Transform methods for frequency‐dependent complex stiffness to time domain using real or imaginary data only

Abstract

SUMMARYThe author has studied the transform method of complex stiffness, which is strongly dependent on frequency, to the time domain. In this paper, new transform methods that use only the real part or the imaginary part data are proposed. By applying them to example problems, it is confirmed that the accuracy of the proposed methods is almost high in both causal and noncausal cases. These methods can also be thought as a standby for the Hilbert transform, because the undefined part is easily calculated by the recovering complex function from the obtained impulse response.

Extended Rayleigh Damping Model

“…This causal model is clearly independent of the element type, and different types of element can be employed in the same way. Nakamura (2008) proposed a method for simultaneously calculating the real part and the impulse response in the time domain with only the imaginary part of the complex function. This was done using the Kramers-Kroning relation (Nakamura, 2007).…”

Application of a Highly Reduced One- Dimensional Spring-Dashpot System to Inelastic SSI Systems Subjected to Earthquake Ground Motions

“…Since this method was first developed in the 1980s, many transform methods in the time domain have been proposed and improved to overcome difficulties in various frequency dependencies in IFs (Wolf & Motosaka, 1989;Meek, 1990;Motosaka & Nagano, 1992;Hayashi & Katsukura, 1990). Nakamura (2006a;2006b;2008a;2008b) has developed various sophisticated transform methods that can deal with strong frequency dependency in IFs, non-causal impedance with large hysteretic damping, and soil nonlinearity.…”