FEATURES OF THE NATURAL MODES OF FREE TRANSVERSE VIBRATIONS OF THE ROD WITH MASS DAMPER - , А. И. (Municipal economy of cities. Series: «Economy science», 2017)
The problem of free transverse vibrations of the rod with mass damper is considered. The equation of mode shapes is obtained using Fourier method. For the given parameters the natural frequencies and modes of transverse vibrations of the rod with mass damper are defined. The features of the natural modes for different parameters of stiffness of the rod and the damper, as well as coordinate points of attachment of the damper to the supporting rod, are investigated. It is established that the configuration of the natural modes is determined by the position of the corresponding natural frequencies in the frequency spectrum of the rod without the damper. Natural mode of the rod with mass damper can coincide with the mode shapes of the rod without the damper, to be like her or be transitional between the closest mode shapes of the rod without the damper. This may disrupt the sequence of number of nodes with increasing number of the natural mode, which is characteristic of the rod without the damper. The solution of the problem takes into account the peculiarities of features of the natural modes of the rod with mass damper, substantially in the application of numerical methods of determination of characteristics of the system, in particular, in problems with other boundary conditions or for rods of variable cross-section, as well as to predict future behaviour of a system under a given external perturbation. Keywords: mass damper, free transverse rod vibrations, natural mode.