Wave Propagation in Rods , Shells , and Rotating Shafts with Non - Uniform Geometry

Title of dissertation: WAVE PROPAGATION IN RODS, SHELLS, AND ROTATING SHAFTS WITH NON-UNIFORM GEOMETRY Mario Toso, Doctor of Philosophy, 2004 Dissertation directed by: Professor Amr Baz Department of Mechanical Engineering The propagation of waves in rods, shells and rotating shafts with variable thickness is studied through numerical models and experimental measurements. All numerical models are formulated using the Transfer Matrix approach, which accurately reproduces the dynamic behavior and wave propagation characteristics of the considered structures at each frequency. The numerical predictions show that exponential and linear thickness profiles generate a cut-off frequency, below which waves do not propagate along the structure. Hence, the considered rods and shells are capable of filtering out low frequency and they behave as high-pass mechanical filters. The filtering capabilities of the considered class of rods and shells are investigated for different types of profiles. Furthermore, the effect introduced by using periodicity and changing the material properties of the structure in a functionally graded manner is investigated. The effect of linear profiles is practically evaluated by determining both the frequency and time response for excitations applied at one side of the structure. These results are compared to uniform profiles through the Wavelet Transform (WT), which visualizes the structure vibrational energy simultaneously in both the time and frequency domain. The agreement between the theoretical and experimental results validates the numerical models and demonstrates the effectiveness of the proposed design configurations in attenuating the propagation of waves especially in the low-frequency range. The filtering characteristics are also investigated for rotating shafts with tapered and stepped geometry. It is found out that rotation at a constant speed does not significantly modify the flexural wave propagation characteristics of the system. Also, the interest is extended to studying the Campbell diagrams of tapered and periodically stepped profiles. Experiments on the propagation of vibration from a gearbox through rotating shafts prove that tapered and periodic profiles can effectively redistribute the energy spectrum by confining the propagation to specific frequency bands. Such characteristics become more evident when the shaft is provided with active periodic piezoelectric inserts. The effectiveness of the constant axial loads and feedback control on the shaft performance is determined and compared to the alternative passive periodic treatments. WAVE PROPAGATION IN RODS, SHELLS, AND ROTATING SHAFTS WITH NON-UNIFORM GEOMETRY