Dynamic Actions of a Two-Layer Freely Supported Beam

The article deals with the issues of studying the stress-strain state of a structure presented in the form of a multilayer system made of various materials. A solution to the theory of elasticity and a classical solution based on Kirchhoff's hypotheses are presented. Formulas for determining the frequencies of free vibrations of the plate are determined. The results obtained are used in the construction of refined technical theories for the calculation of two-layer plates and shells. However, the problem that lies in the classical theory is significantly important, namely, this definition of the stress-strain state when a multilayer plate is investigated. The results obtained do not give any more accurate values ​​that are required in the first place, but get an approximate solution, which significantly reduces the quality of the produced process. Thus, the developed calculation methodology is presented, which makes it possible to obtain accurate and high-quality calculations applicable for any number of layers and plate sizes.