Title page for ETD etd-08012012-040358

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
  • Aerothermodynamics
Date of Defense 1988-02-05
Availability restricted
The 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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