Own vibrations of the loaded flexible rod

The dynamic response of a construction in many respects is defined by frequencies and mode of its own vibrations, therefore the problem of definition of characteristics of own vibrations in the general problem of dynamics makes a powerful part. As a rule, at definition of characteristics of own vibrations the construction is assumed not loaded. At the same time, there are such elements of construction, for example elastic rods, springs, etc. which can be intensively deformed while working, but to be within the limits of elasticity. Frequencies of vibrations of such intensively deformed elements can considerably differ from frequencies of strainless configuration. An example is the known problem about vibrations of the direct rod compressed by axial force. In this problem frequency of the first tone of own vibrations at growth of compressing force up to value of the first critical force converges to zero. Therefore following problem statement appears.