Spectral analysis of wave propagation in connected waveguides
Abstract
The spectral element method combined with the Fast Fourier Transform (FFT) is a powerful and versatile tool for analysis of wave propagation problems in connected structures. They are formulated entirely in the frequency domain and use matrix assembly procedures analogous to the finite element method. This thesis extends the approach to connected structures involving non-uniformities and discontinuities. To handle situations involving deep waveguides, spectral elements are formulated based on the higher order waveguide theories of Timoshenko beam and Mindlin-Herrmann rod. Approximate tapered elements (derived using a frequency domain Ritz method) are formulated to handle situations involving member cross-section variations. For waveguides with embedded discontinuities like cracks and holes, the irregular behavior near the discontinuity is isolated by performing Local/Global analysis via the super spectral element concept. Efficient computation of the super element stiffness is the key to the success of the method and it is addressed directly. The formulated element is verified by comparison with the conventional finite element solution. Some interesting problems involving joints, cracks and holes are solved. One of the distinct advantages of the spectral approach is the capability to perform inverse problems. The concept is demonstrated with some illustrative examples involving multiple boundaries.
Degree
Ph.D.
Advisors
Doyle, Purdue University.
Subject Area
Aerospace materials
Off-Campus Purdue Users:
To access this dissertation, please log in to our
proxy server.