Signal to be measured plus one adc channel for an

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Unformatted text preview: us one ADC channel for an input signal.) Shorter testing time than SISO. Transducers not necessarily moved. Consistent frequency and damping for data acquired simultaneously. Time invariance problems between measurements from different inputs. • • • • Multiple input/single output. (MISO) • Multiple channel system required (3 or more.). (One ADC channel for each input signal to be measured plus one ADC channel for a response signal.) Long testing time. Roving response transducer. More than one input location per measurement cycle. Detects repeated roots. Maxwell reciprocity checks are possible. • • • (5-2) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + • • Time invariance problems between measurements from different responses. Multiple input/multiple output. (MIMO) • Multiple channel system (up to 512 channels). Increased set-up time. Large amount of data to be stored and organized. Shortest testing time. Consistent frequency and damping for all data acquired simultaneously. Detects repeated roots. Maxwell reciprocity checks are possible. Best overall testing scheme. • • • • 5.2 Frequency Response Function Estimation Frequency response functions are normally used to describe the input-output (force-response) relationships of any system. Most often, the system is assumed to be linear and time invariant although this is not necessary. In the cases where assumptions of linearity and time invariance are not valid, the measurement of frequency response functions are also dependent upon the independent variables of time and input. In this way, a conditional frequency response function is measured as a function of other independent variables in addition to frequency. Note that the different possible formulations listed in Table 5-1 can all be considered frequency response functions since each of these formulations can be numerically manipulated (synthetic differentiation, integration, etc.) into the equivalent displacement over force relationship. This assumes that initial conditions can be ignored. (5-3) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + Receptance Acceleration Force Force Acceleration Velocity Force Force Velocity Displacement Force Force Displacement Effective Mass Mobility Impedance Dynamic Compliance Dynamic Stiffness TABLE 5-1. Frequency Response Function Formulations The estimation of the frequency response function depends upon the transformation of data from the time to frequency domain. The Fourier transform is used for this computation. Unfortunately, though, the integral Fourier transform definition requires time histories from negative infinity to positive infinity. Since this is not possible experimentally, the computation is performed digitally using a fast Fourier transform (FFT) algorithm which is based upon only a limited time history. In this way the theoretical advantages of the Fourier transform can be implemented in a digital computation scheme. The frequency response...
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