This paper introduces the mathematics and procedures used in developing a time-dependent damping model for integration analyses of structural response. To establish the time-dependent viscous damping model, frequency-dependent damping ratios of the structure under a series of steady-state unit impulses corresponding to actual loads are first calculated. For simplicity, the ratios can be incorporated with the static stiffness of the structure to model approximately the impulse induced damping spectrum. According to the nature of the problem, these ratios can be calculated from the theoretical impedance functions and experimental observations. With the computed damping spectrum, the damping coefficient in the time domain can be obtained with the Fourier transform technique. Adopting the impulse–response method, the damping can be modeled rationally through integration with changing loads. Numerical examples are presented to show the feasibility of this model while the transform criterion is satisfied.
Soil Dynamics and Earthquake Engineering 19(8), pp.551-558