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Shock Response Characteristics of Damped Linear Oscillators with Application for the Shock Measurement

Publication year Port and Airport Research Institute Technical Note 0033 1967.11
Author(s) Yoshimi GODA
Department
/Divison
Hydraulic Engineering Division Wave Laboratory
Executive Summary

 The effect of impulsive loads on structures is different from that of statical loads. The measurement of and the stress analysis associated with impulsive loads must be carried out with due consideration for shock response characteristics. The responses of a single-degree-of-freedom oscillating system with linear damping to pulse excitations are calculated in this note as a model of a measurement system or a structure subject to impulsive loads. The number of pulse excitation functions treated are eight: rectangular, triangular (vertical rise, symmetric, and vertical fall), sine, versed cosine, and two exponential-sine pulses. The responses of a two-step oscillator, which represents the combination of an undamped pick-up and a galvanometer with good damping, to rectangular and sine pulse excitations are calculated also. All the results are presented in ten diagrams of shock response spectra, which show the variation of displacement ratio against the frequency ratio with the damping ratio as a paramenter.
 The shock response is characterized with the absence of resonant oscillation; the maximum displacement of oscillator under an impulsive load is less than twice the statical displacement under the statical load having a magnitude of the peak value of the impulsive load. If the duration time of shock is shorter than about three-tenth of the natural period of oscillating system, the response is the free oscillation with an amplitude proportional to the impact of shock, without being affected by the shape of shock pulse.
 The damping ratio of pick-up is required to be as large as possible for better reproduction of shock profile. When the damping ratio of pick-up is small, the use of a low-pass filter or a galvanometer with the natural frequency being about one-half of the pick-up is recommended for the suppression of free oscillations of pick-up induced by the shock. The problem of mounting vibration is discussed also with recommendations of large weight for mounting as well as of high natural frequency.

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