Scientific paper ID 484 : 2011/1

: It is known that the deformable solid body is an object of research of Strength of Materials, and the absolutely solid body is within the scope of Theoretical Mechanics. Very often practical tasks of deformable solid mechanics can be disclosed through the methods of Theoretical Mechanics. Such a method is used in the article investigating the eigen vibrations of a flexible pullable rope.

The rope is on two fixed supports, and it is divided into an equal number of elements forming a multiangle. The weight of the rope is also taken into account. Adopting the Strength of Materials approach the elements are linearly deformed and they are linked to each other by non-elastic supports. The eigen frequencies of the free vibrations are found using Lagrange?s equations of second order and the element elongation can be detected via the potential energy of deformation

To apply the methods of Theoretical Mechanics, another model is investigated? a multi-angle with absolutely solid elements connected by elastic supports. Their elasticity coefficient can be found through an equation of the potential energy of deformation involved in the two models.