Shock protection with a nonlinear spring

Using the simplest case of a nonlinear spring with a cubic restoring force, we show that a hard characteristic might be advisable for structural elements which are able to withstand high accelerations (decelerations), while the maximum displacement has to be made small by any means. Application of a spring with a soft characteristic can result in appreciably lower maximum accelerations (decelerations) than in a linear system; therefore, such application can be recommended in the case when the requirement for the lowest displacement possible is not very stringent. However, if the maximum drop height is not known with certainty (which is typically the case) the advantages of a soft spring cannot be utilized to a full extent, because of the possibility of a “rigid impact”. In such a case (which occurs if the initial potential energy of the element is too high and significantly exceeds the work of the restoring force within the actual “breaking distance”), 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 when designing spring protectors for vulnerable structural elements in portable electronics. These results can be useful for a rather broad class of nonlinear springs, not necessarily with cubic restoring forces