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-degree-of-freedom linear system subjected to a shock load during accidental drop or drop tests is evaluated in application to packaging of electronic products. We show that the dynamic response of such a system depends on the magnitude of the parameter η=R/2√(KM), where M is the mass of the system, K is its spring constant, and R is the coefficient of damping. We found that the “stopping distance” always decreases with an increase in damping, and that the effect of damping is larger for low level damping. As to the maximum acceleration (deceleration), it has a minimum, when the parameter η is about 0.265. This minimum is about 81% of the maximum acceleration in the undamped system. For η=0.5, the maximum acceleration is equal to that for an undamped system, and then increases linearly with an increase in the parameter η. Maximum accelerations occur, as a rule, earlier than maximum displacements. Only in a system without damping both the maximum acceleration and the maximum displacement take place simultaneously, after a quarter period from the beginning of the oscillations. For η⩾0.5, the maximum accelerations take place at the initial moment of time. We conclude that application of “smart” materials, characterized by high energy absorption due to elevated viscous damping, should be carried out with care and with consideration of the system´s mass and spring constant, otherwise the resulting acceleration (deceleration) can be even higher than that in an undamped system. Although actual electronic products can be substantially different from one-degree-of-freedom linear systems, it is the author´s belief that even the over-simplified case, examined in this paper, provides useful insight into the problem in question