| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 788384 | Journal of Applied Mathematics and Mechanics | 2006 | 8 Pages |
The dependence of the natural frequencies and modes of the oscillations of distributed elastic system with characteristics of the stiffness and density that are variable along a coordinate of the cross section for arbitrary boundary conditions is investigated. It is proved that the presence of an external elastic medium, described by the Winkler model, may lead to an increase in the natural frequencies of the lower oscillation modes when the length of a one-dimensional elastic system is increased. The fine properties of the change in the natural frequencies as a function of the length of the system and the number of the oscillation mode are also established. A numerical-analytical investigation of examples which illustrate the characteristic anomalous behaviour of the lowest natural frequencies is presented.
