DYNAMIC-RESPONSE OF A ONE-DEGREE-OF-FREEDOM LINEAR-SYSTEM TO A SHOCK LOAD DURING DROP TESTS - EFFECT OF VISCOUS DAMPING

The effect of viscous damping on the maximum displacement (''stopping distance'') and the maximum acceleration (deceleration) of a one-degre e-of-freedom linear system subjected to a shock load during accidental drop or drop tests is evaluated in application to packaging of electr onic products. We show that the dynamic response of such a system depe nds on the magnitude of the parameter eta = R/2 root/KM, where M is th e mass of the system, K is its spring constant, and R is the coefficie nt of damping. We found that the ''stopping distance'' always decrease s with an increase in damping, and that the effect of damping is large r for low level damping. As to the maximum acceleration (deceleration) , it has a minimum, when the parameter eta is about 0.265. This minimu m is about 81% of the maximum acceleration in the undamped system. For eta = 0.5, the maximum acceleration is equal to that for an undamped system, and then increases linearly with an increase in the parameter eta. Maximum accelerations occur, as a rule, earlier than maximum disp lacements. Only in a system without damping both the maximum accelerat ion and the maximum displacement take place simultaneously, after a qu arter period from the beginning of the oscillations. For eta greater t han or equal to 0.5, the maximum accelerations take place at the initi al moment of time. We conclude that application of ''smart'' materials , characterized by high energy absorption due to elevated viscous damp ing, should be carried out with care and with consideration of the sys tem's mass and spring constant, otherwise the resulting acceleration ( deceleration) can be even higher than that in an undamped system. Alth ough actual electronic products can be substantially different from on e-degree-of-freedom linear systems, it is the author's belief that eve n the over-simplified case, examined in this paper, provides useful in sight into the problem in question.