Basic Study on the Transform Method of Frequency-Dependent Functions into Time Domain: Relation to Duhamel’s Integral and Time-Domain-Transfer Function

The time-domain evaluation of the frequency-dependent dynamic stiffness was studied, and some transform methods were proposed. Although various kinds of stiffness have been well-transformed by these methods, some problems remain. In this paper, the following two problems are studied. First, the relationship between the proposed transform methods and Duhamel’s integral is studied to understand the meaning of the two series of impulse responses obtained by the methods. Next, the time-domain transfer function, obtained by the transform of frequency-domain transfer function, is shown to expand the applicability of the methods. Seismic response values are easily calculated in the time domain using the function without FFT. The efficiency of the function is confirmed with a practical example problem.