## 1 Introduction  
Manufacturing defects, low reproducibility of manufacturing process, and in situ material damages due to in service loads are some of the most critical factors that limit the widespread diffusion of composite materials, whose mechanical and weight characteristics are extremely desirable for structural applications. In this context, nondestructive techniques for the determination of the health state of composite components are becoming more and more important. Among the others, thanks to rather simple and rapid testing applications, vibrational methods are increasingly adopted for manufacturing quality control or damage assessment [1, 2]. Furthermore, differently from other techniques, such as the micro-computed tomography, these methods are able to quantitatively assess the material properties of a component. Vibrational methods usually adopt an inverse problem formulation that intends to determine the elastic properties from the measured resonant frequencies [3, 4, 5, 6]. In this regard, material constants are calculated through an optimization process based on Finite Element models, Rayleigh-Ritz formulations, and analytical formulas. Four resonant frequencies are usually sufficient to obtain a reasonable set of elastic estimates [7]. The robustness of the assessed elastic properties is a critical aspect of vibrational methods. Therefore, further information is usually considered within the inverse problem, such as the modal shape and/or further frequencies. However, multiple resonant frequencies can be difficult to recognize, while the investigation of the modal shape can require expensive equipment developed for laboratory [8]. Furthermore, vibrational methods usually account for the global response of the component [9]. Thus, the presence of local defects can be concealed or averaged by the global behavior of the component. Indeed, the local assessment of material properties still represents a challenging field [10; 11; 12]. Recently, a new experimental methodology has been presented that allows nondestructively assessing local elastic properties of composite laminates [13]. The methodology aims to:  
1. Isolate a region of the component through a specific equipment, which clamps the extremities of the region without damaging the material;
2. Adopt the Impulse Excitation Technique to measure the first resonant frequency of the retained region;
3. Exploit the material anisotropy to obtain at least four different measures of the first resonant frequency, particularly by varying the relative orientation between the clamping system and the material;
4. Assess the elastic properties of the investigated region from the measured resonant frequencies through an optimization process. The methodology adopts a testing machine to compress two rectangular frames on the plate and isolate the region to investigate. Thus, the use of the testing machine represents a preliminary setup. However, even though this clamping system is not suitable for real-world composite structures, it is particularly useful to investigate the methodology in laboratory testing conditions. In particular, it was possible to investigate the inverse problem, which intends to assess the elastic properties from the measured first resonant frequencies. The inverse problem can be undetermined, i.e., the measured frequencies can be obtained with multiple sets of elastic estimates. In order to increase the accuracy of the methodology, the number of relative orientations can be increased. Instead, the use of higher mode frequencies is limited by the proximity of the clamped boundaries, whose noninfinite stiffness can consistently affect the result. Indeed, the higher modes increasingly involve in the modal displacement the material in proximity of the clamped boundaries. As a consequence, the effect of the nonfinite stiffness, which is for the first mode as shown in [13], increasingly affects the measurement of the higher resonant frequencies.