ABSTRACT

In this thesis, two well-known mathematical models hove been considered: the string­-like model and the beam-like model. Based upon these two models the energy estimates for the string-like model and the beam-like model under viscous damping have been constructed. These energy estimates have been calculated for almost all possible cases for the different boundary conditions (BCs). From the physical viewpoint the problem as described in this thesis can easily be utilized as the simple mathematical models, such as. the conveyor belt systems, the data storage devices, chains and band-saw blades. In both of these models. the axial velocity and the damping co-efficient are assumed to be constant and positive .The positive damping refers to energy dissipation in the axially translating systems and the positive axial velocity refers to belt moving horizontally to only positive direction. it is shown that, due to change in geometry of boundary conditions (BCs), the energy behavior of the system also changes and it can affect the stability properties of the system. also shown that in some cases of BCs the system is unstable and energy is growing without bound, and in some cases it is not possible to draw a concIusion whether the energy of the string and beam Is increasing or decreasing due to continuous and outflow of energy at the boundaries.