AN ANALYTICAL APPROACH TO DETERMINING THE DYNAMIC CHARACTERISTICS OF A CYLINDRICAL SHELL WITH CLOSING CRACKS

Abstract The paper is devoted to developing mathematical models of the elastic oscillations of a cylindrical shell with surface closing cracks. The respective forms of shell vibrations have been chosen to represent various types of damage of the shell. In the case of dispersed and single-surface damage, the transverse shell vibrations are simulated. The cycle of vibrations is assumed to be subdivided into two parts, in one of them the damaged surface fibers are compressed so closing the cracks and negating their influence. For the second part, the cracks are open, so their influence is taken into account. The problem is solved in a piecewise linear with different frequencies and amplitudes at each vibrations cycle interval. The vibration parameters are calculated by means of Relay's energy conservation method and are represented by analytical expressions, the system being assumed to be conservative. The functions determining the vibration process are decomposed by a Fourier analysis using the averaged frequency, the coefficients of the resulting series being obtained as analytical expressions. Vibrodiagnostic functions, which enable the geometrical parameters of the cracks to be determined depending on the geometry of the shell and type of damage, have been plotted.