Marynoshenko O. Dynamic deformation of elongated beam systems in interactions with air stream

On a basis of substantive provisions of the spatial theory of elasticity the method of forming of approximations of movements in any points of cantilever beam system (CBS) is offered. Proposed approximations on the one hand are capable to describe different types bending, torsion and longitudinal movements, and on the other - are rather simple for practical applications. On the basis of presented method the formula for definition of a components of deformations stresses tensors in any points of cross section of CBS are obtained. The new approach for definition of force factors which operate on surface CBS is formulated. The uniform method - a principle of possible movements (PPM) for the dynamic analysis of loads and kinematic characteristics in points CBS and an air stream (AS) is offered. For system CBS-AS the PPM in vector and scalar representations is formulated. The components of vectors of movements, stresses and deformations tensors components, and characteristics of the air stream in any points and cross sections of CBS such as a concrete wing are calculated on the basis of the obtained formulas and the equations of movement. The reliability of the proposed model of CBS and methods of calculation is confirmed on the basis of the results of the carried numerical and real experiments.