Abstract :
Shock-excited vibrations of a conservative Duffing oscillator are examined in application
to shock protection of a vulnerable product during accidental drop. We show that a hard characteristic
of the oscillator might be advisable for a product which is able to withstand high accelerations
(decelerations), while the maximum displacement has to be made small by any means. On the other
hand, application of a spring with a soft characteristic can result in appreciably lower maximum
accelerations (decelerations) than in a linear system and therefore can be recommended in the case
when the requirement for the lowest displacement possible is not very stringent. However, if the
drop height is not known with certainty (which is typically the case) the advantages of a soft spring
cannot be utilized to the full extent, because of the possibility of a “rigid impact”. In such a case a
probabilistic approach can be effectively used to design a soft spring with a low enough probability
of a rigid impact. The obtained results can be helpful, particularly, when designing spring protectors
in portable electronics. The author believes that these results can be useful for a rather broad class
of nonlinear springs, not necessarily with cubic restoring forces. Copyright 0 1996 Published by
Elsevier Science Ltd.
