Type of Document Master's Thesis Author Studebaker, Karen F. URN etd-08012012-040358 Title Probalistic vibration analysis of nearly periodic structures Degree Master of Science Department Aerospace Engineering Advisory Committee
Advisor Name Title Nikolaidis, Efstratios Committee Chair Haftka, Raphael T. Committee Member Kapania, Rakesh K. Committee Member Singh, Mahendra P. Committee Member Keywords
Date of Defense 1988-02-05 Availability restricted AbstractThe localization of modes of nearly periodic structures causes a concentration of energy
in one part of the mode shape. It occurs for a disordered structure with weakly coupled
subsystems. The forced excitation of localized modes may affect the maximum response
amplitude of the system. Two nearly periodic structures are analyzed herein: a two span
beam and a pair of coupled pendula. Results show that the sensitivity of the forced
response to the degree of localization depends on a combination of the symmetry of the
mode which is excited and the phase difference between the forces acting on each
substructure. These results attempt to explain the range of contrasting conclusions of
previous research on the effects of forced response on mistuned structures.
Furthermore, a theoretical explanation of the results is given in terms of transfer admittance.
A probabilistic analysis of the free and forced response of a nearly periodic structure is
shown to be useful in the design of such structures which are sensitive to the degree
of localization. The second moment method is used in the analysis with results verified by
Monte Carlo simulation. The probabilities of localization and failure are calculated given
the statistics of the system parameters, and the localization and failure tolerances respectively.
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