## 1 Introduction
Furthermore, in order to guarantee the robustness of the methodology, limits on the design domain of the elastic properties, i.e., \(E_{11},\ E_{22},\ G_{12},\) and \(v_{12}\), are to be considered, which is undesirable, especially when assessing damage level. Here, the design domain identifies the space where the aforementioned material properties can vary, while the optimization problem minimizes the discrepancy between the measured and the numerical resonant frequencies. Indeed, if the methodology has to be adopted for detecting local material variations, limitations on the material properties can be particularly inconvenient. In this paper, a new approach based on this experimental methodology is presented, which allows increasing the robustness of the inverse problem. In particular, information related to the modal shape is retained within the inverse problem only by considering the effect of a concentrated mass on the first resonant frequency. The modal shape strictly depends on the material properties and, when dealing with anisotropic material, its isolines are not necessary parallel to the clamped boundaries, as also observed in other works in literature [14; 15; 16]. It is the case of an orthotropic material whose axes of orthotropy are not parallel to the boundaries. The modal response is here analyzed with the use of a concentrated additional mass, whose effect on the first resonant frequency depends on its position on the plate in accordance with the modal shape. Indeed, according to the modal shape and to the position of the mass, different values of the first resonant frequency are obtained. Here, two positions of the additional mass, i.e., two values of the resonant frequency, in addition to the unloaded resonant frequency of the clamped plate, are considered for each material orientation. Thus, the modal response is accountedwithin the optimization process, which consistently enhances the sensitivity of the inverse problem to the elastic properties. A numerical validation of the proposed approach is here performed, which considers materials with different elastic constants. A Rayleigh-Ritz formulation based on higher order theory is adopted to compute the first resonant frequency of the clamped plate loaded by a concentrated mass. The use of Rayleigh-Ritz formulation indeed allows consistently decreasing the computational cost with respect to the finite element-based optimization adopted in [13]. Thus, the Rayleigh-Ritz formulation represents a further step toward the application of the proposed methodology to real-world composite structures. After validating the Rayleigh-Ritz formulation on experimental data taken from the literature, for each retained material, the frequencies are calculated for the different material orientations and mass positions, thus constituting the reference values. Then, the elastic properties are handled as the design variables of an optimization process, which minimizes the discrepancy between the resonant frequency calculated at each iteration and the corresponding reference value. Results show that with the proposed approach, the modal shape can be identified only through a concentrated mass positioned in two different spots, thus avoiding the need for costly equipment. Finally, by accounting for the modal response within the optimization process, the sensitivity of the inverse problem to the elastic properties is particularly enhanced.