Nonstationary random analysis of structures with hybrid mass damper system

The building structure is modeled as a linear single-degree-of-freedom system, and an active mass damper (AMD) is also adopted as the control device in order to reduce the structural response due to the external random load. In addition, suppose that the input acceleration of earthquake can be modeled as the product of nonstationary envelope function and narrow-band stationary random process with Kanai-Tajimi spectrum. In order to obtain the nonstationary stochastic response of control system due to the narrow-band nonstationary random process, in consideration of exchanging the active control mode for the passive one, considerable efforts are generally required in the analytical formulation. This paper, therefore, proposes an analytical technique to acquire the response covariance matrix by utilizing the state transition matrix method in state space. The proposed technique is evaluated by comparing the analytical results with those from numerical simulations.