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Nonlinear response spectrum analysis of structures equipped with nonlinear power law viscous dampers
تجزیه و تحلیل طیف پاسخ غیرخطی سازه های مجهز به میراگر چسبناک قانون غیرخطی-2020 Response spectrum analysis is recognized as a reliable and practical method for dynamic analysis of structures
subjected to earthquake excitation. However, for structures equipped with nonlinear viscous dampers (NVDs),
the classical linear response structural analysis cannot be applied due to the nonlinearity induced by such devices,
typically in the form of a power law function of the velocity. In this paper, the nonlinear differential
equation governing the dynamic response of a single-degree-of-freedom (SDOF) system equipped with NVD is
first converted into a set of surrogate linear differential equations using the perturbation technique. The first
linear system (zero order) is excited by the real earthquake acceleration time-history, whereas the other SDOF
surrogate systems are subjected to virtual excitations based on the velocity responses resulting from the previous
linear equations (in a recursive fashion). By performing response spectrum analysis on each surrogate SDOF
linear equation and combining the results, the nonlinear response spectrum is estimated. By using Fourier
transform and simplifying the frequency-dependent functions, a convenient method is presented for practical
design purposes. The proposed method lends itself to be readily adopted in international codes of practice by
establishing an equivalent damping ratio. The proposed method, introduced for a SDOF system, is easily extended
to multi-storey building structures equipped with different NVDs, and applied to a two-story and to two
six-story building frames. The results obtained through the proposed method are in very good agreement with
results obtained by nonlinear time-history analyses for a wide set of parameter combinations. Keywords: Nonlinear response spectrum analysis | Nonlinear viscous damper | Earthquake engineering | Perturbation technique | Power law damping | Fourier transform | Seismic analysis | Response spectrum method |
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