تخمین بیشینه‌ی پاسخ سیستم‌های غیرخطی تحت اثر طیف طرح حوزه‌ی نزدیک گسل بابه کارگیری روش‌های خطی‌سازی معادل

در مطالعه‌ی حاضر، پاسخ غیرخطی سیستم‌های هیسترزیس دوخطی تحت اثر زمین‌لرزه‌های سازگار با طیف طرح هدف با به‌کارگیری روش‌های خطی‌سازی آماری معادل مرتبه‌های دوم و سوم محاسبه شده است. طیف طرح هدف براساس طیف آیین‌نامه‌ی لرزه‌یی ایران در منطقه با لرزه‌خیزی خیلی زیاد، خاک نوع i‌i و در دو حالت با و بدون آثار حوزه‌ی نزدیک به گسل در نظر گرفته شده است. طیف پاسخ سیستم‌های خطی معادل به‌دست آمده از رویکردهای تئوری ارتعاش‌های تصادفی و تحلیل تاریخچه‌ی زمانی در محدوده‌ی رفتار کشسان با متوسط طیف پاسخ حاصل از تحلیل‌های تاریخچه‌ی زمانی غیرخطی مربوط به 250 رکورد مصنوعی سازگار شده با طیف هدف در مقادیر مختلف جابه‌جایی تسلیم و نسبت صلبیت سیستم مقایسه شده‌اند. براساس نتایج به‌دست آمده، انطباق مطلوب نتایج خطی‌سازی مرتبه‌ی سوم با نتایج تحلیل تاریخچه‌ی زمانی غیرخطی، بیانگر کارآمد بودن و دقت مناسب روش در تخمین پاسخ سیستم‌های غیرخطی تحت تحریک‌های شدید است.

estimation of the peak response of nonlinear systems under the effect of nearfield design spectrum using equivalent linearization methods

one of the important issues in performancebased earthquake engineering is the accurate estimation of the response statistics of nonlinear systems under seismic excitation. in this study, the nearfield 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. nearfield 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 highseismicity zone and the ground type is considered as type ii. second and thirdorder 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 quasistationary 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 nonstationary 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 secondorder 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 thirdorder 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.