Shock-excited vibrations of a conservative Duffing oscillator with application to shock protection in portable electronics

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.