Yegarmina L. Three-dimensional effects in the stressedly-deformed state of the bars and beams in the time of non-stationary elastic waves distribution.

The research object is three-dimensional dynamic equations of elasticity theory. The subject of the research is one-dimensional equations that allow to learn three-dimensional effects near the elastic nonstationary wave fronts in the bars and beams. A purpose of the work is finding a new specified unidimensional dynamic models of constructions that would let solve a problem of the nonstationary elastic waves distribution in the time of suddenly loaded boundary and learn the average three-dimensional picture such waves. The research method is the asymptotic-group analysis that was used both on the phase of derivation of the specified equations and on the phase of searching their analytical solutions. To get new dynamical models a nonminimal simplification of three-dimensional dynamic equations of elasticity theory was used. The main idea of this method consists of combining two investigated by A. D. Shamrovskii orthogonal variants of a "minimal" simplifications. The result of such combining is the transition from the three-dimensional dynamic equations of elasticity theory to the one-dimensional dynamic equations which are more accurate than the known ones. The solution of the problem of elastic waves spreading from suddenly loaded bars and beams border is received in series of self-stimulating functions whose coefficients are found using the recursive formulas and some are the integration constants and are found from the boundary conditions. There has been developed the methodology of building unidimensional dynamic bending equations and equations of longitudinal deformation of bars and beams from the three-dimensional dynamic equations of elasticity theory. Along with that in all cases of derived equations their degree is the same as in known ones that describe longitudinal and transversal waves. That is, practically new specified equations have the same applied structure as the known equations but there appears an opportunity to take into account the three-dimensional effects in the perturbated area both well-known (displacement, rotary inertia) and the new ones. In particular, there are first taken into account cross-section deformations in bars and beams and also there is found the effect of two-dimensional and one-dimensional wave quasi-fronts arising in bars and beams with the rectangle cross-section. All speeds of the nonstationary elastic waves fronts for all received equations are the same as for elasticity theory three-dimensional dynamic equations. The comparison of the research results with the classic theory and Timoshenko theory results showed that the well-known results have a slowly varying asymptotic behavior comparing to the more accurate solutions. Results of the work are implemented on a construction phase and a phase of new machine designing in joint-stock company "Motor-Sich" as well as in Building And Water Resources faculty of Zaporizhzhya State Engineering Academy in the studying process. A range of application is aircraft building, rocket production and planning and designing work.