Non-linear vibrations of a beam-mass system with both ends clamped
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A clamped-clamped beam-mass system is considered. The non-linear equations of motion including stretching due to immovable end conditions were derived previously [1] (Ozkaya et al. 1997 Journal of Sound and Vibration 199, 679-696). In addition to five different end conditions considered in reference [1], the case of clamped-clamped edge conditions is treated in this work. Exact solutions for the mode shapes and frequencies are given for the linear part of the problem. For the non-linear problem, approximate solutions using perturbations are searched, Alternatively, the natural frequencies and non-linear corrections are used in training a multi-layer, feed-forward, back propagation artificial neural network (ANN) algorithm. Using the algorithm, the numerical calculations are drastically reduced for obtaining the natural frequencies and non-linear corrections corresponding to different input parameters. (C) 1999 Academic Press.