Finite Elements for a Beam System With Nonlinear Contact Under Periodic Excitation. (arXiv:0910.2092v1 [math.NA])

Solar arrays are structures which are connected to satellites; during launch,
they are in a folded position and submitted to high vibrations. In order to
save mass, the flexibility of the panels is not negligible and they may strike
each other; this may damage the structure. To prevent this, rubber snubbers are
mounted at well chosen points of the structure; a prestress is applied to the
snubber; but it is quite difficult to check the amount of prestress and the
snubber may act only on one side; they will be modeled as one sided springs
(see figure 2). In this article, some analysis for responses (displacements) in
both time and frequency domains for a clamped-clamped Euler-Bernoulli beam
model with a spring are presented. This spring can be unilateral or bilateral
fixed at a point. The mounting (beam +spring) is fixed on a rigid support which
has a sinusoidal motion of constant frequency. The system is also studied in
the frequency domain by sweeping frequencies between two fixed values, in order
to save the maximum of displacements corresponding to each frequency. Numerical
results are compared with exact solutions in particular cases which already
exist in the literature. On the other hand, a numerical and theoretical
investigation of nonlinear normal mode (NNM) can be a new method to describe
nonlinear behaviors, this work is in progress.

Published by

Original source : http://arxiv.org/abs/0910.2092...