Damping of a structure means its capacity of energy dissipation or absorption when it is subjected to excitation. The energy is mostly converted into heat and partially transmitted to ambient media and to the base on which the structure is supported. Damping has two primary effects ; for steady-state excitations it suppresses the vibration amplitude of the structure to given level and for transient excitations it increases the rates at which the free vibrations of the structure decay.
Reduction of vibrations in general decreases oscillatory stress in the structure and, hence, consequently increases the fatigue life of structures and their reliability. Reduction of vibrations also decreases the sound generation.
For a beam or plate structure, dissipation of the vibration energy may be attributed to both internal material damping and external damping at the boundary supports, which means that additional damping can be provided also in two ways. Free or constrained damping layer treatments on the vibrating surfaces are examples of the former, and insertion of damping materials at the boundaries are examples of the latter. Surface Damping treatment by viscoelastic layers has been successful especially for the beam and plate-like structures. Although such surface damping treatments are very effective in general for vibration control, it may not be always possible to implement them in real situations. In such cases, one must rely on the damping treatment at the supports. One of the support damping treatments is to insert damping materials between the structure and the supports.
An analytical model to study the vibration of beam with viscoelastic boundary supports is described in this thesis. The governing equations of motion of the system are derived using the Hamilton's principle. Equations of motion are derived separately for the supported and the unsupported regions. Then, using the natural boundary conditions, forced boundary conditions and continuity conditions, the equations to obtain the natural frequencies, loss factors and mode shapes of those systems are developed. Since, this approach involves too many unknown parameter, another method to estimate modal properties of a beam with viscoelastic boundary supports is proposed. In the proposed method, the subsystems of the support regions are described analytically in terms of dynamic stiffness parameters at the joints and then, subsequently characteristic equations for the beam structure supported at the boundary ends by springs with known stiffness are derived. The stiffness parameters are inherently frequency dependent complex quantities due to the complex modulus of viscoelastic materials. The modal parameters of the assembled system are obtained by solving the transcendental characteristic equations numerically.
The effects of the material properties and dimensions of the viscoelastic support layers on the natural frequencies and loss factors of the system are discussed. The same approach is applied to estimate the modal properties of a rectangular plate with viscoelastic boundary supports. Finally, finite element analysis and experimental results are compared to verify the proposed technique.
