VIBRATIONS OF A BEAM-MASS SYSTEMS USING ARTIFICIAL NEURAL NETWORKS

The nonlinear vibrations of an Euler-Bernoulli beam with a concentrate d mass attached to it are investigated. Five different sets of boundar y conditions are considered. The transcendental equations yielding the exact values of natural frequencies are presented. Using the Newton-R aphson method, natural frequencies are calculated for different bounda ry conditions, mass ratios and mass locations. The corresponding nonli near correction coefficients are also calculated for the fundamental m ode. The calculated natural frequencies and nonlinear corrections are used in training a multi-layer, feed-forward, backpropagation artifici al neural network (ANN) algorithm. The algorithm produces results with in 0.5 and 1.5% error limits for linear and nonlinear cases, respectiv ely. 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.