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

摘要

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. © 2012 American Society of Civil Engineers Article Outline Introduction Outline of the Proposed Time-Domain Transform Method Definitions of the Input and Output Functions and the Transform Function Method A: Basic Method Method B: Method of Considering Virtual Mass Method C: Correction in Cases with Strong Noncausality Relationship between Δt and ωN Study for Clarifying the Relationship with Other Theories Causality and Duhamel’s Integral Relationship between the Discretized Duhamel’s Integral and the Transform Method Examination of an Example Problem Transfer Function of the Single Degree-of-Freedom Series Time-Domain Transform Comparison between Calculated Impulse Responses and Theoretical Solutions Meaning of the Two Series of Impulse Responses Study on Expansion of the Applicable Scope Theoretical Explanation and the Response Analysis Method Transfer Function of Soil–Structure Interaction Calculation of Time-History Responses Conclusions