Some Shock Spectra Characteristics and Uses

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Abstract
A shock spectrum is a plot showing the peak response of a linear variable-frequency oscillator (of single degree of freedom) to a specific shock wave, as a function of the frequency of the oscillator. Such a spectrum may be measured, for example, by multifrequency reed gages and is sometimes used as a basis either for specifying the shock wave or for computing the response of a multi-degree-of-freedom structure to such a shock. In this paper these applications of the shock spectrum are discussed. In particular, it is shown that, if the fundamental frequency (f1, cps) of the structure is sufficiently high, a close approximation of the peak response of a multi-degree-of-freedom system can be obtained by the algebraic sum (not the sum of absolute values) of the peak responses of the individual degrees of freedom. Numerical results for a uniform cantilever beam subjected to a shock load uniformly distributed over its span show that the high-frequency requirement is satisfied if 2f1tm ≥ 1, where tm(sec) is the rise time of the pulse.

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