Sensitivity analysis with respect to elastic boundary conditions and laser spatial variables within experimental spatial dynamic modeling

• Main Author: Venter, Gerhardus
• Other Authors: Mechanical Engineering
• Format: Others
• Language: en
• Published: Virginia Tech 2014
• Subjects: LD5655.V855 1995.V468
• Online Access: http://hdl.handle.net/10919/40560; http://scholar.lib.vt.edu/theses/available/etd-01102009-063257/

Experimental spatial dynamics modeling is a new method used to obtain a dynamic model of a harmonically excited vibrating structure. The continuous three-dimensional, complexed-valued velocity field of the structure is solved from a weighted least-squares finite element formulation, making use of high spatial density data obtained from a scanning laser Doppler vibrometer. Analytical expressions for the first- and second-order error sensitivity of the obtained model with respect to model parameters of the finite element model are developed. A frequency response analysis, resulting in a pseudo-dynamic stiffness matrix and the direct method of differentiation are used to obtain the required sensitivities. These sensitivities may be used to update the parameters to obtain a more accurate model, and also to yield a signal-to-noise level for which the data must be obtained. Analytical expressions are also developed for the first-order error sensitivity of the obtained model with respect to the spatial variables (position and orientation) of the laser. A parametric representation of both the laser beam as well as the surface of the structure is used. A variation in the spatial variables of the laser leads to a shift in the measured velocity, compared to the analytical model. The influence of changes in the spatial variables on the accuracy of the model is thus crucial. Once again, the results obtained may also be used to yield a signal-to-noise level for which the data must be obtained. The formulations developed are examined by making use of a theoretical model of a beam structure with out-of-plane harmonic excitation. === Master of Science