagnetic acoustic transducers [5, 6]. These guided waves are currently used for the non-destructive testing and evaluation (NDT) of thin film type materials [7]. Usually, they are excited when thevibrations of an acoustic transducer are transferred to the investigated item by direct contact via a coupling liquid. The contact liquids are impossible to use in many cases, as the investigated item may be contaminated, damaged or otherwise negatively affected [8; 9]. This is relevant in the cases of thin films or composite structures. Some defects are detected by optical methods, but some defects such as holes and especially thickness variations can be better found by ultrasonic methods using guided waves [10; 11; 12]. Therefore, air-coupled ultrasonic investigation using guided waves can be a very attractive technique for the investigation of such type of materials. The attenuation of ultrasonic waves in air and in the object under investigation increases with the frequency. The loss of ultrasonic signals may be reduced by generating guided waves while using lower frequencies [13; 14; 15]. At lower frequencies, the velocity of the ultrasonic-guided waves in thin films may become lower than the ultrasound velocity in air, which complicates excitation and reception of ultrasonic signals by air-coupled methods [16; 17]. Therefore, it is appropriate to develop novel air-coupled ultrasonic measurement methods based on the excitation and reception of guided waves for a study of such objects. Special problems arise in the case of excitation and reception of symmetrically guided wave modes, which require fundamentally new methods of excitation and reception. The guided waves in thin film type materials may be excited via air gap in two different ways depending on the ratio of propagation velocities of ultrasonic waves in the material and air. When the phase velocity of the guided waves in the object is bigger than the ultrasound velocity in air, then the optimal incident angle of the ultrasonic wave incident from air onto the plate exists at which the biggest amplitude of guided wave is obtained. The propagating guided wave in a thin film then radiates a leaky wave into air, which may be used for air-coupled reception. This mode is commonly applied for detecting defects inside thin plates and film type materials as the leakage increases at the defective zone [18; 19; 20].