Vibrations of a beam-mass systems using artificial neural networks

The nonlinear vibrations of an Euler-Bernoulli beam with a concentrated mass attached to it are investigated. Five different sets of boundary conditions are considered. The transcendental equations yielding the exact values of natural frequencies are presented. Using the Newton-Raphson method, natural frequencies are calculated for different boundary conditions, mass ratios and mass locations. The corresponding nonlinear correction coefficients are also calculated for the fundamental mode. The calculated natural frequencies and nonlinear corrections are used in training a multi-layer, feed-forward, backpropagation artificial neural network (ANN) algorithm. The algorithm produces results within 0.5 and 1.5% error limits for linear and nonlinear cases, respectively. By employing the ANN algorithm, computational time is drastically reduced compared with the conventional numerical techniques. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.