AN EXPERIMENTALLY VERIFIED NON-LINEAR DAMPING MODEL FOR LARGE AMPLITUDE RANDOM VIBRATION OF A CLAMPED–CLAMPED BEAM

Abstract

An empirical non-linear damping model, for use with single-degree-of-freedom clamped–clamped beam vibrations driven by band-limited white noise, is calibrated by using large amplitude experimental measurements. To verify the model, two parameter estimation methods are initially tested on simulated data using (1) the state variable filter, and (2) a Markov based moment method—the moment method being preferred in this particular application. Model verification with real data, then proceeds by using moment based parameter estimation and finite element solutions of the stationary Fokker–Planck equation, where deliberate attempts have been made to avoid excitation of higher modes. By systematically building up from a simple linear to a three-term damping model, comparison between measurement and prediction, via the calibrated model, shows excellent agreement for probability density functions associated with the central beam displacement up to a normalized non-linear beam amplitude ratio=7·0. But the subsequent comparisons of measured and predicted extreme value exceedance probabilities up to a maximum normalized amplitude ratio=10·0, using the same calibrated SDOF model, shows significant differences, suggesting the occurrence of considerable non-linear coupling of beam vibrations. This finding would suggest, for the case of forced random vibration of a clamped-clamped beam, that a SDOF beam model is adequate for moderately large amplitude prediction but wholly inadequate at very large amplitudes.