Optimal Design of Viscoelastic Structures.

Damping layers for beams are used in two basic configurations, unconstrained and constrained. In the unconstrained configuration, damping material is bonded to the beam surface. In the constrained layers, an additional metallic facing is attached to the viscoelastic coating. Here shape optimization for such damping treatments is considered. A key question addressed is, for a given volume of damping material, how much the peak displacement can be reduced over the uniform distribution case, if the profile of the damping layer is optimized. Alternations in fatigue life times are monitored as additional performance measures. The base beam and face sheets are treated as Euler-Bernoulli beams and the viscoelastic coatings are taken to be Timoshenko beams. The viscoelastic layers are assumed to be Kelvin solids. A finite element approach is used in which rod and beam element interpolation functions are used for the longitudinal and transverse displacements, respectively. Displacement response is obtained using both modal analysis and a direct method. Neuber's rule is used to calculate fatigue lifetimes. Optimization is approached using mathematical programming techniques, the method chosen being a sequential, unconstrained minimization technique. The finite element modeling was validated by comparing natural frequencies and loss factors for a three-layered beam with published values. The optimization phase of the program was checked by solving a mathematical problem with a known solution. Results on optimum profiles, displacement performance measures and fatigue lifetimes changes are given, for both unconstrained and constrained damping layers. Both low and high excitation frequencies are considered. For unconstrained layers, optimization of the layer profile led to significant improvement in displacement performance as well as fatigue performance, for two classes of materials and for both low and high frequency excitation. Constraining the layer led to substantial improvement, over the unconstrained case, in the displacement performance. However at low frequency, it was found to lead to degradation of the fatigue life times.Ph.D.Mechanical engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/161682/1/8801362.pd