# Unless the mathematical representation of all

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Unformatted text preview: ay become signiﬁcant. In either case, the variance error will be a function of the signal-to-noise ratio and the amount of averaging. 5.3.4 Random Excitation Methods Inputs which can be used to excite a system in order to determine frequency response functions [6-8] . Random signals are (FRFs) belong to one of two classiﬁcations, random or deterministic widely utilized for general single-input and multiple-input shaker testing when evaluating structures that are essentially linear. Signals of this form can only be deﬁned by their statistical properties over some time period. Any subset of the total time period is unique and no explicit mathematical relationship can be formulated to describe the signal. Random signals can be further classiﬁed as stationary or non-stationary. Stationary random signals are a special case where the statistical properties of the random signals do not vary with respect to translations with time. Finally, stationary random signals can be classiﬁed as ergodic or non-ergodic. A stationary random signal is ergodic when a time average on any particular subset of the signal is the same for any arbitrary subset of the random signal. All random signals which are commonly used as input signals fall into the category of ergodic, stationary random signals. Deterministic signals can be characterized directly by mathematical formula and the characteristic of the excitation signal can be computed for any instance in time. While this is true for the theoretical signal sent to the exciter, it is only approximately true for the actual excitation signal due to the ampliﬁer/shaker/structure interaction that is a function of the impedances of these electromechanical systems. Deterministic signals can, nevertheless, be controlled more precisely and are frequently utilized in the characterization of nonlinear systems for this reason. The random classiﬁcation of excitation signals is the only signal type discussed in this paper. The choice of input to be used to excite a system in order to determine frequency response functions depends upon the characteristics of the system, upon the characteristics of the modal parameter estimation, and upon the expected utilization of the data. The characterization of the system is primarily concerned with the linearity of the system. As long as the system is linear, all input forms should give the same expected value. Naturally, though, all real systems have some degree of nonlinearity. Deterministic input signals result in frequency response functions (5-47) +UC-SDRL-RJA CN-20-263-663/664 Revision: June 12, 2001 + that are dependent upon the signal level and type. A set of frequency response functions for different signal levels can be used to document the nonlinear characteristics of the system. Random input signals, in the presence of nonlinearities, result in a frequency response function that represents the best linear representation of the nonlinear characteristics for a given RMS level...
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