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Spectra of amplitudes sustained for a given number of cycles: An interpretation of response duration for strong-motion earthquake records

U.S. GEOLOGICAL SURVEY, 345 MIDDLEFIELD ROAD, MENLO PARK, CALIFORNIA 94025

Abstract

To answer the question, "What response amplitude is sustained for a duration equal to a specified number of cycles?", a technique was developed using the response of a single-degree-of-freedom, lightly damped oscillator to generate a spectrum of amplitudes that corresponds to a specific number of cycles. This technique provides a simple approach by which to compare the amplitude sustained for given numbers of cycles as a percentage of the maximum response.

The response as a function of time may consist of one or a very few oscillations of high amplitude followed by many oscillations of lower amplitude. An "effective response" defined in terms of the amplitude sustained for a chosen number of cycles might indicate the severity of the response to a particular earthquake. Preliminary analyses of 12 accelerograms indicate that for oscillators with 5 percent damping and with periods in the range of 0.04 to 4 sec, the mean "effective response" for four cycles lies between 52 to 76 per cent of maximum response.