Shock Response of a Nonlinear System

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Abstract
The dynamic response of a nonlinear, single-degree-of-freedom spring-mass system to shock loading is investigated. A specific value of the maximum deflection is chosen as a characteristic quantity called the “maximum allowable deflection”—which forms the starting point for a simplified presentation of the analytical results. The shock-response characteristics of each nonlinear system is compared with that of an associated linear system. In particular, the ratio of the magnitudes of the loads applied as a pulse to produce the same maximum allowable deflection in a nonlinear system and its associated linear system is defined as the “loading ratio.” This loading ratio, in combination with the usual “shock spectrum” for a linear system, can be used to determine the maximum dynamic load which a nonlinear system can withstand without exceeding the allowable deflection. A number of other engineering applications will be discussed also.

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