ABSTRACT

In this thesis the damped linear homogeneous string-like equation has been considered. The two ends of the string are being held fixed and the general initial conditions are considered. From physical point of view the problem can be used as a simple mathematical model to describe damped vertical vibrations of a conveyor belt system, a band-saw blade, or a chain drive. The second order partial differential equation for axially moving continuum has been formulated from energy principle such as Hamilton's principle. The axial velocity of the string is assumed to be positive, constant and small compared to wave velocity, and it is also assumed that the introduced viscous damper generates small damping in the system. To solve the mathematical equation of motion a two timescales perturbation method is used to find the approximate analytic solutions. It will be shown that the introduced damping does in fact affect the solution responses and reduces the vibration and unnecessary noise in the system. It will also be shown that the damping generated in the system does not.
depend on the mode number k.