###### Abstract
In [10] (by [PERSON] and others), a method for identifying the material constants of a multilayer composite plate is presented based on solving an optimization problem with an objective function connecting the experimental and calculated natural frequencies. In [11] (by [PERSON] and others), a method for determining the bending stiffness of an orthotropic plate is proposed based on the method for determining the distribution of external forces acting on a structure. To solve the inverse ill-posed problem, a regularization method is constructed that allows overcoming the high sensitivity to noise in the input data. The study in the field of modeling plates with PS in the case of [PERSON]'s hypotheses was carried out by [PERSON] in [12], in which a scheme for their identification for a homogeneous plate was constructed in the case of an inverse problem of the first type (when the deflection function at all points of the plate is considered known). As for the modeling of inhomogeneous plates, in particular, functional-gradient (FG) plates, their study is also presented in modern papers, for example, [13; 14; 15; 16]. The papers [13; 14] are quite extensive studies of methods for measuring the properties of FGM based on the study of free vibrations and dynamic stability of FG plates. Various types of mixtures of initial materials, from which FG plates are made, and the influence of their distribution over the volume of the body on the dynamic characteristics are considered. In [15; 16], the modeling of FG vibrations in finite element packages, in particular, ANSYS, is presented. The study of the influence of the laws of change in the properties of plates on their dynamic characteristics, i.e., deflection and amplitude-frequency characteristics is carried out. A large number of modern publications are devoted to the measurement of prestresses. Many of them are devoted to the determination of PS arising in the process of welding operations during plate processing. In the paper [17], [PERSON] and [PERSON] present the modeling of the three-dimensional distribution of residual stresses in welds in high-temperature nickel-based alloys used in the development of robust and reliable aeroengine components. Artificial intelligence (AI) and fuzzy techniques, showing a good match with experiments, were used to build a three-dimensional eigenstrain-creep model. In the article [18], the PS field in the weld of an annular structure simulated by a cylindrical hoop is studied. The blind hole method was used to test the residual stress distribution of the hoop structure, and the test results were compared with the finite element simulation results to verify the reliability of the simulation calculation method and the reliability of the calculation results. This made it possible to give recommendations on the optimal mode of welding of circular structures. In [19], the residual stresses arising in two samples of composite three-layer plates during the manufacture of the gas tungsten arc welding method were investigated. The values of tensile PS were measured at the boundaries of the joining of materials. Article [20] is devoted to the measurement of longitudinal and transverse PS arising from friction stir welding at different temperatures. It was shown that with a slight deepening into the weld, the longitudinal stresses are tensile in nature, and the transverse stresses are compressive, while welding with a lower temperature caused a higher level of PS. Article [21] contains an experimental study on the application of a new method of formation of residual stresses--laser shock peening. The influence of the thickness of the processed plates on the formed PS field is investigated. It is shown that in thicker plates, a significantly higher level of PS is achieved. Other practical methods for measuring PN are also worth mentioning. In [22], the authors proposed an ultrasonic experimental technique for measuring the PS distribution.