Prediction of Smoothed Frequency Responses Using General Orthogonal Polynomials,
BRUNEL UNIV UXBRIDGE (ENGLAND) DEPT OF MECHANICAL ENGINEERING
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Smoothed frequency responses describe vibration behaviour without regard to resonant-antiresonant detail. The object in this paper is to show how they can be predicted from information about stiffness coefficients and masses, using a series-expansion in general orthogonal polynomials not just the Tchebyshev polynomials. Resonant-antiresonant detail concerns sharpness, range, and location of resonant peaks and antiresonant notches in the true vibration response, and for many purposes constitutes the most important feature of that response. Nevertheless, there is some interest in the part of the vibration response that still can be examined when resonant-antiresonant detail is unknown, witness two known approaches Statistical Energy Analysis and the Mean-Value Method. A recently-introduced method is to apply smoothing by means of an orthogonal polynomial fit. Using a series-expansion, there is heavier smoothing as fewer orthogonal polynomial terms are employed, but resonant-antiresonant detail can be recovered if the number of terms is sufficiently increased.