The basic purpose of given article is consideration of the problems connected with application of a method of concentrated weights in the tasks of mechanical systems dynamics at non-classic internal and external constraints. The method of the concentrated weights is convenient means of the analysis of dynamic properties of elastic mechanical systems. It has relative simplicity of definition of the parameters of equivalent discrete system, the clearness of computing algorithms and provides comprehensible accuracy of definition of the lowest natural frequencies. Doubtless advantage of a method is convenience of modeling of non-classic constraints of fastening and internal constraints between elements of complex systems. Such problems arise at the decision of practice tasks of the analysis of dynamics of real systems. The method is used for the analysis of vibra-tions of a beam with variable parameters at presence of elastic supporting of the beam and the attached additional concentrated weight. A result of dynamic analysis has a good correlation with the fatigue damages observed at fatigue test of a beam.

The phenomenon of the Lamb wave interaction with fatigue crack in Al2024-T3 sheet was investigated at cyclic loading. Mentioned effect is associated with the crack open/close that change acoustic impedance of a crack. Analytical simulation of fatigue crack opening using the generalized Dugdale’s model of a crack in thin plate shows good accordance between the intensity of ultrasonic signal and a crack opening.