Response functions are obtained for all input

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Unformatted text preview: forced normal mode excitation experimental modal analysis in which a structure is excited by a forcing vector which is proportional to the modal vector of interest. For this analysis, the coefficients of a preliminary experimental modal analysis are used to weight the frequency response functions, so that the sum emphasizes the modal vector that is sought. The revised set of conditioned frequency response functions is analyzed to improve the accuracy of the modal vector. A simple example of this approach for a structure with approximate geometrical symmetry would be to excite at two symmetric locations. The sum of the two frequency response functions at a specific response location should enhance the symmetric modes. Likewise, the difference of the two functions should enhance the antisymmetric modes. (5-17) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + Multiple Input versus Single Input Advantages • Better energy distribution reduces nonlinearities at input location. Better energy distribution excites the structure more evenly. Data collected simultaneously has consistent frequency and damping information which is consistent with parameter estimation algorithms. Advances in hardware/software has kept data collection time the same for single input/multiple output. More measurements per measurement cycle. Multiple input data permits the detection of repeated or closely spaced roots. • • • • Disadvantages: • • Inputs must not be correlated. More equipment required. The theoretical basis of multiple-input frequency response function analysis is well documented in a number of sources [1-3,18-27]. While much had been written about multiple input theory, the application of multiple input theory to experimental modal analysis apparently had not been seriously investigated prior to 1980 [18-27]. It also needs to be noted that this application of multiple input-output theory represents a very special case of multiple-input, multiple-output data analysis. For this case, everything about the inputs is known or can be controlled. The number of inputs, the location of the inputs, and the characteristics of the inputs are controlled by the test procedure. For the general case, none of these characteristics may be known. Consider the case of N i inputs and N o outputs measured during a modal test on a dynamic (5-18) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + system as shown in Figure 5-6. The model assumed for the dynamics is: ˆ Xp − ηp = Σ q=1 Ni ˆ H pq * ( F q − υ q ) (5.21) where: • • • • • ˆ F = F − υ = Actual input ˆ X = X − η = Actual output ˆ X p = Spectrum of the p − th output, measured ˆ F q = Spectrum of the q − th input, measured H pq = Frequency response function of output p with respect to input q = Spectrum of the noise part of the input = Spectrum of the noise part of the output • υq ηp • • X p = Spectrum of the p − th output, theoretical F q = Spectrum of the q − th input, theoretical υ1 υ2 υ Ni ˆ F1...
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This note was uploaded on 09/29/2013 for the course MECHANICAL ME taught by Professor Regalla during the Fall '11 term at Birla Institute of Technology & Science, Pilani - Hyderabad.

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