The Theory of Fuzzy Structures and its Application to Waves in Plates and Shells.

The theory of fuzzy structures was introduced by Dr. Christian Soize of ONERA in 1986, as a method for predicting the average vibrational response of the complex structure with an imprecisely known internal substructure, at a reasonable computational cost. The primary effect of the internal substructure is an apparent added damping and mass loading which remain finite even when the internals have no damping. This thesis presents an introduction to the fuzzy structure theory of Soize, discussing the probabilistic modeling of the internal substructure by a system of random 1-DOF oscillators, and outlining the finite element formulation and medium frequency method designed to reduce computational cost. The physical concepts behind the apparent damping and mass loading effects are investigated with a simpler fuzzy model due to Pierce, Sparrow, and Russell. The key parameter of this simpler fuzzy model is the distribution of the mass of the fuzzy 1-DOF oscillators with respect to their natural frequencies. The resulting expressions for the apparent damping and mass are shown to be valid for steady state excitation as long as the number of fuzzy attachments N and damping zeta satisfy Nzeta > 2. Furthermore, the apparent added damping and mass are shown to satisfy the Kramers -Kronig dispersion relationships. The major portion of this thesis is a study of how a distribution of fuzzy 1-DOF oscillators affects the modal response and propagation of waves in plates and shells. An analysis of the target strength from a baffled plate strip shows that a distribution of fuzzy attachments can significantly reduce the modal response of a structure, as well as shifting resonance frequencies. It is shown that a distribution of fuzzy attachments can significantly attenuate flexural waves in a plate, as well as altering the dispersive nature of the waves. Dispersion curves for waves in a circular cylindrical shell are shown to be distorted considerably because of the fuzzy attachments. Furthermore, the transition between membrane and bending motion of the shell surface associated with the axial propagation of flexural waves is shown to be strongly affected by the fuzzy attachments.