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.