Approximate analytical solution of non-zero-mean nonstationary response of MDOF hysteretic systems subject to pulse-like stochastic ground motions

• Published in: Mechanical systems and signal processing Vol. 221; p. 111742
• Main Authors: Han, Renjie, Kong, Fan, Peng, Yongbo
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.12.2024
• Subjects: Hysteretic systems; Multi-degree-of-freedom; Non-zero-mean; Nonstationary; Pulse-like stochastic ground motions; Statistical linearization techniques; Statistical linearization techniques; Nonstationary; Multi-degree-of-freedom; Non-zero-mean; Hysteretic systems; Pulse-like stochastic ground motions
• ISSN: 0888-3270
• DOI: 10.1016/j.ymssp.2024.111742

The present study proposes an approximate analytical method combining statistical linearization techniques and Runge–Kutta algorithm (SLT-RKA) to efficiently compute non-zero-mean responses of multi-degree-of-freedom (MDOF) hysteretic systems subjected to pulse-like stochastic ground motions. Recognizing the unique characteristics of pulse-like ground motions, distinct from non-pulse-like counterparts, which consistently exhibit a short-time pulse velocity component, the present work models them as a non-zero-mean stochastic process. In this model, the part of mean corresponds to the pulse-like component, and the part of evolutionary power spectral density is employed to characterize the non-pulse-like component representing randomness associated with ground motions. The presence of the mean part of the stochastic excitation leads to the response of the system becoming a non-zero-mean stochastic process. The nonlinearity inherent in the system renders the superposition principle inapplicable, preventing the separate calculation of the mean and the zero-mean parts of the response. The analytical method introduced in this study utilizes the state space method to derive the differential equations with respect to the mean part. Subsequently, statistical linearization techniques and Lyapunov differential equations are employed to establish a set of supplemental equations. By combining the mean-part differential equations with these supplemental equations and using the Runge–Kutta algorithm, the final response of the system is obtained. The accuracy of SLT-RKA is verified using Monte Carlo simulations. Additionally, the applicability of SLT-RKA is demonstrated through its implementation on a single-degree-of-freedom system, a 4-story base-isolated system, and a 15-story steel building frame. •An analytical method for pulse-like stochastic ground motions in hysteretic systems.•Modeling pulse-like ground motions with non-zero-mean stochastic processes.•Revealing mean and standard deviation relation in hysteretic system responses.•Comparing method accuracy with Monte Carlo simulations.