تخمين بيشينه‌ي پاسخ سيستم‌هاي غيرخطي تحت اثر طيف طرح حوزه‌ي نزديك گسل بابه كارگيري روش‌هاي خطي‌سازي معادل

Estimation of the peak response of nonlinear systems under the effect of near-field design spectrum using equivalent linearization methods

در مطالعه‌ي حاضر، پاسخ غيرخطي سيستم‌هاي هيسترزيس دوخطي تحت اثر زمين‌لرزه‌هاي سازگار با طيف طرح هدف با به‌كارگيري روش‌هاي خطي‌سازي آماري معادل مرتبه‌هاي دوم و سوم محاسبه شده است. طيف طرح هدف براساس طيف آيين‌نامه‌ي لرزه‌يي ايران در منطقه با لرزه‌خيزي خيلي زياد، خاك نوع I‌I و در دو حالت با و بدون آثار حوزه‌ي نزديك به گسل در نظر گرفته شده است. طيف پاسخ سيستم‌هاي خطي معادل به‌دست آمده از رويكردهاي تئوري ارتعاش‌هاي تصادفي و تحليل تاريخچه‌ي زماني در محدوده‌ي رفتار كشسان با متوسط طيف پاسخ حاصل از تحليل‌هاي تاريخچه‌ي زماني غيرخطي مربوط به 250 ركورد مصنوعي سازگار شده با طيف هدف در مقادير مختلف جابه‌جايي تسليم و نسبت صلبيت سيستم مقايسه شده‌اند. براساس نتايج به‌دست آمده، انطباق مطلوب نتايج خطي‌سازي مرتبه‌ي سوم با نتايج تحليل تاريخچه‌ي زماني غيرخطي، بيانگر كارآمد بودن و دقت مناسب روش در تخمين پاسخ سيستم‌هاي غيرخطي تحت تحريك‌هاي شديد است.

One of the important issues in performance-based earthquake engineering is the accurate estimation of the response statistics of nonlinear systems under seismic excitation. In this study, the near-field effects contained in the building design regulations against earthquakes (Standard No. 2800, fourth edition) are investigated on the nonlinear response of single degree of freedom systems with bilinear hysteretic restoring force characteristics. Near-field effects are presented in the Standard No. 2800 as spectral correction factor “N” in different seismicity regions. In this study, the site is located in a very high-seismicity zone and the ground type is considered as type II. Second- and third-order linearization methods are used to estimate the response of nonlinear systems. These methods are applied to derive equivalent linear properties. To achieve research goals, it is necessary to represent the input excitation as a quasi-stationary stochastic process compatible with target elastic design spectrum. In this regard, an effective numerical method in the field of random vibrations was used to determine the response spectrum compatible power spectra. After calculating the equivalent parameters related to linearization methods, random vibration theory and time history analysis approaches within the linear range were used to calculate the response of equivalent linear systems. In order to validate the results, the response values obtained from equivalent linearization methods for both approaches were compared with the results of nonlinear time history analysis (NTHA). For this purpose, 250 artificial non-stationary records compatible with two modes of the target spectrum were used to provide reasonable estimates of the peak response of the bilinear hysteretic systems. Artificial records were generated using simulation methods in the field of random vibrations by considering specified envelope functions and power spectral density. According to the results of this study, the second-order linearization method has insufficient accuracy in estimating the response of nonlinear systems under severe excitation. As the natural period of the systems increases, the discrepancy between the results of the equivalent linear system and the results of NTHA increases. Moreover, the good agreement between the third-order linearization results and the results of NTHA indicates the high efficiency of this method in estimating the response of nonlinear systems under the near field excitation.