The meaning of the maximum velocity response spectrum
SV obtained by an electric resonance analyser cannot be explained by expressing the ground motion by Fourier series and it is also difficult to explain
SV(
h) by the expression by Fourier integral.
When the spectrum of ground motion is expressed by “a group of sinusoidal vibrations with finite duration”,
SV for an arbitrary damping constant
h is denoted by the following equation:
SV≠
a/
p1/2
h{1-exp(-
h/√1-
h2πκ)},
where
a,
p/2π and πκ/
p are the amplitude, the frequency and the duration of a component of the acceleration spectrum of the ground motion, respectively. Examples of
SV are well explained by the equation.
It is also pointed out that the fact that
SV(
h≥0.2) is almost constant for any natural frequency of the analyser does not necessarily indicate that the velocity spectrum of ground motion is regarded as constant. And it may be concluded that
SV expresses the property of a short period vibration which is generally contained predominatingly in an acceleration seismogram.
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