Optimal mode localization in disordered, periodic structures
Citable URI
https://hdl.handle.net/1912/5632DOI
10.1575/1912/5632Keyword
Oscillations; Random vibrationAbstract
Periodic structures which are slightly disordered undergo dramatic changes in mode shapes
such that the responses go from being spatially extended to spatially localized. This phenomenon
called mode localization, offers an excellent option for passive vibration isolation.
In the first part of the thesis, we provide analytical prediction of modes exhibiting
moderate localization using a newly developed Jordan Block Perturbation Method. We
estimate and compare convergence zones of our newly developed method with perturbation
techniques used to describe localized modes.
In the second part of the thesis, we provide numerical evidence that complex branch
points, which occur for complex disorder values in the mode-disorder relation, are responsible
for modal sensitivity. We investigate the effects of the strength of the branch point and
their location in the complex plane.
In the third part of the thesis we perform an optimization study involving the selection
of parameters which ensure a minimum level of localization of all modes. Optimal solutions
were found to lie at maximum distances from the branch points, and the convergence basin
of each optimum was demarcated by the branch point surface. The number of local optima
were found to grow exponentially with the number of pendula. A statistical analysis showed
that sampling of 10% provided an estimate that was within 2% of the global optimum,
thereby reducing the computational effort for small to moderate systems of pendula. For
larger systems of pendula, the problem of obtaining the global optimum in reasonable time
still remains an open problem.
In the fourth part of the thesis we propose an application for mode localization in
vibration isolation. An oceanographic mooring with regularly spaced buoys is investigated
for localization of inline elastic oscillations. Localization is found to be useful for confining
the harmonics in deep water moorings of 1000 - 4000m.
Description
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Woods Hole Oceanographic Institution and the Massachusetts Institute of Technology February 1995
Suggested Citation
Thesis: Rajagopal, Gopalkrishna, "Optimal mode localization in disordered, periodic structures", 1995-02, DOI:10.1575/1912/5632, https://hdl.handle.net/1912/5632Related items
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