Shock Spectrum Research Articles

Submarine Shock Motions Resulting from Underwater Explosions

When a depth charge is exploded in the vicinity of a submerged submarine, damage of two kinds may result from the compression wave. This paper discusses, in qualitative terms, the motions of the submarine which may lead to shock damage of equipment installed or carried inside the boat. Damage to the boat itself is not considered here. These motions, often called shock motions, are approximate inputs to equipments being analyzed for shock response. Because of the behavior of the underwater explosion three rather distinct types of submarine motions are observed. Equipment response to each of these is dependent upon the relation between the “characteristic frequencies” of the input motions and the responding systems. A convenient measure of the damage potential of these shock motions is the shock spectrum, and the usefulness of this plot in response analyses is briefly discussed.

Some Shock Spectra Characteristics and Uses

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.

Response Spectra by Means of Oscillograph Galvanometers

A response spectrum (shock spectrum) is the response of a series of single-degree-of-freedom systems of given damping to a shock or vibratory motion, as a function of the frequencies of the simple systems. An oscillographic galvanometer is a single-degree-of-freedom system having a rotational response to an exciting current. If the exciting current is made proportional to the amplitude of the motion, the response of the galvanometer to the current will be proportional to that of a single-degree-of-freedom system to the motion, provided their natural frequencies and damping properties are the same. A commercial galvanometer-type oscillograph has been obtained having twelve undamped galvanometer elements with natural frequencies in the range between 10 and 2500 cps. Damping, by electrical means, has been made adjustable between about 3 and 50% of critical. Associated circuitry has been constructed so that electrical playback of recordings of shock and vibratory motions can be conveniently analyzed. Calibration techniques are described and examples are given for analysis of simple and complex shock motions.

Some Secondary Effects Related to Impact Wave Forms

This paper considers changes in the shock spectrum that may arise from minor variations in the form of an applied pulse. In addition to the rise and decay times the nature and symmetry of the discontinuities has a profound effect on the high-frequency components. The selection of parameters in the design of a square wave accelerator is discussed. The effects of shock excited resonances in a machine are investigated together with methods of minimizing their effect.

Response Spectra by Means of Oscillograph Galvanometers

A response spectra (shock spectra) is the response of a series of single-degree-of-freedom systems of given damping to a shock or vibratory motion as a function of the frequencies of the systems. An oscillographic galvanometer can be considered a single-degree-of-freedom system having a rotational response to an exciting current. If the exciting current is made proportional to the amplitude of a motion, the response of the galvanometer to the current will be proportional to the response of a single-degree-of-freedom system to the motion, provided their natural frequencies and damping properties are the same. A commercial galvanometer-type oscillograph has been obtained having twelve undamped galvanometer elements with natural frequencies in the range between 10 and 2500 cps. Damping by electrical means has been made adjustable between 2% and 50% of critical. Associated circuitry has been constructed so that electrical playback of recordings of shock and vibratory motions can be conveniently analyzed. Calibration techniques are described and examples are given for analysis of simple and complex shock motions, and for nonperiodic vibrational motions.

Shock Spectrum as a Criterion of Severity of Shock Impulses

Shock impulses have not as yet yielded to any practical method of spectral analysis that would permit convenient exact calculation of all the peak internal responses of hardware subject to such accelerations, and also permit comparison of shock severities by inspection. The shock spectrum with a few supplementary techniques, provides adequate insight into the responses of a one degree of freedom resonator. As an indication of the responses of a system with several coupled degrees of freedom, a second-order shock spectrum is defined. An oscillatory constituent of the spectrum is also defined in such a way as to be applicable to any order of spectrum. Investigation of these two concepts leads to the conclusion that if the first-order shock spectrum technique is to be used as a basis for comparison of the severity of a laboratory test shock with that of a service shock, spectra should be plotted for both positive and negative directions. Moreover, when feasible, such spectra should ordinarily be plotted as distinct curves for the intervals during and after the test shock, and the oscillatory constituent for the interval during the shock should be estimated.

On Physical Equivalents to Spectra Notions

The notion of a Fourier spectral equivalent of an arbitrary function has been known for a long time in its basic mathematical form. Calculations of these spectral quantities are conventionally based on the Fourier integral. It is not so well known that the Laplace transformation also yields a spectral notion of which the Fourier form is a special case. In addition, vibration engineers have made extensive use in recent years of the concept of a shock spectrum. Simple physical experiments are described which yield direct quantitative spectral values at specified frequencies for any of the three spectra mentioned in the foregoing. These equivalents are useful in assigning physical significance to the quantities under discussion.

Sawtooth Shock as a Component Test

The shock effect of a terminal-peak sawtooth of acceleration obtained by a drop onto a lead pellet has been investigated experimentally using the shock spectrum as the criterion of severity. It is shown that this spectrum obtained by analysis of the acceleration-time data can be made to approximate closely over a wide frequency range that obtained theoretically for an ideal sawtooth. The smoothness of the spectrum which results from the extreme asymmetry. of the pulse shape makes the sawtooth particularly attractive standard pulse shape for shock test in the laboratory.

Shock Spectrum Computer for Frequencies up to 2000 cps

The shock spectrum for an acceleration impulse applied to an electronic equipment or other component is a measure of severity of mechanical shock in terms of possible peak response at each frequency within the component structure. It is commonly measured by a reed gauge, which is intended to simulate the possible resonant characteristics of the internal structure. The reed gauge is bulky, however, and provides data at a limited number of frequencies. The shock spectrum computer operates on an accelerometer signal, either direct or recorded, and permits measurement of as many points in the spectrum as desired. It is a device which solves the differential equation of a simple undamped resonant mechanical appendage for any applied impulse of acceleration to yield the response. In the present version, the response is made available as an output signal which is applied to a commercial cathode-ray oscilloscope. Peak accelerations and their time of occurance may be obtained readily from the oscilloscope display. The computer can be tuned to any frequency up to 2000 cps. Control circuitry is used to damp the computer shortly after each impulse and to undamp it immediately before the next so that the impulse under study can be applied repeatedly from a recirculating loop of magnetic tape. Shock spectra obtained from the computer and oscilloscope display are used as a measure of the severity of shocks experienced by electronic apparatus and as a basis for deriving shock specifications for use in design approval tests.

The Effect of Pulse Shape on Simple Systems Under Impulsive Loading

Abstract This paper proposes modified parameters for presenting “shock spectra” for elastic systems acted upon by acceleration pulses. It is shown that the ratio of maximum response acceleration to maximum acceleration of the pulse is a function of the pulse shape. By introducing a parameter which includes velocity change of the pulse and the natural frequency of the elastic system, in place of maximum acceleration of the pulse, the influence of pulse shape on the spectrum is reduced materially. The significance of the spectrum for lightly damped systems is considered where failure may result from fatigue after many cycles of stress reversal induced by a single pulse.