Abstract:
The paper is devoted to the study of averaged processes, which take place in fast varying periodic structures. Particularly, oscillations of a string and bending oscillations of a beam with variable cross-sections are considered. The method of direct separation of motions and the concept of vibrational me- chanics [1,2] are used for the analysis of these systems. Thus, the applicability range of this method is broadened. The in uence of fast spatial modulations on the e ective values of systems parameters is revealed and described. Par- ticularly, it is obtained that the variability of beams cross-section, along with other e ects, leads to the emergence of the additional slow longitudinal force. It is noted that the order of equations, which describe the averaged processes in the examined periodic structures, under certain conditions may be di erent from the order of corresponding equations, which characterize systems in the absence of modulations.