Abstract
Many mathematical models, which describe oscillations in elastic structures such as suspension bridges, conveyor belts and elevator cables, can be formulated as initialboundary value problems for string (wave) equations, or for beam equations. In order to build more durable, elegant and lighter mechanical structures, the undesired vibrations can be suppressed by using dampers.
In this thesis, the effect of boundary damping on elastic structures is studied. In Chapter 2, as a simple model of oscillations of a cable, a semiinfinite stringlike problem is modelled by an initial boundary value problem with (non)classical boundary conditions. We apply the classical method of D'Alembert to obtain the exact solution which provides information about the efficiency of the damper at the boundary.
In Chapter 3, initialboundary value problems for a beam equation on a semiinfinite interval and on a finite interval have been studied. The method of Laplace transforms is applied to obtain the Greens function for a transversally vibrating homogeneous semiinfinite beam, and the exact solution for various boundary conditions are examined. The analytical results confirm earlier obtained results, and are validated by explicit numerical approximations of the damping and oscillating rates. The study shows that the numerical results approximate the exact results for sufficiently large domain lengths and for a sufficiently high number of modes. Moreover, the study provides an understanding of how the Greens functions for a semiinfinite beam can be computed analytically for (non)classical boundary conditions.
Finally, in Chapter 4 the studies as presented in Chapter 2 and in Chapter 3 are extended to inclined structures. A model is derived to describe the rainwind induced oscillations of an inclined cable. For a linearly formulated initialboundary value problem for a tensioned beam equation describing the inplane transversal oscillations of the cable, the effectiveness of a boundary damper is determined by using a two timescales perturbation method. Not only the influence of boundary damping but also the influence of the bending stiffness on the stability properties of the solution have been studied.
In this thesis, the effect of boundary damping on elastic structures is studied. In Chapter 2, as a simple model of oscillations of a cable, a semiinfinite stringlike problem is modelled by an initial boundary value problem with (non)classical boundary conditions. We apply the classical method of D'Alembert to obtain the exact solution which provides information about the efficiency of the damper at the boundary.
In Chapter 3, initialboundary value problems for a beam equation on a semiinfinite interval and on a finite interval have been studied. The method of Laplace transforms is applied to obtain the Greens function for a transversally vibrating homogeneous semiinfinite beam, and the exact solution for various boundary conditions are examined. The analytical results confirm earlier obtained results, and are validated by explicit numerical approximations of the damping and oscillating rates. The study shows that the numerical results approximate the exact results for sufficiently large domain lengths and for a sufficiently high number of modes. Moreover, the study provides an understanding of how the Greens functions for a semiinfinite beam can be computed analytically for (non)classical boundary conditions.
Finally, in Chapter 4 the studies as presented in Chapter 2 and in Chapter 3 are extended to inclined structures. A model is derived to describe the rainwind induced oscillations of an inclined cable. For a linearly formulated initialboundary value problem for a tensioned beam equation describing the inplane transversal oscillations of the cable, the effectiveness of a boundary damper is determined by using a two timescales perturbation method. Not only the influence of boundary damping but also the influence of the bending stiffness on the stability properties of the solution have been studied.
Original language  English 

Awarding Institution 

Supervisors/Advisors 

Award date  29 Jan 2018 
Print ISBNs  9789463660051 
DOIs  
Publication status  Published  2018 
Keywords
 Semiinfinite String Equations
 SemiInfinite Beam
 Boundary Damping
 Rainwind oscillations
 Inclined cable