Applicability of Time Domain Transform Methods for Frequency Dependent Dynamic Stiffness

Some types of dynamic stiffness, such as the dynamic ground stiffness used in soil-structure interaction analyses and the viscoelastic body used in vibration control systems, have strong frequency dependency. To perform seismic response analysis considering this frequency dependence and the nonlinearity of the model, the dynamic stiffness in the frequency domain must be transformed into the time domain, and a time-history nonlinear response analysis is required. Therefore, many studies on these time-domain transforms have been conducted. One of the present authors has already studied and proposed transform methods for this purpose, and some of their results were used to design new types of damping models. In the present study, the outline and characteristics of the proposed methods (A to C) for this transform are described first. Next, typical problems with strong frequency dependency (i.e., the dynamic soil stiffness, Maxwell element, viscoelastic body, Biot model, and causal hysteretic damping) were transformed into the time domain using these transform methods. The applicability of the transform methods was examined. Subsequently, the characteristics of each problem in the frequency domain and the characteristics of the obtained impulse response in the time domain were analyzed. Finally, it was confirmed that the proposed methods were applicable to all studied problems. These studies are important to understand the physical meaning of these problems, which have strong frequency dependency.