Abstract
The presented paper is devoted to completing the development of an asymptotic method for solving boundary value problems of the hyperbolic boundary layer in elastic shells of revolution of arbitrary shape under three types of non-self-balanced end shock loading: longitudinal tangential, bending, and normal. The hyperbolic boundary layer is a component of the decomposition scheme for the non-stationary stress-strain state of thin shells localized in the vicinity of the leading fronts of dilatation and shear waves. The proposed asymptotic method for solving boundary value problems for all three types of stress strain state is based on obtaining an exact solution for the Laplace transforms using the integral transformation method in the case of cylindrical shells. The solution thus obtained, in the form of an expansion in vibration modes, which are an asymptotic representation of the vibration modes for a plane layer described by the Rayleigh – Lamb dispersion equation, is generalized to the case of shells of revolution of arbitrary form using the method of exponential representations. The originals of the transforms are presented in the form of series in Bessel functions. The studies of hyperbolic boundary layers are carried out in special near-front coordinate systems associated with the wave-front geometry, whose asymptotic model is defined by normals rotated to the middle surface.